Details

Time bar (total: 5.1s)

analyze374.0ms (7.3%)

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 (59.1%)

Results
1.5s2038×body2048valid
495.0ms1182×body1024valid
462.0ms1587×body512valid
267.0ms2541×body128valid
174.0ms812×body256valid
78.0ms96×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
31.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶31.3b
(/.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
✓1.6b
(-.f64 1 (cos.f64 x))
✓15.2b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series7.0ms (0.1%)

Counts
2 → 16
Calls

2 calls:

4.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms
(-.f64 1 (cos.f64 x))

rewrite15.0ms (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:

6.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms
(-.f64 1 (cos.f64 x))

simplify97.0ms (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

prune78.0ms (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
32.1b
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
▶15.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
45.6b
(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 (cos.f64 x)))))
44.3b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3))
30.3b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
31.3b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
31.4b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 x (fma.f64 x (cos.f64 x) x)))
31.6b
(*.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))))
Compiler

Compiled 1750 to 883 computations (49.5% 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)))
✓0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.3b
(+.f64 1 (cos.f64 x))
✓15.0b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series40.0ms (0.8%)

Counts
4 → 40
Calls

4 calls:

18.0ms
(/.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)))
5.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

rewrite35.0ms (0.7%)

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:

9.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
6.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

simplify104.0ms (2%)

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

prune152.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2006206
Fresh617
Picked101
Done000
Total2077214
Error
0b
Counts
214 → 7
Alt Table
StatusErrorProgram
0.7b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
31.3b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
1.8b
(exp.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
15.5b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
15.8b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
14.8b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 (fma.f64 x (cos.f64 x) x)))
▶0.3b
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
Compiler

Compiled 4392 to 1969 computations (55.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (sin.f64 x) x)
✓0.2b
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
✓0.2b
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))

series27.0ms (0.5%)

Counts
3 → 28
Calls

3 calls:

12.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
11.0ms
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
3.0ms
(/.f64 (sin.f64 x) x)

rewrite30.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
49×add-exp-log_binary64
31×add-sqr-sqrt_binary64
31×add-cbrt-cube_binary64
28×times-frac_binary64
26×associate-*l*_binary64
Counts
3 → 116
Calls

3 calls:

10.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
9.0ms
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
3.0ms
(/.f64 (sin.f64 x) x)

simplify116.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
720×times-frac_binary64
585×associate-/l*_binary64
553×fma-def_binary64
372×*-commutative_binary64
270×associate-/r*_binary64
Counts
144 → 180
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01992810
14842445
214342435
342012425
449592425
549452425

prune139.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1791180
Fresh156
Picked101
Done000
Total1816187
Error
0b
Counts
187 → 6
Alt Table
StatusErrorProgram
0.7b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
31.3b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
1.8b
(exp.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
15.5b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
15.8b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
▶0.3b
(*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
Compiler

Compiled 3743 to 2077 computations (44.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
✓0.2b
(*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)))

series36.0ms (0.7%)

Counts
3 → 36
Calls

3 calls:

13.0ms
(*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
12.0ms
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
10.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite26.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
49×add-exp-log_binary64
31×add-sqr-sqrt_binary64
31×add-cbrt-cube_binary64
28×times-frac_binary64
26×*-un-lft-identity_binary64
Counts
3 → 111
Calls

3 calls:

9.0ms
(*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
6.0ms
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify126.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
782×times-frac_binary64
594×associate-/l*_binary64
531×fma-def_binary64
384×*-commutative_binary64
260×associate-/r*_binary64
Counts
147 → 168
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01882978
14412600
214982592
343182584
449702584
549502584

prune271.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1680168
Fresh055
Picked011
Done000
Total1686174
Error
0b
Counts
174 → 6
Alt Table
StatusErrorProgram
0.7b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
31.3b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
1.8b
(exp.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
15.5b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
15.8b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
✓0.3b
(*.f64 (/.f64 1 x) (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
Compiler

Compiled 3461 to 2205 computations (36.3% saved)

regimes230.0ms (4.5%)

Accuracy

Total 0.1b remaining (81.1%)

Threshold costs 0.1b (81.1%)

Counts
90 → 1
Compiler

Compiled 2705 to 1831 computations (32.3% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01121
11221
21221

end129.0ms (2.5%)

Compiler

Compiled 112 to 76 computations (32.1% saved)

Profiling

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