Details

Time bar (total: 10.0s)

analyze1.6s (16.2%)

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)

sample92.0ms (0.9%)

Algorithm
intervals
Results
46.0ms108×body1024valid
16.0ms50×body512valid
7.0ms70×body128valid
5.0ms24×body256valid
4.0msbody2048valid
Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify114.0ms (1.1%)

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_114 add-exp-log_binary64_116
add-sqr-sqrt_binary64_100
add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
pow1_binary64_139
associate-*l*_binary64_19 add-log-exp_binary64_117 times-frac_binary64_84 associate-*r*_binary64_18 associate-/r*_binary64_22
cbrt-unprod_binary64_111 cbrt-undiv_binary64_112 prod-exp_binary64_127 div-exp_binary64_129
*-commutative_binary64_9 frac-2neg_binary64_89 div-inv_binary64_75 associate-/l*_binary64_23 pow-prod-down_binary64_149 unswap-sqr_binary64_46 cos-sum_binary64_212 clear-num_binary64_77
Counts
3 → 47
Calls

3 calls:

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

series245.0ms (2.5%)

Counts
3 → 9
Calls

3 calls:

170.0ms
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
51.0ms
(*.f64 r (sin.f64 b))
24.0ms
(cos.f64 (+.f64 a b))

simplify113.0ms (1.1%)

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
05418692

prune62.0ms (0.6%)

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)

localize19.0ms (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))))

rewrite44.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_100
15×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
12×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
10×pow1_binary64_139
associate-*l*_binary64_19 associate-*r*_binary64_18
add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 associate-/r/_binary64_24
*-commutative_binary64_9 times-frac_binary64_84 associate-/r*_binary64_22 pow-prod-down_binary64_149 unswap-sqr_binary64_46 sin-mult_binary64_233 cos-mult_binary64_232
cbrt-undiv_binary64_112 div-exp_binary64_129
frac-sub_binary64_87 flip3--_binary64_82 frac-2neg_binary64_89 div-inv_binary64_75 flip--_binary64_53 associate-/l*_binary64_23 clear-num_binary64_77 sub-div_binary64_85
Counts
4 → 81
Calls

4 calls:

9.0ms
(*.f64 (cos.f64 a) (cos.f64 b))
9.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
7.0ms
(*.f64 r (sin.f64 b))
5.0ms
(*.f64 (sin.f64 a) (sin.f64 b))

series484.0ms (4.9%)

Counts
4 → 12
Calls

4 calls:

348.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
52.0ms
(*.f64 (sin.f64 a) (sin.f64 b))
46.0ms
(*.f64 (cos.f64 a) (cos.f64 b))
38.0ms
(*.f64 r (sin.f64 b))

simplify73.0ms (0.7%)

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049931420
149931420

prune157.0ms (1.6%)

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 (0.1%)

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))))

rewrite60.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64_100
24×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
23×associate-*r*_binary64_18
19×times-frac_binary64_84
15×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
10×pow1_binary64_139
associate-*l*_binary64_19
associate-/r/_binary64_24
sin-mult_binary64_233 cos-mult_binary64_232
add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 unswap-sqr_binary64_46
*-commutative_binary64_9 associate-/l*_binary64_23 associate-/r*_binary64_22 pow-prod-down_binary64_149
cbrt-undiv_binary64_112 div-exp_binary64_129 frac-sub_binary64_87 flip3--_binary64_82 div-inv_binary64_75 flip--_binary64_53 sub-div_binary64_85
frac-2neg_binary64_89 associate-*r/_binary64_20 clear-num_binary64_77
Counts
4 → 105
Calls

4 calls:

19.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms
(*.f64 (cos.f64 a) (cos.f64 b))
8.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
5.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

series677.0ms (6.8%)

Counts
4 → 12
Calls

4 calls:

359.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
171.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
75.0ms
(*.f64 (sin.f64 b) (sin.f64 a))
72.0ms
(*.f64 (cos.f64 a) (cos.f64 b))

simplify112.0ms (1.1%)

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
061332652

prune117.0ms (1.2%)

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)

localize24.0ms (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 (0.5%)

Algorithm
rewrite-expression-head
Rules
34×add-exp-log_binary64_116
32×add-sqr-sqrt_binary64_100
24×*-un-lft-identity_binary64_78
23×add-cube-cbrt_binary64_113
22×add-cbrt-cube_binary64_114
21×associate-*r*_binary64_18
20×times-frac_binary64_84
14×prod-exp_binary64_127 pow1_binary64_139
associate-*l*_binary64_19
cbrt-unprod_binary64_111 associate-/r/_binary64_24
div-exp_binary64_129
pow-prod-down_binary64_149 sin-mult_binary64_233
add-log-exp_binary64_117 unswap-sqr_binary64_46 cos-mult_binary64_232 associate-*r/_binary64_20
*-commutative_binary64_9 cbrt-undiv_binary64_112 1-exp_binary64_122 associate-/l*_binary64_23 rec-exp_binary64_128 associate-/r*_binary64_22
frac-sub_binary64_87 flip3--_binary64_82 un-div-inv_binary64_76 div-inv_binary64_75 flip--_binary64_53 sub-div_binary64_85
inv-pow_binary64_163 frac-2neg_binary64_89 pow-flip_binary64_152 clear-num_binary64_77
Counts
4 → 118
Calls

4 calls:

15.0ms
(*.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))))))
8.0ms
(/.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))

series766.0ms (7.7%)

Counts
4 → 12
Calls

4 calls:

446.0ms
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
160.0ms
(*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
119.0ms
(/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
41.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

simplify88.0ms (0.9%)

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
056562985

prune109.0ms (1.1%)

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)

regimes498.0ms (5%)

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%)

sample4.4s (44.1%)

Algorithm
intervals
Results
1.6s3512×body1024valid
430.0ms1366×body512valid
254.0ms2341×body128valid
182.0ms188×body2048valid
127.0ms593×body256valid
1.0msbody1024invalid
Compiler

Compiled 1161 to 689 computations (40.7% saved)

Profiling

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