Details

sample98.0ms

Algorithm

intervals

Results

35.0ms	118×	body	1280	valid
32.0ms	208×	body	10240	exit
15.0ms	74×	body	640	valid
4.0ms	35×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	14×	body	80	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (42.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
1.5b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv` `expm1-udef`

Counts

2 → 40

Calls

2 calls:

1.0ms	(fma 1 1 (exp (+ x x)))
3.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series91.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
69.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	150	395
1	512	351
2	2464	344
3	5002	343

prune101.0ms

Filtered

46 candidates to 39 candidates (84.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 1.4b

Counts

47 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0b	(- x (* 1/3 (pow x 3)))
0.1b	(* 1/3 (pow x 3))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 63

Calls

3 calls:

1.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
3.0ms	(- x (* 1/3 (pow x 3)))
6.0ms	(* 1/3 (pow x 3))

series168.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
77.0ms	(- x (* 1/3 (pow x 3)))
39.0ms	(* 1/3 (pow x 3))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5002	292

prune142.0ms

Filtered

72 candidates to 48 candidates (66.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Merged error: 1.4b

Counts

74 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* 1/3 (pow x 3)))
0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.1b	(* 1/3 (pow x 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `associate-l` `prod-diff` `prod-exp`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `expm1-log1p` `flip3--` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

3.0ms	(- x (* 1/3 (pow x 3)))
1.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
1.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
6.0ms	(* 1/3 (pow x 3))

series322.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- x (* 1/3 (pow x 3)))
54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
154.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
37.0ms	(* 1/3 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	305	475
1	1203	415
2	5001	395

prune193.0ms

Filtered

86 candidates to 58 candidates (67.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	85	5	90

Merged error: 1.4b

Counts

90 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.7b	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.7b	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.7b	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
1.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

series547.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
133.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
133.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
135.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

simplify158.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	303	1267
1	1040	1174
2	4666	1078
3	5001	1030

prune270.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	92	6	98

Merged error: 1.4b

Counts

98 → 6

regimes32.0ms

Accuracy

0% (1.0b remaining)

Error of 1.7b against oracle of 0.6b and baseline of 1.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	5
1	18	5
2	18	5

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7610×	body	10240	exit
1.0s	3363×	body	1280	valid
438.0ms	2455×	body	640	valid
129.0ms	1201×	body	320	valid
38.0ms	570×	body	160	valid
15.0ms	411×	body	80	valid

Details

sample98.0ms

simplify44.0ms

prune6.0ms

localize8.0ms

rewrite5.0ms

series91.0ms

simplify72.0ms

prune101.0ms

localize10.0ms

rewrite11.0ms

series168.0ms

simplify39.0ms

prune142.0ms

localize12.0ms

rewrite12.0ms

series322.0ms

simplify44.0ms

prune193.0ms

localize14.0ms

rewrite11.0ms

series547.0ms

simplify158.0ms

prune270.0ms

regimes32.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling