Details

Time bar (total: 7.0s)

analyze1.0s (14.6%)

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
0%99.9%0.1%6
6.2%93.6%0.1%7
9.4%90.5%0.1%8
14%85.8%0.1%9
19.5%80.4%0.1%10
20.7%79.2%0.1%11
22%77.8%0.1%12
23.5%76.4%0.1%13
23.8%76%0.1%14
Compiler

Compiled 10 to 9 computations (10% saved)

sample61.0ms (0.9%)

Algorithm
intervals
Results
30.0ms108×body1024valid
10.0ms50×body512valid
5.0ms70×body128valid
3.0ms24×body256valid
2.0msbody2048valid
Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify103.0ms (1.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02114
12114

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
13.9b
Counts
2 → 1
Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b
(*.f64 r (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
3.9b
(cos.f64 (+.f64 a b))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
add-sqr-sqrt_binary64_441
*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
pow1_binary64_480
times-frac_binary64_425 add-log-exp_binary64_458 associate-*r*_binary64_359 associate-*l*_binary64_360 associate-/r*_binary64_363
prod-exp_binary64_468 cbrt-unprod_binary64_452 div-exp_binary64_470 cbrt-undiv_binary64_453
pow-prod-down_binary64_490 clear-num_binary64_418 cos-sum_binary64_553 div-inv_binary64_416 unswap-sqr_binary64_387 *-commutative_binary64_350 frac-2neg_binary64_430 associate-/l*_binary64_364
Counts
3 → 47
Calls

3 calls:

5.0ms
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms
(cos.f64 (+.f64 a b))
4.0ms
(*.f64 r (sin.f64 b))

series166.0ms (2.4%)

Counts
3 → 9
Calls

3 calls:

119.0ms
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
31.0ms
(*.f64 r (sin.f64 b))
16.0ms
(cos.f64 (+.f64 a b))

simplify89.0ms (1.3%)

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
05418692

prune52.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New49756
Fresh000
Picked101
Done000
Total50757
Error
0.1b
Counts
57 → 7
Compiler

Compiled 848 to 227 computations (73.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (cos.f64 a) (cos.f64 b))
0.1b
(*.f64 r (sin.f64 b))
0.2b
(*.f64 (sin.f64 a) (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite29.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_441
15×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
12×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
10×pow1_binary64_480
associate-*r*_binary64_359 associate-*l*_binary64_360
add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452 associate-/r/_binary64_365
pow-prod-down_binary64_490 times-frac_binary64_425 unswap-sqr_binary64_387 sin-mult_binary64_574 cos-mult_binary64_573 *-commutative_binary64_350 associate-/r*_binary64_363
div-exp_binary64_470 cbrt-undiv_binary64_453
clear-num_binary64_418 div-inv_binary64_416 flip3--_binary64_423 frac-2neg_binary64_430 flip--_binary64_394 sub-div_binary64_426 frac-sub_binary64_428 associate-/l*_binary64_364
Counts
4 → 81
Calls

4 calls:

9.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms
(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms
(*.f64 (cos.f64 a) (cos.f64 b))
4.0ms
(*.f64 r (sin.f64 b))

series370.0ms (5.3%)

Counts
4 → 12
Calls

4 calls:

267.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
38.0ms
(*.f64 (sin.f64 a) (sin.f64 b))
35.0ms
(*.f64 (cos.f64 a) (cos.f64 b))
30.0ms
(*.f64 r (sin.f64 b))

simplify61.0ms (0.9%)

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049931420
149931420

prune100.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New831093
Fresh606
Picked101
Done000
Total9010100
Error
0.0b
Counts
100 → 10
Compiler

Compiled 2195 to 466 computations (78.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (cos.f64 a) (cos.f64 b))
0.1b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b
(*.f64 (sin.f64 b) (sin.f64 a))
0.2b
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite43.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64_441
24×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
23×associate-*r*_binary64_359
19×times-frac_binary64_425
15×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
10×pow1_binary64_480
associate-*l*_binary64_360
associate-/r/_binary64_365
sin-mult_binary64_574 cos-mult_binary64_573
add-log-exp_binary64_458 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452
pow-prod-down_binary64_490 *-commutative_binary64_350 associate-/r*_binary64_363 associate-/l*_binary64_364
div-inv_binary64_416 flip3--_binary64_423 flip--_binary64_394 sub-div_binary64_426 div-exp_binary64_470 frac-sub_binary64_428 cbrt-undiv_binary64_453
clear-num_binary64_418 associate-*r/_binary64_361 frac-2neg_binary64_430
Counts
4 → 105
Calls

4 calls:

13.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
8.0ms
(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms
(*.f64 (cos.f64 a) (cos.f64 b))

series482.0ms (6.9%)

Counts
4 → 12
Calls

4 calls:

260.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
151.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
38.0ms
(*.f64 (sin.f64 b) (sin.f64 a))
33.0ms
(*.f64 (cos.f64 a) (cos.f64 b))

simplify88.0ms (1.2%)

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
061332652

prune111.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1143117
Fresh369
Picked011
Done000
Total11710127
Error
0b
Counts
127 → 10
Compiler

Compiled 3056 to 619 computations (79.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
0.2b
(*.f64 (sin.f64 b) (sin.f64 a))
0.2b
(*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b
(/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite53.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
34×add-exp-log_binary64_457
32×add-sqr-sqrt_binary64_441
24×*-un-lft-identity_binary64_419
23×add-cube-cbrt_binary64_454
22×add-cbrt-cube_binary64_455
21×associate-*r*_binary64_359
20×times-frac_binary64_425
14×prod-exp_binary64_468 pow1_binary64_480
associate-*l*_binary64_360
cbrt-unprod_binary64_452 associate-/r/_binary64_365
div-exp_binary64_470
pow-prod-down_binary64_490 sin-mult_binary64_574
add-log-exp_binary64_458 unswap-sqr_binary64_387 associate-*r/_binary64_361 cos-mult_binary64_573
1-exp_binary64_463 rec-exp_binary64_469 *-commutative_binary64_350 associate-/r*_binary64_363 associate-/l*_binary64_364 cbrt-undiv_binary64_453
div-inv_binary64_416 flip3--_binary64_423 un-div-inv_binary64_417 flip--_binary64_394 sub-div_binary64_426 frac-sub_binary64_428
clear-num_binary64_418 inv-pow_binary64_504 frac-2neg_binary64_430 pow-flip_binary64_493
Counts
4 → 118
Calls

4 calls:

13.0ms
(*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
12.0ms
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
11.0ms
(/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
5.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

series566.0ms (8%)

Counts
4 → 12
Calls

4 calls:

267.0ms
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
141.0ms
(*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
121.0ms
(/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
37.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

simplify84.0ms (1.2%)

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
056562985

prune108.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh178
Picked101
Done011
Total1319140
Error
0b
Counts
140 → 9
Compiler

Compiled 3105 to 719 computations (76.8% saved)

regimes377.0ms (5.4%)

Accuracy

Total 0.3b remaining (93.2%)

Threshold costs 0.3b (93.2%)

Compiler

Compiled 4564 to 2694 computations (41% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04226
14226

end0.0ms (0%)

sample3.0s (42.6%)

Algorithm
intervals
Results
1.2s3512×body1024valid
275.0ms1366×body512valid
163.0ms2341×body128valid
110.0ms188×body2048valid
83.0ms593×body256valid
0.0msbody1024invalid
Compiler

Compiled 1161 to 689 computations (40.7% saved)

Profiling

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