Details

sample107.0ms

Algorithm

intervals

Results

43.0ms	245×	body	10240	exit
33.0ms	113×	body	1280	valid
13.0ms	70×	body	640	valid
5.0ms	45×	body	320	valid
1.0ms	17×	body	160	valid
0.0ms	11×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize9.0ms

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))))

series110.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
18.0ms	(expm1 (+ x x))
71.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify82.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (72.0ms)

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

prune144.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(+ (exp (* 2 x)) 1)
0.5b	(/ (expm1 (+ x x)) (+ (exp (* 2 x)) 1))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`associate-/r*` `log1p-expm1-u`
3×	`pow1` `expm1-log1p-u` `fma-def` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `expm1-udef`
1×	`cbrt-undiv` `+-commutative` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

1.0ms	(expm1 (+ x x))
4.0ms	(+ (exp (* 2 x)) 1)
6.0ms	(/ (expm1 (+ x x)) (+ (exp (* 2 x)) 1))

series78.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(expm1 (+ x x))
10.0ms	(+ (exp (* 2 x)) 1)
50.0ms	(/ (expm1 (+ x x)) (+ (exp (* 2 x)) 1))

simplify36.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	218	515
1	914	461
2	5001	452

prune155.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (exp (* 2 x)))
0.3b	(cbrt (exp (* 2 x)))
0.3b	(cbrt (exp (* 2 x)))
0.5b	(/ (expm1 (+ x x)) (fma (* (cbrt (exp (* 2 x))) (cbrt (exp (* 2 x)))) (cbrt (exp (* 2 x))) 1))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

2.0ms	(cbrt (exp (* 2 x)))
2.0ms	(cbrt (exp (* 2 x)))
2.0ms	(cbrt (exp (* 2 x)))
3.0ms	(/ (expm1 (+ x x)) (fma (* (cbrt (exp (* 2 x))) (cbrt (exp (* 2 x)))) (cbrt (exp (* 2 x))) 1))

series534.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (exp (* 2 x)))
82.0ms	(cbrt (exp (* 2 x)))
82.0ms	(cbrt (exp (* 2 x)))
288.0ms	(/ (expm1 (+ x x)) (fma (* (cbrt (exp (* 2 x))) (cbrt (exp (* 2 x)))) (cbrt (exp (* 2 x))) 1))

simplify74.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	180	947
1	528	861
2	2462	792
3	5002	784

prune259.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

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))

rewrite12.0ms

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))

series175.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(- x (* 1/3 (pow x 3)))
55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
40.0ms	(* 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

prune159.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

regimes23.0ms

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	15	6
1	17	6
2	17	6

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	7420×	body	10240	exit
1.0s	3353×	body	1280	valid
452.0ms	2455×	body	640	valid
136.0ms	1203×	body	320	valid
42.0ms	567×	body	160	valid
16.0ms	422×	body	80	valid