Details

Time bar (total: 5.8s)

analyze439.0ms (7.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
25%74.9%0.1%6
37.4%62.4%0.1%7
56.2%43.7%0.1%8
56.2%43.7%0.1%9
65.5%34.3%0.1%10
76.5%23.4%0.1%11
76.5%23.4%0.1%12
81.9%17.9%0.1%13
87.8%12.1%0.1%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (49.5%)

Results
1.5s2036×body1024valid
736.0ms4615×body128valid
448.0ms1052×body512valid
159.0ms550×body256valid
4.0msbody2048valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify15.0ms (0.3%)

Algorithm
egg-herbie
Rules
171×fma-def_binary64
87×fma-neg_binary64
36×cancel-sign-sub-inv_binary64
23×distribute-rgt-neg-in_binary64
20×sub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11714
22814
34514
46714
510114
615314
721414
825814
928014
1030014
1130614
1227514

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.1b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 y)
0.0b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.1b
(*.f64 z (sin.f64 y))
0.1b
(*.f64 x (cos.f64 y))

series33.0ms (0.6%)

Counts
4 → 88
Calls

4 calls:

13.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
10.0ms
(*.f64 x (cos.f64 y))
6.0ms
(*.f64 z (sin.f64 y))
4.0ms
(cos.f64 y)

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 65
Calls

4 calls:

3.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
3.0ms
(*.f64 z (sin.f64 y))
3.0ms
(*.f64 x (cos.f64 y))
1.0ms
(cos.f64 y)

simplify92.0ms (1.6%)

Algorithm
egg-herbie
Rules
614×fma-neg_binary64
542×fma-def_binary64
292×cancel-sign-sub-inv_binary64
289×distribute-rgt-neg-in_binary64
255×*-commutative_binary64
Counts
153 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01531664
13691608
211361575
324831575
445711575
549071575

prune124.0ms (2.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11314127
Fresh000
Picked101
Done000
Total11414128
Error
0.0b
Counts
128 → 14
Alt Table
StatusErrorProgram
31.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
28.9b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
16.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.2b
(-.f64 (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
26.7b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
23.7b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (*.f64 (*.f64 (*.f64 z z) z) (*.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
32.5b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
32.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 2416 to 877 computations (63.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 z (sin.f64 y))
0.1b
(*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))))
0.1b
(expm1.f64 (log1p.f64 (cos.f64 y)))
0.2b
(log1p.f64 (cos.f64 y))

series198.0ms (3.4%)

Counts
3 → 48
Calls

3 calls:

190.0ms
(log1p.f64 (cos.f64 y))
7.0ms
(*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))))
2.0ms
(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 42
Calls

3 calls:

2.0ms
(*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))))
0.0ms
(log1p.f64 (cos.f64 y))
0.0ms
(expm1.f64 (log1p.f64 (cos.f64 y)))

simplify103.0ms (1.8%)

Algorithm
egg-herbie
Rules
518×fma-neg_binary64
477×distribute-rgt-neg-in_binary64
387×distribute-lft-neg-in_binary64
337×sub-neg_binary64
268×*-commutative_binary64
Counts
90 → 86
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
091719
1199668
2555652
31442652
42731652
54612652
64996652
74910652

prune156.0ms (2.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1230123
Fresh01313
Picked011
Done000
Total12314137
Error
0.0b
Counts
137 → 14
Alt Table
StatusErrorProgram
31.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
28.9b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
16.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.2b
(-.f64 (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
26.7b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
23.7b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (*.f64 (*.f64 (*.f64 z z) z) (*.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
32.5b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
32.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 2479 to 939 computations (62.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))
0.2b
(*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
0.3b
(*.f64 (cos.f64 y) (cos.f64 y))
0.3b
(cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

series21.0ms (0.4%)

Counts
4 → 60
Calls

4 calls:

11.0ms
(*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))
5.0ms
(*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
3.0ms
(*.f64 (cos.f64 y) (cos.f64 y))
2.0ms
(cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
32×pow1_binary64
16×add-sqr-sqrt_binary64
15×add-cbrt-cube_binary64
13×add-exp-log_binary64
11×*-un-lft-identity_binary64
Counts
4 → 96
Calls

4 calls:

5.0ms
(*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
4.0ms
(*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))
4.0ms
(cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))
3.0ms
(*.f64 (cos.f64 y) (cos.f64 y))

simplify120.0ms (2.1%)

Algorithm
egg-herbie
Rules
935×fma-neg_binary64
741×fma-def_binary64
437×unswap-sqr_binary64
369×sub-neg_binary64
300×cancel-sign-sub-inv_binary64
Counts
156 → 160
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01431491
13091168
28861146
317421095
436181041
545041041
648321041
748851041

prune224.0ms (3.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1582160
Fresh01212
Picked011
Done011
Total15816174
Error
0.0b
Counts
174 → 16
Alt Table
StatusErrorProgram
31.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
28.9b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
16.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.3b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
26.7b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
23.7b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (*.f64 (*.f64 (*.f64 z z) z) (*.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
32.5b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.4b
(-.f64 (*.f64 (*.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))) (*.f64 z (sin.f64 y)))
32.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 3673 to 1333 computations (63.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y)))
0.3b
(*.f64 (cos.f64 y) (cos.f64 y))
0.3b
(cbrt.f64 (cos.f64 y))
0.4b
(cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))

series417.0ms (7.2%)

Counts
3 → 36
Calls

3 calls:

230.0ms
(cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))
185.0ms
(cbrt.f64 (cos.f64 y))
2.0ms
(*.f64 (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y)))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod_binary64
13×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
associate-*r*_binary64
Counts
3 → 56
Calls

3 calls:

5.0ms
(*.f64 (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y)))
2.0ms
(cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))
1.0ms
(cbrt.f64 (cos.f64 y))

simplify121.0ms (2.1%)

Algorithm
egg-herbie
Rules
566×sub-neg_binary64
505×cancel-sign-sub-inv_binary64
482×associate-*l*_binary64
429×associate-*r*_binary64
420×log-prod_binary64
Counts
92 → 103
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
0105967
1223938
2674930
32229698
43791682
54175680
64730680
74984680
84867680

prune234.0ms (4%)

Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New1480148
Fresh01313
Picked011
Done022
Total14816164
Error
0.0b
Counts
164 → 16
Alt Table
StatusErrorProgram
31.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
28.9b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
16.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.3b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
26.7b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
23.7b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (*.f64 (*.f64 (*.f64 z z) z) (*.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
32.5b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.4b
(-.f64 (*.f64 (*.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))) (*.f64 z (sin.f64 y)))
32.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 3433 to 1168 computations (66% saved)

regimes347.0ms (6%)

Accuracy

Total 0.1b remaining (69.6%)

Threshold costs 0.1b (69.6%)

Counts
82 → 1
Compiler

Compiled 5572 to 3674 computations (34.1% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11814
22614
33114
43314
53314

end195.0ms (3.4%)

Compiler

Compiled 325 to 194 computations (40.3% saved)

Profiling

Loading profile data...