Details

sample104.0ms

Algorithm

intervals

Results

42.0ms	249×	body	10240	exit
32.0ms	109×	body	1280	valid
13.0ms	74×	body	640	valid
4.0ms	38×	body	320	valid
1.0ms	19×	body	160	valid
1.0ms	16×	body	80	valid

simplify45.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
2.0b	(/ (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))))

series88.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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: 1.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (log1p (exp (* 2 x))))
2.0b	(log1p (exp (* 2 x)))
2.0b	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

2.0ms	(exp (log1p (exp (* 2 x))))
1.0ms	(log1p (exp (* 2 x)))
4.0ms	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

series261.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(exp (log1p (exp (* 2 x))))
53.0ms	(log1p (exp (* 2 x)))
132.0ms	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	182	523
1	556	477
2	2509	465
3	5001	451

prune155.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.8b

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)))
0.1b	(* 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:

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))

series166.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
78.0ms	(- x (* 1/3 (pow x 3)))
39.0ms	(* 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	5002	292

prune163.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.8b

localize12.0ms

Local error

Found 4 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)))
0.1b	(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:

1.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
3.0ms	(- 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))

series320.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
79.0ms	(- x (* 1/3 (pow x 3)))
152.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
35.0ms	(* 1/3 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (36.0ms)

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

prune219.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.8b

regimes25.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	17	7
2	17	7

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7570×	body	10240	exit
1.0s	3389×	body	1280	valid
437.0ms	2410×	body	640	valid
132.0ms	1171×	body	320	valid
43.0ms	598×	body	160	valid
16.0ms	432×	body	80	valid