Details

sample103.0ms

Algorithm

intervals

Results

37.0ms	233×	body	10240	exit
31.0ms	102×	body	1280	valid
17.0ms	79×	body	640	valid
5.0ms	39×	body	320	valid
2.0ms	24×	body	160	valid
0.0ms	12×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

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))))

rewrite6.0ms

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)))
5.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series89.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ (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

prune114.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
0.2b	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `associate-/r*`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `associate-/r/` `fma-udef` `inv-pow`

Counts

3 → 117

Calls

3 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
5.0ms	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
12.0ms	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

series158.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(fma 1 1 (exp (+ x x)))
63.0ms	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
69.0ms	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	387	1449
1	1742	1257
2	5001	1169

prune218.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (expm1 (+ x x))) (cbrt (expm1 (+ x x))))
0.6b	(cbrt (expm1 (+ x x)))
0.6b	(cbrt (expm1 (+ x x)))
0.6b	(cbrt (expm1 (+ x x)))

rewrite15.0ms

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:

11.0ms	(* (cbrt (expm1 (+ x x))) (cbrt (expm1 (+ x x))))
1.0ms	(cbrt (expm1 (+ x x)))
1.0ms	(cbrt (expm1 (+ x x)))
1.0ms	(cbrt (expm1 (+ x x)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (cbrt (expm1 (+ x x))) (cbrt (expm1 (+ x x))))
107.0ms	(cbrt (expm1 (+ x x)))
100.0ms	(cbrt (expm1 (+ x x)))
103.0ms	(cbrt (expm1 (+ x x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	176	684
1	626	604
2	3890	533
3	5001	522

prune246.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

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))

rewrite20.0ms

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:

6.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
13.0ms	(* 1/3 (pow x 3))

series166.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify35.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	206	343
1	832	296
2	5001	295

prune156.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.7b 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

1.3s	7580×	body	10240	exit
965.0ms	3253×	body	1280	valid
450.0ms	2519×	body	640	valid
142.0ms	1224×	body	320	valid
45.0ms	610×	body	160	valid
17.0ms	394×	body	80	valid