Details

Time bar (total: 6.1s)

analyze457.0ms (7.5%)

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)

sample3.0s (49.4%)

Results
1.5s2040×body1024valid
855.0ms4662×body128valid
447.0ms1034×body512valid
161.0ms515×body256valid
7.0msbody2048valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify17.0ms (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
0.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.2b
(-.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
(sin.f64 y)
0.0b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.1b
(*.f64 x (cos.f64 y))
0.2b
(*.f64 z (sin.f64 y))

series32.0ms (0.5%)

Counts
4 → 88
Calls

4 calls:

15.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
9.0ms
(*.f64 z (sin.f64 y))
7.0ms
(*.f64 x (cos.f64 y))
1.0ms
(sin.f64 y)

rewrite13.0ms (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
(sin.f64 y)

simplify92.0ms (1.5%)

Algorithm
egg-herbie
Rules
634×fma-neg_binary64
554×fma-def_binary64
310×cancel-sign-sub-inv_binary64
272×distribute-rgt-neg-in_binary64
262×*-commutative_binary64
Counts
153 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01531664
13691606
211441571
325011571
445431571
548751571

prune111.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New11215127
Fresh000
Picked101
Done000
Total11315128
Error
0.0b
Counts
128 → 15
Alt Table
StatusErrorProgram
22.1b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
0.2b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y)))))
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
22.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
0.5b
(-.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
30.0b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
0.9b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
3.2b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
33.4b
(-.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))))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
34.7b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 2458 to 889 computations (63.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 y)
0.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
0.2b
(*.f64 z (sin.f64 y))

series16.0ms (0.3%)

Counts
1 → 36
Calls

1 calls:

15.0ms
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))

simplify63.0ms (1%)

Algorithm
egg-herbie
Rules
867×fma-neg_binary64
806×cancel-sign-sub-inv_binary64
392×associate-*l*_binary64
384×fma-def_binary64
326×associate-*r*_binary64
Counts
46 → 28
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040656
190627
2214627
3626623
42397623
54589623
65113623

prune128.0ms (2.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh31114
Picked101
Done000
Total831497
Error
0.0b
Counts
97 → 14
Alt Table
StatusErrorProgram
0.6b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (*.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))))))
33.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
0.5b
(-.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
30.0b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
0.9b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))))
22.1b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
22.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
3.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
34.7b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 1696 to 722 computations (57.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.4%)

Counts
4 → 84
Calls

4 calls:

16.0ms
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))))
7.0ms
(*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))
2.0ms
(expm1.f64 (sin.f64 y))
2.0ms
(log1p.f64 (expm1.f64 (sin.f64 y)))

rewrite6.0ms (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
4 → 52
Calls

4 calls:

3.0ms
(*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))
0.0ms
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))))
0.0ms
(expm1.f64 (sin.f64 y))
0.0ms
(log1p.f64 (expm1.f64 (sin.f64 y)))

simplify80.0ms (1.3%)

Algorithm
egg-herbie
Rules
765×fma-neg_binary64
313×associate-*l*_binary64
297×fma-def_binary64
270×distribute-rgt-in_binary64
246×associate-*r*_binary64
Counts
136 → 113
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01191391
12701296
27771270
321141269
446821269
549821269

prune122.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1112113
Fresh21113
Picked011
Done000
Total11314127
Error
0.0b
Counts
127 → 14
Alt Table
StatusErrorProgram
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))))
6.9b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (log.f64 (exp.f64 (expm1.f64 (sin.f64 y))))))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
0.6b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (log1p.f64 (expm1.f64 (sin.f64 y)))))))
0.5b
(-.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
30.0b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
0.9b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
22.1b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (*.f64 z (sin.f64 y)))
22.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
3.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))))
33.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
34.7b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 2273 to 917 computations (59.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series917.0ms (15%)

Counts
4 → 72
Calls

4 calls:

546.0ms
(*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
232.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
128.0ms
(cbrt.f64 (cos.f64 y))
7.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite24.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
25×pow1_binary64
22×cbrt-prod_binary64
20×add-exp-log_binary64
16×*-un-lft-identity_binary64
Counts
4 → 102
Calls

4 calls:

7.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
7.0ms
(*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
5.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms
(cbrt.f64 (cos.f64 y))

simplify122.0ms (2%)

Algorithm
egg-herbie
Rules
630×fma-neg_binary64
609×unswap-sqr_binary64
447×*-commutative_binary64
410×cancel-sign-sub-inv_binary64
351×log-prod_binary64
Counts
174 → 172
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01522118
13561762
212171642
323541606
444171588
548821588
649471588

prune263.0ms (4.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New2182220
Fresh11112
Picked101
Done011
Total22014234
Error
0.0b
Counts
234 → 14
Alt Table
StatusErrorProgram
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))))
6.9b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (log1p.f64 (log.f64 (exp.f64 (expm1.f64 (sin.f64 y))))))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
0.6b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (log1p.f64 (expm1.f64 (sin.f64 y)))))))
30.0b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
0.9b
(-.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.3b
(-.f64 (*.f64 (*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
22.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3)) (*.f64 z (sin.f64 y)))
3.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))))
33.4b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
22.1b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))) (cos.f64 y))) (*.f64 z (sin.f64 y)))
16.1b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.6b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
34.7b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 5267 to 1537 computations (70.8% saved)

regimes390.0ms (6.4%)

Accuracy

Total 0.1b remaining (69%)

Threshold costs 0.1b (69%)

Counts
88 → 1
Compiler

Compiled 5998 to 3738 computations (37.7% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
distribute-lft-neg-in_binary64
distribute-rgt-neg-in_binary64
+-commutative_binary64
cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
12014
22914
33414
43814
54014
63814

end178.0ms (2.9%)

Compiler

Compiled 304 to 175 computations (42.4% saved)

Profiling

Loading profile data...