Details

sample103.0ms

Algorithm

intervals

Results

41.0ms	246×	body	10240	exit
34.0ms	117×	body	1280	valid
11.0ms	68×	body	640	valid
4.0ms	38×	body	320	valid
1.0ms	18×	body	160	valid
1.0ms	15×	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

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

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

series87.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
67.0ms	(/ (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

prune116.0ms

Filtered

46 candidates to 39 candidates (84.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (expm1 (+ x x)) (* (hypot 1 (exp x)) (hypot 1 (exp x))))
1.0b	(* (hypot 1 (exp x)) (hypot 1 (exp x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
4×	`hypot-udef`
3×	`times-frac` `swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `rem-square-sqrt` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `expm1-udef` `unswap-sqr`

Counts

2 → 53

Calls

2 calls:

4.0ms	(/ (expm1 (+ x x)) (* (hypot 1 (exp x)) (hypot 1 (exp x))))
4.0ms	(* (hypot 1 (exp x)) (hypot 1 (exp x)))

series218.0ms

Counts

2 → 6

Calls

2 calls:

142.0ms	(/ (expm1 (+ x x)) (* (hypot 1 (exp x)) (hypot 1 (exp x))))
75.0ms	(* (hypot 1 (exp x)) (hypot 1 (exp x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	250	509
1	1184	419
2	5002	384

prune125.0ms

Filtered

59 candidates to 42 candidates (71.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

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:

79.0ms	(- x (* 1/3 (pow x 3)))
55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
36.0ms	(* 1/3 (pow x 3))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune161.0ms

Filtered

72 candidates to 48 candidates (66.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

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))))
0.0b	(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))

series324.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- x (* 1/3 (pow x 3)))
54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
153.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
38.0ms	(* 1/3 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	305	480
1	1200	419
2	5001	398

prune226.0ms

Filtered

86 candidates to 60 candidates (69.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.5b

regimes14.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.6b 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

1.3s	7569×	body	10240	exit
952.0ms	3252×	body	1280	valid
435.0ms	2475×	body	640	valid
129.0ms	1204×	body	320	valid
46.0ms	641×	body	160	valid
15.0ms	428×	body	80	valid