Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	76×	body	1280	valid
6.0ms	60×	body	640	valid
3.0ms	169×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	14×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 42.4b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.0b	(- (exp x) 1.0)

rewrite14.0ms

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:

7.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
19.0ms	(- (exp x) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

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

prune141.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	2	75

Merged error: 0.0b

Counts

75 → 2

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:

1.0ms

(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))

simplify25.0ms

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

prune35.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.0b

Counts

15 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.1b	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
5.0b	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`unpow-prod-down` `cube-prod`
4×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `rem-cbrt-cube` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `fma-udef` `rem-cube-cbrt`

Counts

3 → 59

Calls

3 calls:

1.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
2.0ms	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
3.0ms	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

series76.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
35.0ms	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
20.0ms	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

simplify257.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	163	366
1	636	347
2	4979	341
3	5001	341

prune137.0ms

Filtered

68 candidates to 39 candidates (57.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	68	3	71

Merged error: 0.0b

Counts

71 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
0.1b	(pow (cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)) 3)
5.0b	(cbrt (pow (cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)) 3))
5.0b	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
48×	`unpow-prod-down` `cube-prod`
30×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cube-mult` `pow-unpow` `unpow3` `sqr-pow`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `rem-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow1/3` `rem-cube-cbrt`
2×	`pow-to-exp` `pow-exp`

Counts

4 → 148

Calls

4 calls:

2.0ms	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
5.0ms	(pow (cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)) 3)
6.0ms	(cbrt (pow (cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)) 3))
3.0ms	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

series105.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)
30.0ms	(pow (cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)) 3)
25.0ms	(cbrt (pow (cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3)) 3))
20.0ms	(cbrt (pow (fma 1/6 (pow x 2) (fma 1/2 x 1)) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	287	1056
1	819	984
2	5002	960

prune234.0ms

Filtered

160 candidates to 63 candidates (39.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	160	3	163

Merged error: 0.0b

Counts

163 → 3

regimes22.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.6b

bsearch30.0ms

Steps

Iters	Range		Point
10	-85019.06990604498	-4.503960361653909e-11	-0.00018041726414346648

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample886.0ms

Algorithm

intervals

Results

390.0ms	2309×	body	1280	valid
175.0ms	1633×	body	640	valid
101.0ms	5284×	body	80	valid
61.0ms	849×	body	320	valid
21.0ms	471×	body	160	valid