Details

sample109.0ms

Algorithm

intervals

Results

47.0ms	273×	body	10240	exit
34.0ms	116×	body	1280	valid
12.0ms	70×	body	640	valid
4.0ms	40×	body	320	valid
1.0ms	16×	body	160	valid
1.0ms	14×	body	80	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (43.0ms)

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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.5b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.7b	(/ (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))))

series88.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune98.0ms

Filtered

46 candidates to 39 candidates (84.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	45	3	48

Merged error: 0.5b

Counts

48 → 3

localize10.0ms

Local error

Found 3 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	(* 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:

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

series170.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- x (* 1/3 (pow x 3)))
55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
37.0ms	(* 1/3 (pow x 3))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5001	292

prune133.0ms

Filtered

72 candidates to 48 candidates (66.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	71	4	75

Merged error: 0.5b

Counts

75 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

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

series543.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
94.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
353.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
40.0ms	(* 1/3 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	306	465
1	1191	409
2	5001	389

prune193.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	77	4	81

Merged error: 0.5b

Counts

81 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

1.0ms	(log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
1.0ms	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
1.0ms	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
7.0ms	(* 1/3 (pow x 3))

series618.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
191.0ms	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
253.0ms	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
36.0ms	(* 1/3 (pow x 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	414	629
1	1800	547
2	5002	539

prune226.0ms

Filtered

78 candidates to 58 candidates (74.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	77	5	82

Merged error: 0.5b

Counts

82 → 5

regimes51.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	13	6
2	13	6

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	7433×	body	10240	exit
967.0ms	3241×	body	1280	valid
438.0ms	2428×	body	640	valid
138.0ms	1249×	body	320	valid
46.0ms	648×	body	160	valid
16.0ms	434×	body	80	valid