Details

Time bar (total: 5.6s)

analyze482.0ms (8.5%)

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)

sample3.1s (55.7%)

Results
1.5s2094×body1024valid
805.0ms4578×body128valid
561.0ms1082×body512valid
192.0ms497×body256valid
7.0msbody2048valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify20.0ms (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 3 expressions with local error:

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

series34.0ms (0.6%)

Counts
3 → 84
Calls

3 calls:

20.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
7.0ms
(*.f64 x (cos.f64 y))
7.0ms
(*.f64 z (sin.f64 y))

rewrite11.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 56
Calls

3 calls:

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

simplify88.0ms (1.6%)

Algorithm
egg-herbie
Rules
565×fma-neg_binary64
513×fma-def_binary64
401×sub-neg_binary64
272×distribute-rgt-neg-in_binary64
257×*-commutative_binary64
Counts
140 → 110
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01421548
13421505
210701476
323421476
443381476
549321476

prune99.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New9812110
Fresh000
Picked101
Done000
Total9912111
Error
0.0b
Counts
111 → 12
Alt Table
StatusErrorProgram
18.0b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
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)))
41.7b
(/.f64 (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3)) (+.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (+.f64 (*.f64 (*.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y))) (*.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)))
16.9b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
34.9b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
35.2b
(*.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)))))
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
29.9b
(-.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))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.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))))
Compiler

Compiled 2144 to 732 computations (65.9% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.3%)

Counts
1 → 36
Calls

1 calls:

16.0ms
(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))))

simplify65.0ms (1.1%)

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

prune67.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New65065
Fresh01111
Picked011
Done000
Total651277
Error
0.0b
Counts
77 → 12
Alt Table
StatusErrorProgram
18.0b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
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)))
41.7b
(/.f64 (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3)) (+.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (+.f64 (*.f64 (*.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y))) (*.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)))
16.9b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
34.9b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
35.2b
(*.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)))))
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
29.9b
(-.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))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.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))))
Compiler

Compiled 1393 to 555 computations (60.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 z (sin.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))

series427.0ms (7.6%)

Counts
3 → 48
Calls

3 calls:

245.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
175.0ms
(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)))

rewrite17.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
22×cbrt-prod_binary64
19×pow1_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
Counts
3 → 81
Calls

3 calls:

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

simplify133.0ms (2.4%)

Algorithm
egg-herbie
Rules
780×fma-def_binary64
610×unswap-sqr_binary64
426×fma-neg_binary64
366×*-commutative_binary64
361×log-prod_binary64
Counts
129 → 133
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01291459
12991232
210371167
319771123
443681105
548871105
649861105

prune254.0ms (4.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New2153218
Fresh2810
Picked011
Done011
Total21713230
Error
0.0b
Counts
230 → 13
Alt Table
StatusErrorProgram
18.0b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
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)))
0.3b
(-.f64 (*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
17.0b
(-.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 y) 2/3) (*.f64 x (cbrt.f64 (sqrt.f64 (cos.f64 y))))) (cbrt.f64 (sqrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
34.9b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
41.7b
(/.f64 (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3)) (+.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (+.f64 (*.f64 (*.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y))) (*.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
35.2b
(*.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)))))
0.5b
(-.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
29.9b
(-.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))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.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))))
Compiler

Compiled 5502 to 1592 computations (71.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 z (sin.f64 y))
0.2b
(*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
0.3b
(pow.f64 (cos.f64 y) 2)
0.4b
(cbrt.f64 (cos.f64 y))

series21.0ms (0.4%)

Counts
2 → 28
Calls

2 calls:

14.0ms
(*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
6.0ms
(pow.f64 (cos.f64 y) 2)

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
18×add-exp-log_binary64
11×prod-exp_binary64
associate-*r*_binary64
add-cbrt-cube_binary64
*-un-lft-identity_binary64
Counts
2 → 47
Calls

2 calls:

12.0ms
(*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
3.0ms
(pow.f64 (cos.f64 y) 2)

simplify111.0ms (2%)

Algorithm
egg-herbie
Rules
639×fma-neg_binary64
576×unswap-sqr_binary64
435×sqr-pow_binary64
433×fma-def_binary64
336×*-commutative_binary64
Counts
75 → 76
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01101034
1253880
2787833
31566815
43415635
53980617
64678617
74942617
84901617

prune177.0ms (3.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1361137
Fresh1910
Picked011
Done022
Total13713150
Error
0.0b
Counts
150 → 13
Alt Table
StatusErrorProgram
18.0b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
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)))
0.3b
(-.f64 (*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.2b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
17.0b
(-.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 y) 2/3) (*.f64 x (cbrt.f64 (sqrt.f64 (cos.f64 y))))) (cbrt.f64 (sqrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
34.9b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
41.7b
(/.f64 (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3)) (+.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (+.f64 (*.f64 (*.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y))) (*.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
35.2b
(*.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)))))
0.5b
(-.f64 (*.f64 (*.f64 x (pow.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2))) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
29.9b
(-.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))))
32.9b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 z) (*.f64 (sqrt.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))))
Compiler

Compiled 3238 to 1534 computations (52.6% saved)

regimes238.0ms (4.2%)

Accuracy

Total 0.1b remaining (65.2%)

Threshold costs 0.1b (65.2%)

Counts
56 → 1
Compiler

Compiled 4030 to 2466 computations (38.8% 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

end166.0ms (2.9%)

Compiler

Compiled 297 to 170 computations (42.8% saved)

Profiling

Loading profile data...