Details

sample78.0ms

Algorithm

intervals

Results

38.0ms	118×	body	1280	valid
14.0ms	74×	body	640	valid
7.0ms	35×	body	320	valid
6.0ms	208×	body	80	overflowed
1.0ms	15×	body	160	valid
1.0ms	14×	body	80	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (44.0ms)

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))))

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))))

simplify76.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune107.0ms

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))

series172.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
80.0ms	(- x (* 1/3 (pow x 3)))
41.0ms	(* 1/3 (pow x 3))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	206	343
1	832	296
2	5002	295

prune138.0ms

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

localize16.0ms

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))

rewrite13.0ms

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))

series334.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (* 1/3 (pow x 3)))
58.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
159.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
37.0ms	(* 1/3 (pow x 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (39.0ms)

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

prune208.0ms

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)))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (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))))))
139.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
141.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
143.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

simplify159.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (146.0ms)

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

prune280.0ms

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

regimes34.0ms

Accuracy

0% (1.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	3363×	body	1280	valid
491.0ms	2455×	body	640	valid
240.0ms	7610×	body	80	overflowed
156.0ms	1201×	body	320	valid
45.0ms	570×	body	160	valid
17.0ms	411×	body	80	valid