Details

analyze1.2s

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

sample91.0ms

Algorithm

intervals

Results

57.0ms	108×	body	1280	valid
12.0ms	45×	body	640	valid
6.0ms	29×	body	320	valid
4.0ms	66×	body	80	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms

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: 13.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.6b	(cos.f64 (+.f64 a b))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
13×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `cos-sum_binary64` `-commutative_binary64`

Counts

3 → 67

Calls

3 calls:

8.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
5.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))

series177.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
54.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
17.0ms	(cos.f64 (+.f64 a b))

simplify94.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4989	1258
1	4989	1258

prune64.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.1b

Counts

77 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
23×	`associate-r_binary64`
19×	`times-frac_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-l_binary64`
8×	`associate-/r/_binary64`
5×	`cos-mult_binary64` `sin-mult_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 105

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (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))

series478.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
248.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
151.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
43.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify94.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5722	2593

prune107.0ms

Filtered

88 candidates to 117 candidates (-33.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	7	117
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 0b

Counts

125 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cos-mult_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
5.0ms	(*.f64 (sin.f64 b) r)
10.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series381.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
33.0ms	(*.f64 (sin.f64 b) r)
262.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
45.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify74.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5070	1471

prune72.0ms

Filtered

66 candidates to 93 candidates (-40.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 0b

Counts

103 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
29.0b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `times-frac_binary64`
8×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64` `sin-mult_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-/r/_binary64` `associate-l_binary64` `cube-div_binary64` `associate-/l_binary64`
2×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `cos-mult_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3))))
6.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
6.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

series310.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3))))
42.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
84.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
42.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5305	1909

prune64.0ms

Filtered

70 candidates to 102 candidates (-45.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	102	10	112

Merged error: 0b

Counts

112 → 10

regimes87.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2933×	body	1280	valid
514.0ms	1805×	body	640	valid
159.0ms	771×	body	320	valid
157.0ms	2138×	body	80	valid
52.0ms	353×	body	160	valid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.2s

sample91.0ms

simplify12.0ms

prune2.0ms

localize10.0ms

rewrite20.0ms

series177.0ms

simplify94.0ms

prune64.0ms

localize15.0ms

rewrite36.0ms

series478.0ms

simplify94.0ms

prune107.0ms

localize15.0ms

rewrite27.0ms

series381.0ms

simplify74.0ms

prune72.0ms

localize19.0ms

rewrite30.0ms

series310.0ms

simplify64.0ms

prune64.0ms

regimes87.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.5s

Profiling