Details

analyze817.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample75.0ms

Algorithm

intervals

Results

33.0ms	50×	body	1280	valid
15.0ms	37×	body	640	valid
14.0ms	146×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	49	14
1	49	14

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 17.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
0.3b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
17.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

8.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
5.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
16.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

series23.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
4.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
13.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4945	686
1	4945	686

prune73.0ms

Filtered

49 candidates to 68 candidates (-38.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	57	11	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	11	69

Merged error: 0.1b

Counts

69 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)
0.3b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

9.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)
6.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))

series25.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
4.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)
9.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))

simplify76.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4907	793
1	4907	793

prune69.0ms

Filtered

53 candidates to 75 candidates (-41.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Merged error: 0.0b

Counts

86 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.8b	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
36×	`associate-r_binary64`
28×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
7×	`pow1_binary64` `unswap-sqr_binary64`
6×	`associate-l_binary64`
5×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `cube-div_binary64` `div-inv_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64`
2×	`cbrt-div_binary64` `pow-to-exp_binary64` `cbrt-unprod_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `cbrt-prod_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64`

Counts

4 → 131

Calls

4 calls:

13.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
6.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
7.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
19.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
14.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
12.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

simplify52.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5157	1876

prune100.0ms

Filtered

82 candidates to 143 candidates (-74.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	145	10	155

Merged error: 0b

Counts

155 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.8b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0b	(cbrt.f64 512/27)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
39×	`cbrt-prod_binary64`
38×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
36×	`times-frac_binary64`
26×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64`
2×	`pow1/3_binary64` `sqr-pow_binary64` `cube-div_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `prod-exp_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 121

Calls

4 calls:

6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
6.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0ms	(cbrt.f64 512/27)

series27.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
13.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
7.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
0.0ms	(cbrt.f64 512/27)

simplify56.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5516	1502

prune73.0ms

Filtered

73 candidates to 131 candidates (-79.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	131	10	141

Merged error: 0b

Counts

141 → 10

regimes29.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	1595×	body	1280	valid
614.0ms	4241×	body	80	valid
535.0ms	1262×	body	640	valid
175.0ms	607×	body	320	valid
59.0ms	295×	body	160	valid

Details

analyze817.0ms

sample75.0ms

simplify7.0ms

prune5.0ms

localize10.0ms

rewrite31.0ms

series23.0ms

simplify59.0ms

prune73.0ms

localize11.0ms

rewrite23.0ms

series25.0ms

simplify76.0ms

prune69.0ms

localize12.0ms

rewrite36.0ms

series67.0ms

simplify52.0ms

prune100.0ms

localize13.0ms

rewrite25.0ms

series27.0ms

simplify56.0ms

prune73.0ms

regimes29.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling