Details

sample96.0ms

Algorithm

intervals

Results

35.0ms	220×	body	10240	exit
30.0ms	103×	body	1280	valid
15.0ms	85×	body	640	valid
4.0ms	38×	body	320	valid
1.0ms	18×	body	160	valid
0.0ms	12×	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

prune11.0ms

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 3 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(expm1 (+ x x))
0.5b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

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

series108.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
18.0ms	(expm1 (+ x x))
69.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify80.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	164	440
1	564	391
2	2669	384
3	5001	382

prune125.0ms

Filtered

60 candidates to 49 candidates (81.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	59	3	62

Merged error: 0.5b

Counts

62 → 3

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)))
0.2b	(* 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))

series169.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
79.0ms	(- x (* 1/3 (pow x 3)))
40.0ms	(* 1/3 (pow x 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune134.0ms

Filtered

72 candidates to 48 candidates (66.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Merged error: 0.5b

Counts

75 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.2b	(* 1/3 (pow x 3))
0.2b	(* 1/3 (pow x 3))
0.3b	(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
30×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
20×	`pow1`
16×	`add-exp-log`
12×	`associate-l` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2`
8×	`unpow-prod-down` `cube-prod` `swap-sqr`
7×	`prod-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-prod-down` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 132

Calls

4 calls:

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

series179.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
40.0ms	(* 1/3 (pow x 3))
36.0ms	(* 1/3 (pow x 3))
56.0ms	(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	271	867
1	1151	760
2	5002	719

prune305.0ms

Filtered

144 candidates to 79 candidates (54.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	144	5	149

Merged error: 0.5b

Counts

149 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
0.2b	(* 1/3 (pow x 3))
0.2b	(* 1/3 (pow x 3))
0.3b	(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (expm1 (log1p (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

1.0ms	(expm1 (log1p (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
6.0ms	(* 1/3 (pow x 3))
6.0ms	(* 1/3 (pow x 3))
5.0ms	(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (expm1 (log1p (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(expm1 (log1p (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
41.0ms	(* 1/3 (pow x 3))
35.0ms	(* 1/3 (pow x 3))
385.0ms	(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (expm1 (log1p (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	433	877
1	1581	674
2	5002	600

prune495.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	113	5	118

Merged error: 0.5b

Counts

118 → 5

regimes20.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

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

1.3s	7551×	body	10240	exit
957.0ms	3251×	body	1280	valid
463.0ms	2568×	body	640	valid
128.0ms	1176×	body	320	valid
46.0ms	628×	body	160	valid
14.0ms	377×	body	80	valid