Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	251×	pre	80	false

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	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: 8.0b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
7.2b	(- (/ x0 (- 1.0 x1)) x0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
76×	`times-frac`
69×	`add-cube-cbrt`
63×	`prod-diff`
21×	`fma-neg`
18×	`difference-of-squares`
17×	`distribute-lft-out--`
10×	`associate-/r/`
6×	`flip3--` `flip--`
5×	`associate-/r*` `div-inv`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num`

Counts

2 → 140

Calls

2 calls:

5.0ms	(/ x0 (- 1.0 x1))
15.0ms	(- (/ x0 (- 1.0 x1)) x0)

series79.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ x0 (- 1.0 x1))
46.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify56.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	421	1434
1	1527	945
2	5001	894

prune146.0ms

Filtered

146 candidates to 73 candidates (50.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	2	147

Merged error: 5.3b

Counts

147 → 2

localize9.0ms

Local error

Found 1 expressions with local error:

6.1b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

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 (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series86.0ms

Counts

1 → 3

Calls

1 calls:

86.0ms

(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify155.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	62	143
1	167	123
2	707	119
3	4297	116
4	5001	116

prune31.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	13	2	15

Merged error: 5.3b

Counts

15 → 2

localize13.0ms

Local error

Found 2 expressions with local error:

1.0b	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.1b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity`
3×	`pow1` `log-prod` `exp-sum` `add-log-exp`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `rem-exp-log`
1×	`log-pow` `fma-udef`

Counts

2 → 28

Calls

2 calls:

5.0ms	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
1.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series172.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(exp (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
86.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify159.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (155.0ms)

Iter	Nodes	Cost
0	93	375
1	220	334
2	794	304
3	4603	293
4	5001	290

prune80.0ms

Filtered

34 candidates to 27 candidates (79.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	34	2	36

Merged error: 5.3b

Counts

36 → 2

localize16.0ms

Local error

Found 2 expressions with local error:

1.3b	(pow E (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.1b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `pow-unpow`
3×	`unpow-prod-up` `add-exp-log` `unpow-prod-down` `log-prod`
2×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `e-exp-1` `pow-pow` `log-pow` `fma-udef` `sqr-pow`

Counts

2 → 34

Calls

2 calls:

3.0ms	(pow E (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
1.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series238.0ms

Counts

2 → 6

Calls

2 calls:

149.0ms	(pow E (log (fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
88.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify58.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	165	537
1	475	502
2	1949	475
3	5001	438

prune91.0ms

Filtered

40 candidates to 31 candidates (77.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 5.3b

Counts

42 → 2

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 5.6b against oracle of 5.6b and baseline of 6.6b

bsearch1.0ms

Steps

Iters	Range		Point
0	0.9814	0.999791	0.9905955

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	45
1	26	45

end0.0ms

sample627.0ms

Algorithm

intervals

Results

132.0ms	8000×	body	80	valid
124.0ms	8060×	pre	80	false
123.0ms	8000×	pre	80	true