Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
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

sample94.0ms

Algorithm

intervals

Results

45.0ms	97×	body	1280	valid
15.0ms	52×	body	640	valid
9.0ms	63×	body	80	valid
5.0ms	25×	body	320	valid
3.0ms	19×	body	160	valid

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.7b

Counts

2 → 1

localize14.0ms

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))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
9×	`add-sqr-sqrt_binary64_1201`
7×	`*-un-lft-identity_binary64_1216` `add-cube-cbrt_binary64_1187`
5×	`pow1_binary64_1162`
3×	`associate-l_binary64_1276` `associate-r_binary64_1275` `add-log-exp_binary64_1181` `associate-/r*_binary64_1279` `times-frac_binary64_1211`
2×	`div-exp_binary64_1169` `cbrt-unprod_binary64_1185` `cbrt-undiv_binary64_1186` `prod-exp_binary64_1167`
1×	`pow-prod-down_binary64_1143` `div-inv_binary64_1217` `clear-num_binary64_1219` `unswap-sqr_binary64_1244` `-commutative_binary64_1284` `frac-2neg_binary64_1209` `cos-sum_binary64_1066` `associate-/l_binary64_1280`

Counts

3 → 47

Calls

3 calls:

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

series164.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(*.f64 r (sin.f64 b))
118.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
16.0ms	(cos.f64 (+.f64 a b))

simplify79.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4961	692
1	4961	692

prune272.0ms

Filtered

43 candidates to 56 candidates (-30.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize25.0ms

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))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1201`
15×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
12×	`*-un-lft-identity_binary64_1216` `add-cube-cbrt_binary64_1187`
10×	`pow1_binary64_1162`
9×	`associate-l_binary64_1276` `associate-r_binary64_1275`
4×	`cbrt-unprod_binary64_1185` `associate-/r/_binary64_1281` `prod-exp_binary64_1167` `add-log-exp_binary64_1181`
3×	`pow-prod-down_binary64_1143` `unswap-sqr_binary64_1244` `cos-mult_binary64_1086` `-commutative_binary64_1284` `sin-mult_binary64_1087` `associate-/r_binary64_1279` `times-frac_binary64_1211`
2×	`div-exp_binary64_1169` `cbrt-undiv_binary64_1186`
1×	`flip3--_binary64_1215` `frac-sub_binary64_1207` `div-inv_binary64_1217` `clear-num_binary64_1219` `frac-2neg_binary64_1209` `sub-div_binary64_1205` `associate-/l*_binary64_1280` `flip--_binary64_1242`

Counts

4 → 81

Calls

4 calls:

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

series351.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
29.0ms	(*.f64 r (sin.f64 b))
41.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
246.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify66.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4991	1420
1	4991	1420

prune426.0ms

Filtered

67 candidates to 93 candidates (-38.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	90	12	102

Merged error: 0.0b

Counts

102 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1201`
24×	`*-un-lft-identity_binary64_1216` `add-cube-cbrt_binary64_1187`
23×	`associate-r_binary64_1275`
19×	`times-frac_binary64_1211`
15×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
10×	`pow1_binary64_1162`
9×	`associate-l_binary64_1276`
8×	`associate-/r/_binary64_1281`
5×	`cos-mult_binary64_1086` `sin-mult_binary64_1087`
4×	`cbrt-unprod_binary64_1185` `unswap-sqr_binary64_1244` `prod-exp_binary64_1167` `add-log-exp_binary64_1181`
3×	`pow-prod-down_binary64_1143` `-commutative_binary64_1284` `associate-/r_binary64_1279` `associate-/l*_binary64_1280`
2×	`flip3--_binary64_1215` `div-exp_binary64_1169` `frac-sub_binary64_1207` `div-inv_binary64_1217` `cbrt-undiv_binary64_1186` `sub-div_binary64_1205` `flip--_binary64_1242`
1×	`clear-num_binary64_1219` `associate-*r/_binary64_1277` `frac-2neg_binary64_1209`

Counts

4 → 105

Calls

4 calls:

4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
12.0ms	(.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))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
41.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
256.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
144.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5034	2629

prune497.0ms

Filtered

88 candidates to 117 candidates (-33.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 0.0b

Counts

129 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1201`
28×	`add-exp-log_binary64_1180`
24×	`*-un-lft-identity_binary64_1216`
23×	`add-cube-cbrt_binary64_1187`
22×	`add-cbrt-cube_binary64_1188`
21×	`associate-r_binary64_1275`
20×	`times-frac_binary64_1211`
14×	`pow1_binary64_1162`
11×	`prod-exp_binary64_1167`
9×	`associate-l_binary64_1276`
8×	`cbrt-unprod_binary64_1185` `associate-/r/_binary64_1281`
5×	`pow-prod-down_binary64_1143` `sin-mult_binary64_1087`
4×	`unswap-sqr_binary64_1244` `associate-*r/_binary64_1277` `cos-mult_binary64_1086` `add-log-exp_binary64_1181`
3×	`div-exp_binary64_1169` `rec-exp_binary64_1168` `cbrt-undiv_binary64_1186` `-commutative_binary64_1284` `associate-/r_binary64_1279` `associate-/l*_binary64_1280`
2×	`flip3--_binary64_1215` `un-div-inv_binary64_1218` `frac-sub_binary64_1207` `div-inv_binary64_1217` `sub-div_binary64_1205` `flip--_binary64_1242`
1×	`clear-num_binary64_1219` `pow-flip_binary64_1146` `inv-pow_binary64_1138` `frac-2neg_binary64_1209`

Counts

4 → 115

Calls

4 calls:

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))
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))))))
14.0ms	(.f64 (sin.f64 b) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
43.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
247.0ms	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))))
146.0ms	(.f64 (sin.f64 b) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5005	3091

prune404.0ms

Filtered

83 candidates to 127 candidates (-53.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	127	9	136

Merged error: 0.0b

Counts

136 → 9

regimes361.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	29
1	45	29

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2926×	body	1280	valid
545.0ms	1877×	body	640	valid
158.0ms	783×	body	320	valid
154.0ms	2081×	body	80	valid
53.0ms	333×	body	160	valid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.3s

sample94.0ms

simplify137.0ms

prune20.0ms

localize14.0ms

rewrite15.0ms

series164.0ms

simplify79.0ms

prune272.0ms

localize25.0ms

rewrite25.0ms

series351.0ms

simplify66.0ms

prune426.0ms

localize22.0ms

rewrite33.0ms

series479.0ms

simplify76.0ms

prune497.0ms

localize25.0ms

rewrite42.0ms

series557.0ms

simplify93.0ms

prune404.0ms

regimes361.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling