Details

Time bar (total: 6.3s)

analyze491.0ms (7.8%)

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 (49.7%)

Results
1.6s2022×body1024valid
782.0ms4657×body128valid
520.0ms1046×body512valid
194.0ms526×body256valid
6.0msbody2048valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify15.0ms (0.2%)

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

series31.0ms (0.5%)

Counts
4 → 88
Calls

4 calls:

13.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
11.0ms
(*.f64 z (sin.f64 y))
6.0ms
(*.f64 x (cos.f64 y))
1.0ms
(cos.f64 y)

rewrite113.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
518×log-prod_binary64
391×fma-def_binary64
234×egg-rr
190×fma-neg_binary64
184×expm1-udef_binary64
Counts
4 → 234
Calls

4 calls:

107.0ms
(cos.f64 y)
107.0ms
(-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
107.0ms
(*.f64 x (cos.f64 y))
107.0ms
(*.f64 z (sin.f64 y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0929
119429
2247529
3498429
000
100

simplify110.0ms (1.8%)

Algorithm
egg-herbie
Rules
762×fma-neg_binary64
599×sub-neg_binary64
415×*-commutative_binary64
285×distribute-rgt-neg-in_binary64
281×distribute-lft-neg-in_binary64
Counts
322 → 265
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
066906
1197891
2548866
31726865
43946863
54693863
64930863
74914863

prune190.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2587265
Fresh000
Picked101
Done000
Total2597266
Error
0.0b
Counts
266 → 7
Alt Table
StatusErrorProgram
0.8b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3) (*.f64 z (sin.f64 y)))
18.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
30.5b
(/.f64 1 (/.f64 (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))) (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
0.4b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))) (*.f64 z (sin.f64 y)))
17.6b
(fma.f64 (sqrt.f64 (cos.f64 y)) (*.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (*.f64 z (sin.f64 y))))
34.2b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (*.f64 z (sin.f64 y))))
0.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
Compiler

Compiled 5580 to 1323 computations (76.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
0.1b
(*.f64 z (sin.f64 y))
0.1b
(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))
55.2b
(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

series59.0ms (0.9%)

Counts
3 → 84
Calls

3 calls:

25.0ms
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
17.0ms
(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))
16.0ms
(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

rewrite56.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
897×expm1-log1p-u_binary64
708×prod-diff_binary64
114×add-sqr-sqrt_binary64
104×log1p-expm1-u_binary64
103×add-cbrt-cube_binary64
Counts
3 → 70
Calls

3 calls:

55.0ms
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
54.0ms
(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))
54.0ms
(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01164
122051
2234651
3519151
000
100

simplify77.0ms (1.2%)

Algorithm
egg-herbie
Rules
760×fma-def_binary64
658×distribute-rgt-neg-in_binary64
566×distribute-lft-neg-in_binary64
436×cancel-sign-sub-inv_binary64
408×fma-neg_binary64
Counts
154 → 89
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
044726
1126720
2335708
3890704
43065704
54465704
64937704

prune90.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1131114
Fresh066
Picked011
Done000
Total1138121
Error
0.0b
Counts
121 → 8
Alt Table
StatusErrorProgram
0.8b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3) (*.f64 z (sin.f64 y)))
18.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
30.5b
(/.f64 1 (/.f64 (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))) (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
0.4b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))) (*.f64 z (sin.f64 y)))
17.6b
(fma.f64 (sqrt.f64 (cos.f64 y)) (*.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (*.f64 z (sin.f64 y))))
34.2b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (*.f64 z (sin.f64 y))))
0.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
27.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))))
Compiler

Compiled 2647 to 773 computations (70.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 z (sin.f64 y))
0.2b
(*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))
0.2b
(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
0.3b
(cbrt.f64 (cos.f64 y))

series261.0ms (4.2%)

Counts
3 → 36
Calls

3 calls:

130.0ms
(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
129.0ms
(cbrt.f64 (cos.f64 y))
1.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))

rewrite87.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
797×log1p-udef_binary64
440×log1p-expm1-u_binary64
440×expm1-log1p-u_binary64
302×unpow-prod-down_binary64
222×log-prod_binary64
Counts
3 → 108
Calls

3 calls:

86.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))
86.0ms
(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
86.0ms
(cbrt.f64 (cos.f64 y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0716
112116
2116616
3473816
4611716
000
100

simplify101.0ms (1.6%)

Algorithm
egg-herbie
Rules
733×sub-neg_binary64
513×distribute-rgt-neg-in_binary64
504×cancel-sign-sub-inv_binary64
395×distribute-lft-neg-in_binary64
350×fma-neg_binary64
Counts
144 → 128
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049288
1138284
2362276
31092276
42389276
54366276
64474276
74833276
84864276

prune263.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2061207
Fresh066
Picked011
Done011
Total2069215
Error
0b
Counts
215 → 9
Alt Table
StatusErrorProgram
0.8b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3) (*.f64 z (sin.f64 y)))
18.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
30.5b
(/.f64 1 (/.f64 (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))) (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
0.4b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))) (*.f64 z (sin.f64 y)))
17.6b
(fma.f64 (sqrt.f64 (cos.f64 y)) (*.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (*.f64 z (sin.f64 y))))
34.2b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (*.f64 z (sin.f64 y))))
0.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
0.3b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))) (*.f64 z (sin.f64 y)))
27.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))))
Compiler

Compiled 4665 to 2068 computations (55.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))
0.2b
(pow.f64 (cos.f64 y) 2)
0.3b
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
0.3b
(cbrt.f64 (cos.f64 y))

series181.0ms (2.9%)

Counts
3 → 28
Calls

3 calls:

177.0ms
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
3.0ms
(pow.f64 (cos.f64 y) 2)
1.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))

rewrite85.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
503×log1p-expm1-u_binary64
503×expm1-log1p-u_binary64
405×unpow-prod-down_binary64
259×log-prod_binary64
151×pow2_binary64
Counts
3 → 115
Calls

3 calls:

83.0ms
(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))
83.0ms
(pow.f64 (cos.f64 y) 2)
83.0ms
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0827
115617
2131117
3493417
4506217
000
100

simplify95.0ms (1.5%)

Algorithm
egg-herbie
Rules
684×sub-neg_binary64
671×fma-def_binary64
433×distribute-rgt-neg-in_binary64
417×cancel-sign-sub-inv_binary64
338×distribute-lft-neg-in_binary64
Counts
143 → 134
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
044245
1123235
2329229
3966223
42476223
54358223
64390223
74829223
84848223

prune209.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1880188
Fresh066
Picked011
Done022
Total1889197
Error
0b
Counts
197 → 9
Alt Table
StatusErrorProgram
0.8b
(-.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3) (*.f64 z (sin.f64 y)))
18.8b
(-.f64 (*.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
30.5b
(/.f64 1 (/.f64 (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))) (-.f64 (pow.f64 (*.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
0.4b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))) (*.f64 z (sin.f64 y)))
17.6b
(fma.f64 (sqrt.f64 (cos.f64 y)) (*.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (*.f64 z (sin.f64 y))))
34.2b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (*.f64 z (sin.f64 y))))
0.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
0.3b
(-.f64 (*.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))) (*.f64 z (sin.f64 y)))
27.2b
(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))))
Compiler

Compiled 4243 to 2028 computations (52.2% saved)

regimes467.0ms (7.4%)

Accuracy

Total 0.1b remaining (74.7%)

Threshold costs 0.1b (74.7%)

Counts
104 → 1
Compiler

Compiled 6656 to 4476 computations (32.8% saved)

simplify3.0ms (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
11614
22614
33214
43614
53714
63714

end134.0ms (2.1%)

Compiler

Compiled 197 to 122 computations (38.1% saved)

Profiling

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