Details

Time bar (total: 6.9s)

analyze1.2s (16.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
37.5%62.5%0%4
43.7%56.2%0%5
46.9%53.1%0%6
48.4%51.5%0%7
49.2%50.8%0%8
49.6%50.4%0%9
49.8%50.2%0%10
49.9%50.1%0%11
49.9%50%0%12
50%50%0%13
50%49.9%0%14
Compiler

Compiled 18 to 15 computations (16.7% saved)

sample93.0ms (1.3%)

Algorithm
intervals
Results
48.0ms64×body1024valid
18.0ms142×body128valid
13.0ms35×body512valid
4.0ms15×body256valid
Compiler

Compiled 36 to 30 computations (16.7% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
associate-/l*_binary64
associate-/r/_binary64
associate-*r*_binary64
associate-*l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01322
12022
23122
34122
44922
55122
65022

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
16.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
16.8b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
Compiler

Compiled 61 to 48 computations (21.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
0.4b
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))
16.5b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube_binary64
19×add-exp-log_binary64
10×add-sqr-sqrt_binary64
10×pow1_binary64
*-un-lft-identity_binary64
Counts
3 → 65
Calls

3 calls:

5.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
4.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
3.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))

series37.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

23.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
9.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
5.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))

simplify105.0ms (1.5%)

Algorithm
egg-herbie
Rules
672×times-frac_binary64
637×associate-/l*_binary64
493×fma-def_binary64
403×associate-*l*_binary64
346×associate-*r*_binary64
Counts
101 → 179
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01471967
13461521
210371506
341241499
449371499
549461499

prune114.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New16613179
Fresh000
Picked101
Done000
Total16713180
Error
0.1b
Counts
180 → 13
Alt Table
StatusErrorProgram
17.2b
(/.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x)))
17.4b
(*.f64 (*.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))) (cbrt.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))))) (cbrt.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
16.7b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (sqrt.f64 8/3) (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
0.5b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
30.9b
(/.f64 (log.f64 (exp.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))) (sin.f64 x))
0.6b
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
1.3b
(*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
16.8b
(/.f64 (*.f64 1 (*.f64 8/3 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2))) (sin.f64 x))
27.8b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x))))
26.3b
(/.f64 (cbrt.f64 (*.f64 512/27 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))) (sin.f64 x))
17.3b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (cbrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) (cbrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))) (sin.f64 x))
35.0b
(*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 8/3))
17.5b
(log1p.f64 (expm1.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
Compiler

Compiled 2841 to 2114 computations (25.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
0.2b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
0.4b
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
16×add-cbrt-cube_binary64
Counts
2 → 73
Calls

2 calls:

7.0ms
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
4.0ms
(/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))

series38.0ms (0.5%)

Counts
2 → 24
Calls

2 calls:

21.0ms
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
17.0ms
(/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))

simplify124.0ms (1.8%)

Algorithm
egg-herbie
Rules
575×times-frac_binary64
514×fma-def_binary64
437×associate-/l*_binary64
336×associate-/l/_binary64
327×associate-/r*_binary64
Counts
97 → 180
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01702595
13862210
210942197
340372153
449702153
549082153

prune168.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2255230
Fresh6612
Picked101
Done000
Total23211243
Error
0.0b
Counts
243 → 11
Alt Table
StatusErrorProgram
26.3b
(/.f64 (cbrt.f64 (*.f64 512/27 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))) (sin.f64 x))
22.1b
(/.f64 (sin.f64 (*.f64 x 1/2)) (cbrt.f64 (/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x)) (*.f64 (*.f64 (*.f64 8/3 8/3) 8/3) (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))))))
30.9b
(/.f64 (log.f64 (exp.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))) (sin.f64 x))
0.5b
(*.f64 (/.f64 1 (/.f64 1 8/3)) (/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
16.8b
(/.f64 (*.f64 1 (*.f64 8/3 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2))) (sin.f64 x))
0.3b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))
17.4b
(*.f64 (*.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))) (cbrt.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))))) (cbrt.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
0.6b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) (log1p.f64 (expm1.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))
0.5b
(/.f64 (sin.f64 (*.f64 x 1/2)) (log.f64 (exp.f64 (/.f64 (sin.f64 x) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))
35.0b
(*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 8/3))
17.5b
(log1p.f64 (expm1.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
Compiler

Compiled 4059 to 2993 computations (26.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
0.2b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))
0.4b
(/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))
0.4b
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))

rewrite31.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
234×times-frac_binary64
104×*-un-lft-identity_binary64
104×add-sqr-sqrt_binary64
104×add-cube-cbrt_binary64
61×add-exp-log_binary64
Counts
3 → 215
Calls

3 calls:

8.0ms
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))
4.0ms
(/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
4.0ms
(/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))

series51.0ms (0.7%)

Counts
3 → 36
Calls

3 calls:

22.0ms
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))
14.0ms
(/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
14.0ms
(/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))

simplify245.0ms (3.6%)

Algorithm
egg-herbie
Rules
680×associate-/r/_binary64
525×associate-*l/_binary64
507×fma-def_binary64
505×fma-neg_binary64
299×*-commutative_binary64
Counts
251 → 489
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02437071
15086403
216426373
333466241
446716241
549776241

prune380.0ms (5.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New5845589
Fresh5510
Picked011
Done000
Total58911600
Error
0.0b
Counts
600 → 11
Alt Table
StatusErrorProgram
26.3b
(/.f64 (cbrt.f64 (*.f64 512/27 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))) (sin.f64 x))
22.1b
(/.f64 (sin.f64 (*.f64 x 1/2)) (cbrt.f64 (/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x)) (*.f64 (*.f64 (*.f64 8/3 8/3) 8/3) (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))))))
16.8b
(/.f64 (*.f64 8/3 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)) (sin.f64 x))
0.4b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cbrt.f64 (pow.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))) 3))))
0.3b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))
0.5b
(*.f64 (/.f64 1 (/.f64 1 (/.f64 8/3 1))) (/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))
0.3b
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8))
30.9b
(/.f64 (log.f64 (exp.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))) (sin.f64 x))
0.5b
(*.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))
35.0b
(*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 8/3))
17.5b
(log1p.f64 (expm1.f64 (*.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
Compiler

Compiled 9781 to 7397 computations (24.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8)
0.2b
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8))
0.2b
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt_binary64
29×times-frac_binary64
25×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64
19×add-cbrt-cube_binary64
Counts
3 → 105
Calls

3 calls:

7.0ms
(*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8)
6.0ms
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8))
3.0ms
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))

series65.0ms (0.9%)

Counts
3 → 36
Calls

3 calls:

38.0ms
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8))
15.0ms
(*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8)
10.0ms
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))

simplify114.0ms (1.7%)

Algorithm
egg-herbie
Rules
535×associate-*l/_binary64
480×associate-/r/_binary64
430×associate-/l/_binary64
375×fma-def_binary64
150×distribute-frac-neg_binary64
Counts
141 → 238
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02103069
14882586
215962568
347692564
450232564

prune178.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2353238
Fresh549
Picked101
Done011
Total2418249
Error
0.0b
Counts
249 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3)) -3/8))
26.3b
(/.f64 (cbrt.f64 (*.f64 512/27 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))) (sin.f64 x))
22.1b
(/.f64 (sin.f64 (*.f64 x 1/2)) (cbrt.f64 (/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x)) (*.f64 (*.f64 (*.f64 8/3 8/3) 8/3) (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))))))
0.3b
(*.f64 (/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x 1/2)) -3/8))
0.4b
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (*.f64 (sin.f64 x) (/.f64 1 (sin.f64 (*.f64 x 1/2)))) -3/8))
0.3b
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))
0.5b
(*.f64 (/.f64 1 (/.f64 1 (/.f64 8/3 1))) (/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))
30.9b
(/.f64 (log.f64 (exp.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))) (sin.f64 x))
Compiler

Compiled 3874 to 2874 computations (25.8% saved)

regimes798.0ms (11.6%)

Accuracy

Total 0.3b remaining (83.8%)

Threshold costs 0.3b (83.8%)

Compiler

Compiled 13914 to 11166 computations (19.7% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
+-commutative_binary64
sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
11924
22724
33424
44024
54324
64424
74424

end1.0ms (0%)

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample3.1s (44.7%)

Algorithm
intervals
Results
1.5s1994×body1024valid
611.0ms4479×body128valid
412.0ms1031×body512valid
129.0ms484×body256valid
28.0ms12×body2048valid
Compiler

Compiled 194 to 159 computations (18% saved)

Profiling

Loading profile data...