Details

sample103.0ms

Algorithm

intervals

Results

41.0ms	253×	body	10240	exit
34.0ms	120×	body	1280	valid
12.0ms	68×	body	640	valid
4.0ms	36×	body	320	valid
1.0ms	13×	body	160	valid
1.0ms	19×	body	80	valid

simplify44.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
1.2b	(/ (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)))
70.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune113.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.1b

localize9.0ms

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))

rewrite14.0ms

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))

series176.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(- x (* 1/3 (pow x 3)))
57.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
37.0ms	(* 1/3 (pow x 3))

simplify35.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune165.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.1b

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))

series336.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- x (* 1/3 (pow x 3)))
53.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
160.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
41.0ms	(* 1/3 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

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

prune229.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 1.1b

localize17.0ms

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

151.0ms	(* (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))))))
141.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
144.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
137.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

simplify157.0ms

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

prune292.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.1b

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

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

sample3.2s

Algorithm

intervals

Results

1.2s	7601×	body	10240	exit
1.2s	3314×	body	1280	valid
425.0ms	2416×	body	640	valid
137.0ms	1254×	body	320	valid
40.0ms	603×	body	160	valid
21.0ms	413×	body	80	valid