Details

sample102.0ms

Algorithm

intervals

Results

43.0ms	258×	body	10240	exit
28.0ms	100×	body	1280	valid
14.0ms	83×	body	640	valid
4.0ms	39×	body	320	valid
1.0ms	22×	body	160	valid
0.0ms	12×	body	80	valid

simplify45.0ms

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: 0.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

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))))

series89.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
69.0ms	(/ (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

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.0b	(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
0.0ms	(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.0ms	(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
184.0ms	(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
81.0ms	(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
65.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	190	626
1	623	553
2	2844	544
3	5002	542

prune193.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize13.0ms

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))

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:

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))

series353.0ms

Counts

3 → 9

Calls

3 calls:

263.0ms	(- x (* 1/3 (pow x 3)))
54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
35.0ms	(* 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

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* 1/3 (pow x 3)))
0.0b	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
0.0b	(* (pow x 5) 2/15)
0.2b	(* 1/3 (pow x 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
10×	`associate-l`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`prod-diff` `prod-exp`
5×	`associate-+r+`
4×	`pow1` `expm1-log1p-u` `cube-prod` `log1p-expm1-u` `sqr-pow`
3×	`fma-neg`
2×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r-` `flip3--` `fma-def` `flip3-+` `unpow3` `flip--` `flip-+`

Counts

4 → 101

Calls

4 calls:

2.0ms	(- x (* 1/3 (pow x 3)))
7.0ms	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
5.0ms	(* (pow x 5) 2/15)
7.0ms	(* 1/3 (pow x 3))

series213.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- x (* 1/3 (pow x 3)))
52.0ms	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
48.0ms	(* (pow x 5) 2/15)
38.0ms	(* 1/3 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	355	521
1	1456	467
2	5001	466

prune239.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

regimes16.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	15	8
2	15	8

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7703×	body	10240	exit
955.0ms	3255×	body	1280	valid
444.0ms	2513×	body	640	valid
132.0ms	1218×	body	320	valid
42.0ms	622×	body	160	valid
14.0ms	392×	body	80	valid