Details

Time bar (total: 11.2s)

analyze1.8s (16.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
0%100%0%5
0%100%0%6
0%100%0%7
0%100%0%8
0%100%0%9
0%100%0%10
0%100%0%11
0%100%0%12
0%100%0%13
0.1%99.9%0%14
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample8.1s (73%)

Results
5.0s2085×body2048valid
2.0s3040×body1024valid
659.0ms1561×body512valid
241.0ms818×body256valid
158.0ms119×body4096valid
101.0ms633×body128valid
Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess70.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
583×fma-neg_binary64
430×fma-def_binary64
421×div-sub_binary64
332×times-frac_binary64
157×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11414
22414
34114
47514
513014
626014
754314
8132214
9247914
10329414
11365914
12378814
13381514
14382514
15382914
16382914
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Outputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify61.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
583×fma-neg_binary64
430×fma-def_binary64
421×div-sub_binary64
332×times-frac_binary64
157×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
11414
22414
34114
47514
513014
626014
754314
8132214
9247914
10329414
11365914
12378814
13381514
14382514
15382914
16382914
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Outputs
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
(/.f64 (-.f64 (sin.f64 x) x) (-.f64 (tan.f64 x) x))

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
33.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶33.5b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Compiler

Compiled 39 to 21 computations (46.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓1.4b
(-.f64 x (tan.f64 x))
✓1.4b
(-.f64 x (sin.f64 x))

series6.0ms (0.1%)

Counts
3 → 30
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.0ms
x
@-inf
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.0ms
x
@0
(-.f64 x (sin.f64 x))
1.0ms
x
@0
(-.f64 x (tan.f64 x))
1.0ms
x
@inf
(-.f64 x (tan.f64 x))

rewrite149.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
982×prod-diff_binary64
233×egg-rr
170×log1p-udef_binary64
95×add-sqr-sqrt_binary64
94×*-un-lft-identity_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0726
117026
2277926
Stop Event
1×node limit
Counts
3 → 336
Calls
Call 1
Inputs
(-.f64 x (sin.f64 x))
(-.f64 x (tan.f64 x))
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
Outputs
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(-.f64 x (tan.f64 x))) 2)) (/.f64 (-.f64 x (sin.f64 x)) (cbrt.f64 (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 (-.f64 x (sin.f64 x)) (sqrt.f64 (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) (pow.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) 2)) (cbrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (pow.f64 (cbrt.f64 (-.f64 x (tan.f64 x))) 2)) (/.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) (sqrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (fma.f64 x x (*.f64 (tan.f64 x) (+.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (*.f64 x x) (pow.f64 (tan.f64 x) 2))) (+.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 x (sin.f64 x)) (neg.f64 (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 x (sin.f64 x)) 3) (pow.f64 (-.f64 x (tan.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) 1))))))

simplify51.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
419×unswap-sqr_binary64
338×times-frac_binary64
295×fma-def_binary64
275×sub-neg_binary64
219×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
092658
1261654
2860614
34331602
Stop Event
1×node limit
Counts
366 → 367
Calls
Call 1
Inputs
(*.f64 1/6 (pow.f64 x 3))
(-.f64 (*.f64 1/6 (pow.f64 x 3)) (*.f64 1/120 (pow.f64 x 5)))
(-.f64 (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (*.f64 1/6 (pow.f64 x 3))) (*.f64 1/120 (pow.f64 x 5)))
(-.f64 (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (*.f64 1/6 (pow.f64 x 3))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9))))
x
x
(*.f64 -1/3 (pow.f64 x 3))
(neg.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3))))
(neg.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3)))))
(neg.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 62/2835 (pow.f64 x 9)) (*.f64 1/3 (pow.f64 x 3))))))
x
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
x
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
(-.f64 (+.f64 (*.f64 27/112000 (pow.f64 x 6)) (*.f64 9/40 (pow.f64 x 2))) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
1
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x 3))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x))))
1
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x 3))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x))))
Outputs
(*.f64 1/6 (pow.f64 x 3))
(-.f64 (*.f64 1/6 (pow.f64 x 3)) (*.f64 1/120 (pow.f64 x 5)))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (*.f64 -1/120 (pow.f64 x 5)))
(fma.f64 1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) -1/120))
(fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/6 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (*.f64 1/6 (pow.f64 x 3))) (*.f64 1/120 (pow.f64 x 5)))
(+.f64 (fma.f64 1/5040 (pow.f64 x 7) (*.f64 1/6 (pow.f64 x 3))) (*.f64 -1/120 (pow.f64 x 5)))
(fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) -1/120)))
(fma.f64 (pow.f64 x 5) -1/120 (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/5040 (pow.f64 x 7))))
(-.f64 (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (*.f64 1/6 (pow.f64 x 3))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9))))
(-.f64 (fma.f64 1/5040 (pow.f64 x 7) (*.f64 1/6 (pow.f64 x 3))) (fma.f64 1/120 (pow.f64 x 5) (*.f64 1/362880 (pow.f64 x 9))))
(-.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/5040 (pow.f64 x 7))) (fma.f64 1/120 (pow.f64 x 5) (*.f64 1/362880 (pow.f64 x 9))))
(fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 (pow.f64 x 5) -1/120 (*.f64 (pow.f64 x 9) -1/362880))))
x
x
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(neg.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3))))
(neg.f64 (fma.f64 2/15 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/3)))
(+.f64 (*.f64 (pow.f64 x 5) -2/15) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 5) -2/15))
(neg.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3)))))
(neg.f64 (fma.f64 2/15 (pow.f64 x 5) (fma.f64 17/315 (pow.f64 x 7) (*.f64 (pow.f64 x 3) 1/3))))
(-.f64 (*.f64 (pow.f64 x 5) -2/15) (fma.f64 (pow.f64 x 3) 1/3 (*.f64 (pow.f64 x 7) 17/315)))
(fma.f64 (pow.f64 x 5) -2/15 (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 7) -17/315)))
(neg.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (+.f64 (*.f64 62/2835 (pow.f64 x 9)) (*.f64 1/3 (pow.f64 x 3))))))
(neg.f64 (fma.f64 2/15 (pow.f64 x 5) (fma.f64 17/315 (pow.f64 x 7) (fma.f64 62/2835 (pow.f64 x 9) (*.f64 (pow.f64 x 3) 1/3)))))
(-.f64 (*.f64 (pow.f64 x 5) -2/15) (fma.f64 (pow.f64 x 7) 17/315 (fma.f64 (pow.f64 x 3) 1/3 (*.f64 (pow.f64 x 9) 62/2835))))
(-.f64 (fma.f64 (pow.f64 x 5) -2/15 (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 7) -17/315))) (*.f64 (pow.f64 x 9) 62/2835))
x
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
x
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 x (/.f64 (sin.f64 x) (cos.f64 x)))
-1/2
(-.f64 (*.f64 9/40 (pow.f64 x 2)) 1/2)
(fma.f64 9/40 (*.f64 x x) -1/2)
(fma.f64 x (*.f64 x 9/40) -1/2)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
(-.f64 (*.f64 9/40 (*.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
(+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))
(-.f64 (+.f64 (*.f64 27/112000 (pow.f64 x 6)) (*.f64 9/40 (pow.f64 x 2))) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
(-.f64 (fma.f64 27/112000 (pow.f64 x 6) (*.f64 9/40 (*.f64 x x))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
(-.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
(-.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
1
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (-.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (/.f64 (sin.f64 x) x)))
(-.f64 1 (-.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
(-.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2)))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (*.f64 x x)))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (+.f64 1 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x))))))))
(+.f64 1 (+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x 3))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x))))
(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 3))))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (*.f64 x x)))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2)))))
(+.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 3)))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
(+.f64 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3) (pow.f64 x 3)))) (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
(-.f64 (+.f64 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (pow.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) 3))) (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) x) 3) (pow.f64 (cos.f64 x) 2)))
1
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 1 (/.f64 (sin.f64 x) x)))
(+.f64 1 (-.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (/.f64 (sin.f64 x) x)))
(-.f64 1 (-.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
(-.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2)))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (*.f64 x x)))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (+.f64 1 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x))))))))
(+.f64 1 (+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 x 3))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 3))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x))))
(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 3))))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (*.f64 x x)))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2)))))
(+.f64 (+.f64 1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 3)))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
(+.f64 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3) (pow.f64 x 3)))) (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
(-.f64 (+.f64 (+.f64 1 (+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (pow.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) 3))) (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) x) 3) (pow.f64 (cos.f64 x) 2)))

prune203.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3652367
Fresh000
Picked011
Done000
Total3653368
Error
0b
Counts
368 → 3
Alt Table
StatusErrorProgram
✓33.5b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
33.8b
(+.f64 1 (+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
▶29.9b
(+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))
Compiler

Compiled 16685 to 4203 computations (74.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (pow.f64 x 4) -27/2800)
✓0.1b
(fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))
✓0.1b
(*.f64 x 9/40)

series7.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(*.f64 x 9/40)
1.0ms
x
@inf
(fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))
1.0ms
x
@0
(fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))
1.0ms
x
@-inf
(fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))
1.0ms
x
@0
(*.f64 x 9/40)

rewrite42.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
784×pow1_binary64
731×log1p-expm1-u_binary64
731×expm1-log1p-u_binary64
87×add-sqr-sqrt_binary64
85×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0925
118825
2201925
Stop Event
1×node limit
Counts
3 → 49
Calls
Call 1
Inputs
(*.f64 x 9/40)
(fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 (pow.f64 x 4) -27/2800)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x 9/40))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 9/40) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 9/40) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 9/40)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 9/40)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x 9/40) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 9/40))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x 9/40))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 9/40) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x 9/40)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 4) -27/2800) (*.f64 x (*.f64 x 9/40)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 (pow.f64 x 4) -27/2800))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) 1) (*.f64 (pow.f64 x 4) -27/2800))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 2)) (cbrt.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) (sqrt.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 9/40)) 3) (pow.f64 (*.f64 (pow.f64 x 4) -27/2800) 3)) (+.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) (-.f64 (*.f64 (pow.f64 x 8) 729/7840000) (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 (pow.f64 x 4) -27/2800)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 x (*.f64 x 9/40))) (*.f64 (pow.f64 x 8) 729/7840000)) (-.f64 (*.f64 x (*.f64 x 9/40)) (*.f64 (pow.f64 x 4) -27/2800)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -27/2800))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) -27/2800) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) -27/2800) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -27/2800)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 -27/2800)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 729/7840000))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -27/2800) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -27/2800))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -27/2800) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) -27/2800)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -27/2800)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) -27/2800)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) -27/2800)) 1))))))

simplify41.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
872×fma-def_binary64
666×fma-neg_binary64
395×distribute-rgt-neg-in_binary64
349×cancel-sign-sub-inv_binary64
336×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014297
130279
263279
3186279
4750279
51829279
63094279
74840279
Stop Event
1×node limit
Counts
85 → 56
Calls
Call 1
Inputs
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 (pow.f64 x 2))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(*.f64 -27/2800 (pow.f64 x 4))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(*.f64 -27/2800 (pow.f64 x 4))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 -27/2800 (pow.f64 x 4))
Outputs
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 x)
(*.f64 9/40 (pow.f64 x 2))
(*.f64 9/40 (*.f64 x x))
(*.f64 x (*.f64 9/40 x))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(-.f64 (*.f64 9/40 (pow.f64 x 2)) (*.f64 27/2800 (pow.f64 x 4)))
(+.f64 (*.f64 9/40 (*.f64 x x)) (*.f64 (pow.f64 x 4) -27/2800))
(fma.f64 9/40 (*.f64 x x) (*.f64 (pow.f64 x 4) -27/2800))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -27/2800) 9/40)))
(*.f64 x (fma.f64 -27/2800 (pow.f64 x 3) (*.f64 9/40 x)))
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)
(*.f64 -27/2800 (pow.f64 x 4))
(*.f64 (pow.f64 x 4) -27/2800)

prune37.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New56056
Fresh011
Picked011
Done011
Total56359
Error
0b
Counts
59 → 3
Alt Table
StatusErrorProgram
✓33.5b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶33.8b
(+.f64 1 (+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
✓29.9b
(+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))
Compiler

Compiled 967 to 741 computations (23.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (cos.f64 x) 2)
✓1.8b
(+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
✓1.9b
(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓14.7b
(/.f64 (sin.f64 x) (*.f64 x x))

series10.0ms (0.1%)

Counts
4 → 32
Calls

12 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))
1.0ms
x
@-inf
(+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
1.0ms
x
@inf
(+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
1.0ms
x
@0
(+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
1.0ms
x
@-inf
(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite53.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
215×add-sqr-sqrt_binary64
213×pow1_binary64
212×*-un-lft-identity_binary64
201×add-log-exp_binary64
201×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01779
141279
Stop Event
1×node limit
Counts
4 → 107
Calls
Call 1
Inputs
(/.f64 (sin.f64 x) (*.f64 x x))
(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(pow.f64 (cos.f64 x) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 x) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sin.f64 x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) 2)) (cbrt.f64 (*.f64 (sin.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sin.f64 x)) x) (/.f64 (sqrt.f64 (sin.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (sin.f64 x)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (sin.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) x) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sin.f64 x) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (pow.f64 x -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2)) (neg.f64 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2)) (tan.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2) (neg.f64 (*.f64 (/.f64 1 (cos.f64 x)) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (cos.f64 x))) (sin.f64 x) (*.f64 (/.f64 1 (cos.f64 x)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2)) (neg.f64 (*.f64 (/.f64 1 (cos.f64 x)) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (cos.f64 x))) (sin.f64 x) (*.f64 (/.f64 1 (cos.f64 x)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 4))) (cbrt.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2))) (neg.f64 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simplify30.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
534×times-frac_binary64
383×cancel-sign-sub-inv_binary64
279×fma-def_binary64
278×fma-neg_binary64
262×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
088694
1231690
2595626
31983608
Stop Event
1×node limit
Counts
139 → 143
Calls
Call 1
Inputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/6 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/120 (pow.f64 x 3))) (*.f64 1/6 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/120 (pow.f64 x 3))) (+.f64 (*.f64 1/5040 (pow.f64 x 5)) (*.f64 1/6 x)))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 3))
(+.f64 (*.f64 3/8 (pow.f64 x 5)) (*.f64 1/2 (pow.f64 x 3)))
(+.f64 (*.f64 3/8 (pow.f64 x 5)) (+.f64 (*.f64 53/240 (pow.f64 x 7)) (*.f64 1/2 (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (pow.f64 x 5)) (+.f64 (*.f64 53/240 (pow.f64 x 7)) (+.f64 (*.f64 2839/24192 (pow.f64 x 9)) (*.f64 1/2 (pow.f64 x 3)))))
(pow.f64 x 2)
(+.f64 (*.f64 5/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 5/12 (pow.f64 x 4)) (+.f64 (*.f64 13/60 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (*.f64 5/12 (pow.f64 x 4)) (+.f64 (*.f64 13/60 (pow.f64 x 6)) (+.f64 (*.f64 911/8640 (pow.f64 x 8)) (pow.f64 x 2))))
(/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
1
(-.f64 1 (pow.f64 x 2))
(-.f64 (+.f64 (*.f64 1/3 (pow.f64 x 4)) 1) (pow.f64 x 2))
(-.f64 (+.f64 (*.f64 1/3 (pow.f64 x 4)) 1) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
Outputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/6 x))
(+.f64 (/.f64 1 x) (*.f64 -1/6 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/6))
(fma.f64 x -1/6 (/.f64 1 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/120 (pow.f64 x 3))) (*.f64 1/6 x))
(+.f64 (/.f64 1 x) (-.f64 (*.f64 1/120 (pow.f64 x 3)) (*.f64 x 1/6)))
(+.f64 (fma.f64 1/120 (pow.f64 x 3) (/.f64 1 x)) (*.f64 x -1/6))
(fma.f64 x -1/6 (fma.f64 1/120 (pow.f64 x 3) (/.f64 1 x)))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/120 (pow.f64 x 3))) (+.f64 (*.f64 1/5040 (pow.f64 x 5)) (*.f64 1/6 x)))
(+.f64 (/.f64 1 x) (-.f64 (*.f64 1/120 (pow.f64 x 3)) (fma.f64 1/5040 (pow.f64 x 5) (*.f64 x 1/6))))
(-.f64 (fma.f64 1/120 (pow.f64 x 3) (/.f64 1 x)) (fma.f64 x 1/6 (*.f64 1/5040 (pow.f64 x 5))))
(+.f64 (/.f64 1 x) (fma.f64 1/120 (pow.f64 x 3) (fma.f64 x -1/6 (*.f64 (pow.f64 x 5) -1/5040))))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 1/120 (*.f64 x x) -1/6) (*.f64 (pow.f64 x 5) -1/5040)))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (sin.f64 x) (pow.f64 x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(*.f64 1/2 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) 1/2)
(+.f64 (*.f64 3/8 (pow.f64 x 5)) (*.f64 1/2 (pow.f64 x 3)))
(fma.f64 3/8 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/2))
(fma.f64 (pow.f64 x 5) 3/8 (*.f64 (pow.f64 x 3) 1/2))
(fma.f64 (pow.f64 x 3) 1/2 (*.f64 (pow.f64 x 5) 3/8))
(+.f64 (*.f64 3/8 (pow.f64 x 5)) (+.f64 (*.f64 53/240 (pow.f64 x 7)) (*.f64 1/2 (pow.f64 x 3))))
(fma.f64 3/8 (pow.f64 x 5) (fma.f64 53/240 (pow.f64 x 7) (*.f64 (pow.f64 x 3) 1/2)))
(fma.f64 (pow.f64 x 5) 3/8 (fma.f64 (pow.f64 x 3) 1/2 (*.f64 53/240 (pow.f64 x 7))))
(fma.f64 (pow.f64 x 3) 1/2 (fma.f64 53/240 (pow.f64 x 7) (*.f64 (pow.f64 x 5) 3/8)))
(fma.f64 (pow.f64 x 3) 1/2 (fma.f64 (pow.f64 x 5) 3/8 (*.f64 53/240 (pow.f64 x 7))))
(+.f64 (*.f64 3/8 (pow.f64 x 5)) (+.f64 (*.f64 53/240 (pow.f64 x 7)) (+.f64 (*.f64 2839/24192 (pow.f64 x 9)) (*.f64 1/2 (pow.f64 x 3)))))
(fma.f64 3/8 (pow.f64 x 5) (fma.f64 53/240 (pow.f64 x 7) (fma.f64 2839/24192 (pow.f64 x 9) (*.f64 (pow.f64 x 3) 1/2))))
(fma.f64 (pow.f64 x 5) 3/8 (fma.f64 53/240 (pow.f64 x 7) (fma.f64 (pow.f64 x 3) 1/2 (*.f64 2839/24192 (pow.f64 x 9)))))
(fma.f64 (pow.f64 x 5) 3/8 (fma.f64 (pow.f64 x 3) 1/2 (fma.f64 53/240 (pow.f64 x 7) (*.f64 2839/24192 (pow.f64 x 9)))))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 5/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 5/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 5/12 (pow.f64 x 4)))
(+.f64 (*.f64 5/12 (pow.f64 x 4)) (+.f64 (*.f64 13/60 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 5/12 (pow.f64 x 4) (fma.f64 13/60 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 5/12 (pow.f64 x 4) (fma.f64 x x (*.f64 13/60 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 13/60 (pow.f64 x 6) (*.f64 5/12 (pow.f64 x 4))))
(+.f64 (*.f64 5/12 (pow.f64 x 4)) (+.f64 (*.f64 13/60 (pow.f64 x 6)) (+.f64 (*.f64 911/8640 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 5/12 (pow.f64 x 4) (fma.f64 13/60 (pow.f64 x 6) (fma.f64 911/8640 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 5/12 (pow.f64 x 4) (fma.f64 13/60 (pow.f64 x 6) (fma.f64 x x (*.f64 911/8640 (pow.f64 x 8)))))
(fma.f64 13/60 (pow.f64 x 6) (fma.f64 5/12 (pow.f64 x 4) (fma.f64 911/8640 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 5/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 13/60 (pow.f64 x 6) (*.f64 911/8640 (pow.f64 x 8)))))
(/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x))) (/.f64 (sin.f64 x) x))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x))) (/.f64 (sin.f64 x) x))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x))) (/.f64 (sin.f64 x) x))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(*.f64 -1 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(/.f64 (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x)) x)
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x))) (/.f64 (sin.f64 x) x))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x))) (/.f64 (sin.f64 x) x))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 x 2)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (cos.f64 x) (pow.f64 x 2))) (/.f64 (sin.f64 x) x)))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (cos.f64 x))) (/.f64 (sin.f64 x) x))))
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 x x) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 x (*.f64 x (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
(-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x (*.f64 x (cos.f64 x)))) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (sin.f64 x))) (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) x))
1
(-.f64 1 (pow.f64 x 2))
(-.f64 1 (*.f64 x x))
(-.f64 (+.f64 (*.f64 1/3 (pow.f64 x 4)) 1) (pow.f64 x 2))
(-.f64 (fma.f64 1/3 (pow.f64 x 4) 1) (*.f64 x x))
(-.f64 (fma.f64 (pow.f64 x 4) 1/3 1) (*.f64 x x))
(-.f64 (+.f64 (*.f64 1/3 (pow.f64 x 4)) 1) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
(-.f64 (fma.f64 1/3 (pow.f64 x 4) 1) (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)))
(-.f64 (fma.f64 (pow.f64 x 4) 1/3 1) (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45)))
(-.f64 (fma.f64 (pow.f64 x 4) 1/3 1) (fma.f64 (pow.f64 x 6) 2/45 (*.f64 x x)))

prune117.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1430143
Fresh000
Picked011
Done022
Total1433146
Error
0b
Counts
146 → 3
Alt Table
StatusErrorProgram
✓33.5b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓33.8b
(+.f64 1 (+.f64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x)) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x)))))
✓29.9b
(+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800)))
Compiler

Compiled 5760 to 2193 computations (61.9% saved)

regimes115.0ms (1%)

Accuracy

Total 0.1b remaining (85.2%)

Threshold costs 0.1b (85.2%)

Counts
53 → 3
Compiler

Compiled 1184 to 453 computations (61.7% saved)

bsearch63.0ms (0.6%)

Algorithm
2×binary-search
Calls

2 calls:

32.0ms
x
31.0ms
x
Steps
ItersPointRange
2.4
∈ [
0.0009401983868295332
, 
89041866.05742262
]
-0.0275
∈ [
-218.77341632569187
, 
-4.306661230676509e-8
]
Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
51×cancel-sign-sub-inv_binary64
45×distribute-rgt-neg-in_binary64
34×distribute-lft-neg-out_binary64
33×neg-sub0_binary64
33×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042101
161101
278101
398101
4123101
5147101
6189101
7272101
8342101
9403101
10439101
11443101
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -7926335344172073/288230376151711744) (pow.f64 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))) -1) (if (<=.f64 x 5404319552844595/2251799813685248) (+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) (+.f64 1 (expm1.f64 (log1p.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) (-.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2)) (tan.f64 x))) (-.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))))))))
Outputs
(if (<=.f64 x -7926335344172073/288230376151711744) (pow.f64 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))) -1) (if (<=.f64 x 5404319552844595/2251799813685248) (+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) (+.f64 1 (expm1.f64 (log1p.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) (-.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2)) (tan.f64 x))) (-.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))))))))
(if (<=.f64 x -7926335344172073/288230376151711744) (pow.f64 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))) -1) (if (<=.f64 x 5404319552844595/2251799813685248) (+.f64 -1/2 (fma.f64 x (*.f64 x 9/40) (*.f64 (pow.f64 x 4) -27/2800))) (+.f64 1 (expm1.f64 (log1p.f64 (+.f64 (*.f64 (*.f64 (sin.f64 x) (pow.f64 x -2)) (-.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) -2)) (tan.f64 x))) (-.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (/.f64 (sin.f64 x) x))))))))

end95.0ms (0.9%)

Stop Event
1×done
Compiler

Compiled 191 to 116 computations (39.3% saved)

Profiling

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