Details

sample46.0ms

Algorithm

intervals

Results

19.0ms	71×	body	1280	valid
10.0ms	57×	body	640	valid
5.0ms	157×	body	80	valid
4.0ms	31×	body	320	valid
1.0ms	15×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

13.0ms	(/ (- (exp x) 1.0) x)
6.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify26.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52

prune37.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.1b	(* (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
7.5b	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
7.5b	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 91

Calls

4 calls:

0.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
7.0ms	(* (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
1.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
1.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
21.0ms	(* (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
65.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
63.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	182	598
1	832	532
2	5001	512

prune224.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (fabs (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))) (sqrt (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))) (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
7.5b	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
7.8b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
7.8b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`cbrt-prod` `associate-r` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (* (fabs (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))) (sqrt (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))) (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
1.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (* (fabs (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))) (sqrt (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))) (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
66.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
61.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
55.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify49.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	359	949
1	1403	853
2	5001	840

prune279.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch30.0ms

Steps

Iters	Range		Point
7	-0.00034188071245303247	-1.912514877855927e-06	-0.00012721971246653334

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample1.4s

Algorithm

intervals

Results

594.0ms	2268×	body	1280	valid
294.0ms	1653×	body	640	valid
185.0ms	5430×	body	80	valid
99.0ms	828×	body	320	valid
34.0ms	413×	body	160	valid