Details

Time bar (total: 5.4s)

analyze360.0ms (6.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample3.0s (54.9%)

Results
1.5s2030×body2048valid
474.0ms1132×body1024valid
465.0ms1544×body512valid
293.0ms2673×body128valid
158.0ms772×body256valid
78.0ms105×body4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify25.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
426×fma-def_binary64
293×fma-neg_binary64
85×div-sub_binary64
74×associate-/l*_binary64
63×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47212
511012
615812
725312
838312
952612
1064012
1162512
1257012

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
32.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶32.9b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓1.9b
(-.f64 1 (cos.f64 x))
✓17.1b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series6.0ms (0.1%)

Counts
2 → 16
Calls

2 calls:

4.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))

rewrite14.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
9×prod-diff_binary64
7×add-cbrt-cube_binary64
Counts
2 → 63
Calls

2 calls:

8.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms
(-.f64 1 (cos.f64 x))

simplify101.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
626×fma-neg_binary64
411×associate-*l*_binary64
405×times-frac_binary64
353×associate-*r*_binary64
344×fma-def_binary64
Counts
79 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01251152
12831017
2853961
33327961
44699961
54954961
64828961

prune82.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New83891
Fresh000
Picked101
Done000
Total84892
Error
0.0b
Counts
92 → 8
Alt Table
StatusErrorProgram
32.9b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3)) (*.f64 x x))
32.9b
(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (*.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
30.7b
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (*.f64 x x) (*.f64 1/40320 (pow.f64 x 6))))
47.1b
(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) x) (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
33.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
33.0b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
31.8b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
▶17.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 1776 to 903 computations (49.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.3b
(+.f64 1 (cos.f64 x))
✓17.1b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series34.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

15.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
14.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

rewrite27.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
25×*-un-lft-identity_binary64
22×times-frac_binary64
17×add-sqr-sqrt_binary64
Counts
4 → 122
Calls

4 calls:

8.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
7.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

simplify102.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
610×associate-*l/_binary64
540×associate-/r/_binary64
423×fma-def_binary64
335×fma-neg_binary64
214×cancel-sign-sub-inv_binary64
Counts
162 → 206
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02042904
15042230
217672192
346432192
449352192

prune201.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2006206
Fresh707
Picked101
Done000
Total2086214
Error
0b
Counts
214 → 6
Alt Table
StatusErrorProgram
17.8b
(/.f64 (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 x x) (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))))))
▶0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
18.5b
(*.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (/.f64 1 (*.f64 x x)))
0.7b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
17.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 4384 to 1957 computations (55.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
✓0.1b
(/.f64 (sin.f64 x) x)

series25.0ms (0.5%)

Counts
3 → 28
Calls

3 calls:

11.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
11.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms
(/.f64 (sin.f64 x) x)

rewrite22.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
45×add-sqr-sqrt_binary64
40×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
19×add-cbrt-cube_binary64
Counts
3 → 111
Calls

3 calls:

9.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms
(/.f64 (sin.f64 x) x)

simplify254.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
594×associate-/l*_binary64
557×associate-*l/_binary64
473×associate-*l*_binary64
464×associate-*r/_binary64
426×times-frac_binary64
Counts
139 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862636
14692390
213092366
345062354
449472354
550472354

prune151.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1513154
Fresh325
Picked101
Done000
Total1555160
Error
0b
Counts
160 → 5
Alt Table
StatusErrorProgram
0.1b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
▶0.1b
(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
17.6b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 x 1/2)))))
0.1b
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
17.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 2980 to 1578 computations (47% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓0.1b
(/.f64 x (sin.f64 x))
0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
✓0.1b
(/.f64 1 (/.f64 x (sin.f64 x)))

series24.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

13.0ms
(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
8.0ms
(/.f64 x (sin.f64 x))
3.0ms
(/.f64 1 (/.f64 x (sin.f64 x)))

rewrite43.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
176×times-frac_binary64
128×add-sqr-sqrt_binary64
99×*-un-lft-identity_binary64
95×add-cube-cbrt_binary64
61×add-exp-log_binary64
Counts
3 → 208
Calls

3 calls:

16.0ms
(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms
(/.f64 1 (/.f64 x (sin.f64 x)))
2.0ms
(/.f64 x (sin.f64 x))

simplify175.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
507×fma-neg_binary64
451×associate-/l/_binary64
451×fma-def_binary64
442×associate-/r/_binary64
429×*-commutative_binary64
Counts
236 → 330
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02274573
15434008
217383943
335773915
447043915
550143915

prune369.0ms (6.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3702372
Fresh224
Picked011
Done000
Total3725377
Error
0b
Counts
377 → 5
Alt Table
StatusErrorProgram
0.1b
(/.f64 (*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (tan.f64 (/.f64 x 2))) x)
0.1b
(/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) (/.f64 x (sin.f64 x)))
✓0.1b
(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
17.6b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) (*.f64 x (*.f64 x (cos.f64 (*.f64 x 1/2)))))
17.6b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
Compiler

Compiled 8140 to 4342 computations (46.7% saved)

regimes322.0ms (5.9%)

Accuracy

Total 0.1b remaining (83%)

Threshold costs 0.1b (83%)

Counts
165 → 1
Compiler

Compiled 5617 to 3709 computations (34% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
11420
21320

end83.0ms (1.5%)

Compiler

Compiled 97 to 68 computations (29.9% saved)

Profiling

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