Details

sample98.0ms

Algorithm

intervals

Results

34.0ms	66×	body	1280	valid
24.0ms	335×	body	80	valid
10.0ms	30×	body	640	valid
8.0ms	62×	body	80	overflowed
4.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 28.9b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- 1.0 eps) x))
0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.9b	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`add-exp-log`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*`
3×	`associate-r`
2×	`cbrt-undiv` `exp-to-pow` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`exp-prod` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `flip-+` `fma-udef` `div-inv` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

3.0ms	(exp (* (- 1.0 eps) x))
7.0ms	(* (- 1.0 eps) x)
12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
1.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (* (- 1.0 eps) x))
28.0ms	(* (- 1.0 eps) x)
46.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
229.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	706
1	1474	605
2	5001	586

prune265.0ms

Filtered

86 candidates to 63 candidates (73.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 3.3b

Counts

88 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
3.9b	(/ (pow x 3) eps)
4.4b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-exp-log`
12×	`cube-prod` `associate-/l*`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqr-pow`
4×	`cube-mult` `unpow3` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `div-exp` `associate-l` `prod-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `unpow2`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 106

Calls

3 calls:

5.0ms	(* 0.5 (pow x 2))
5.0ms	(/ (pow x 3) eps)
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

series96.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 0.5 (pow x 2))
25.0ms	(/ (pow x 3) eps)
46.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	305	506
1	1561	465
2	5002	451

prune232.0ms

Filtered

115 candidates to 66 candidates (57.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Merged error: 3.3b

Counts

120 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
8.5b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
8.5b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
8.5b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
369.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
362.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
360.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	123	615
1	351	557
2	1616	548
3	5001	542

prune238.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 3.2b

Counts

70 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.4b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
8.5b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
8.5b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series963.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
47.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
503.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
362.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	123	550
1	351	494
2	1616	488
3	5001	484

prune250.0ms

Filtered

58 candidates to 50 candidates (86.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 3.2b

Counts

61 → 7

regimes133.0ms

Accuracy

95.8% (0.7b remaining)

Error of 5.7b against oracle of 5.0b and baseline of 21.0b

bsearch176.0ms

Steps

Iters	Range		Point
10	0.0031014677214056706	385601024814.3293	0.7142628242866219

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	66
1	66	66
2	66	66

end0.0ms

sample2.7s

Algorithm

intervals

Results

910.0ms	1771×	body	1280	valid
711.0ms	10041×	body	80	valid
394.0ms	1250×	body	640	valid
139.0ms	629×	body	320	valid
138.0ms	1943×	body	80	overflowed
48.0ms	339×	body	160	valid