Details

Time bar (total: 5.2s)

analyze358.0ms (6.9%)

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
37.4%62.4%0.1%6
49.9%49.9%0.1%7
62.4%37.4%0.1%8
62.4%37.4%0.1%9
71.8%28.1%0.1%10
79.6%20.3%0.1%11
79.6%20.3%0.1%12
85%14.8%0.1%13
89.3%10.5%0.1%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample128.0ms (2.5%)

Algorithm
intervals
Results
37.0ms62×body1024valid
12.0ms145×body128valid
8.0ms32×body512valid
3.0ms17×body256valid
Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify20.0ms (0.4%)

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)

localize8.0ms (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 z (sin.f64 y))
0.1b
(*.f64 x (cos.f64 y))

series32.0ms (0.6%)

Counts
3 → 84
Calls

3 calls:

16.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
9.0ms
(*.f64 x (cos.f64 y))
7.0ms
(*.f64 z (sin.f64 y))

rewrite14.0ms (0.3%)

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

simplify88.0ms (1.7%)

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

prune90.0ms (1.7%)

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
27.3b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
0.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
17.2b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
15.4b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.9b
(-.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)))
29.9b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (*.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
32.1b
(*.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)))))
0.6b
(-.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)))))
0.5b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
34.1b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.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 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
Compiler

Compiled 2132 to 721 computations (66.2% saved)

localize8.0ms (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))))

simplify69.0ms (1.3%)

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

prune80.0ms (1.5%)

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
27.3b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
0.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
17.2b
(-.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
15.4b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.9b
(-.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)))
29.9b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (*.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
32.1b
(*.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)))))
0.6b
(-.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)))))
0.5b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
34.1b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.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 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
Compiler

Compiled 1381 to 543 computations (60.7% saved)

localize12.0ms (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)))
0.3b
(cbrt.f64 (cos.f64 y))

series448.0ms (8.7%)

Counts
3 → 48
Calls

3 calls:

250.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
187.0ms
(cbrt.f64 (cos.f64 y))
10.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite21.0ms (0.4%)

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:

8.0ms
(*.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))

simplify104.0ms (2%)

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

prune282.0ms (5.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2153218
Fresh1910
Picked101
Done011
Total21713230
Error
0.0b
Counts
230 → 13
Alt Table
StatusErrorProgram
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)))))
0.5b
(-.f64 (*.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (*.f64 z (sin.f64 y)))
27.3b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
0.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
17.2b
(-.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 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
17.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2/3)) (*.f64 (pow.f64 (cos.f64 y) 2/3) x)) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
15.4b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.9b
(-.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)))
32.1b
(*.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
(-.f64 (*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.5b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
34.1b
(-.f64 (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 5513 to 1597 computations (71% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
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)
0.3b
(cbrt.f64 (cos.f64 y))

series261.0ms (5%)

Counts
3 → 32
Calls

3 calls:

246.0ms
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
11.0ms
(*.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)

rewrite14.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
21×add-exp-log_binary64
14×unpow-prod-down_binary64
11×prod-exp_binary64
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
Counts
3 → 74
Calls

3 calls:

7.0ms
(*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
2.0ms
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
2.0ms
(pow.f64 (cos.f64 y) 2)

simplify86.0ms (1.7%)

Algorithm
egg-herbie
Rules
743×fma-neg_binary64
694×fma-def_binary64
340×*-commutative_binary64
226×cancel-sign-sub-inv_binary64
207×associate-+l+_binary64
Counts
106 → 120
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01481427
13411221
210481093
321001085
445271083
549621083

prune212.0ms (4.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1431144
Fresh2911
Picked011
Done011
Total14512157
Error
0.0b
Counts
157 → 12
Alt Table
StatusErrorProgram
27.3b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
0.1b
(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
17.2b
(-.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 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
17.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2/3)) (*.f64 (pow.f64 (cos.f64 y) 2/3) x)) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
15.4b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
0.9b
(-.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)))
32.1b
(*.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)))))
0.6b
(-.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)))))
0.2b
(-.f64 (*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.5b
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
0.3b
(-.f64 (*.f64 (*.f64 (*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
Compiler

Compiled 3428 to 1662 computations (51.5% saved)

regimes558.0ms (10.8%)

Accuracy

Total 0.1b remaining (65.5%)

Threshold costs 0.1b (65.5%)

Counts
99 → 1
Compiler

Compiled 8024 to 4932 computations (38.5% saved)

simplify3.0ms (0.1%)

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

end0.0ms (0%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample2.2s (43.4%)

Algorithm
intervals
Results
1.0s2048×body1024valid
384.0ms4368×body128valid
273.0ms1060×body512valid
88.0ms518×body256valid
10.0msbody2048valid
Compiler

Compiled 280 to 162 computations (42.1% saved)

Profiling

Loading profile data...