Details

sample99.0ms

Algorithm

intervals

Results

37.0ms	234×	body	10240	exit
34.0ms	110×	body	1280	valid
11.0ms	65×	body	640	valid
5.0ms	42×	body	320	valid
2.0ms	27×	body	160	valid
0.0ms	12×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite3.0ms

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:

0.0ms	(fma 1 1 (exp (+ x x)))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series93.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune114.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* 2 x)) 1)
0.0b	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))
0.0b	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
0.1b	(pow (+ (exp (* 2 x)) 1) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 161

Calls

4 calls:

4.0ms	(+ (exp (* 2 x)) 1)
16.0ms	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))
6.0ms	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
6.0ms	(pow (+ (exp (* 2 x)) 1) 3)

series105.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (exp (* 2 x)) 1)
55.0ms	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))
10.0ms	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
30.0ms	(pow (+ (exp (* 2 x)) 1) 3)

simplify63.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	378	1647
1	1688	1483
2	5001	1425

prune311.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

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))))
0.2b	(* 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:

2.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
7.0ms	(* 1/3 (pow x 3))

series172.0ms

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))))
37.0ms	(* 1/3 (pow x 3))

simplify35.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (6.0ms)

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

prune157.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

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

rewrite11.0ms

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:

2.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
7.0ms	(* 1/3 (pow x 3))

series329.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- x (* 1/3 (pow x 3)))
52.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
155.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
40.0ms	(* 1/3 (pow x 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

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

prune230.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes16.0ms

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	18	8
1	20	8
2	20	8

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	7383×	body	10240	exit
988.0ms	3355×	body	1280	valid
438.0ms	2418×	body	640	valid
129.0ms	1171×	body	320	valid
43.0ms	631×	body	160	valid
15.0ms	425×	body	80	valid