Details

sample92.0ms

Algorithm

intervals

Results

25.0ms	42×	body	1280	valid
23.0ms	321×	body	80	valid
16.0ms	50×	body	640	valid
5.0ms	73×	body	80	overflowed
4.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (39.0ms)

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

prune11.0ms

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: 28.4b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
4.6b	(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)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

15.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
7.0ms	(* (- 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)))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
27.0ms	(* (+ 1.0 eps) x)
169.0ms	(* (- 1.0 eps) x)
254.0ms	(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)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	462	738
1	1805	635
2	5002	628

prune294.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	92	6	98

Merged error: 4.9b

Counts

98 → 6

localize13.0ms

Local error

Found 2 expressions with local error:

4.0b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.5b	(/ (pow x 3) eps)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 77

Calls

2 calls:

1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.0ms	(/ (pow x 3) eps)

series68.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms	(/ (pow x 3) eps)

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	216	398
1	1026	377
2	5002	377

prune192.0ms

Filtered

83 candidates to 49 candidates (59.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 4.9b

Counts

89 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (pow x 3) eps)
9.7b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
9.7b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
9.7b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/l*`
9×	`add-exp-log` `cbrt-prod`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow1/3` `div-exp` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(/ (pow x 3) eps)
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:

22.0ms	(/ (pow x 3) eps)
371.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
365.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
365.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	271	803
1	1222	747
2	5002	738

prune367.0ms

Filtered

118 candidates to 81 candidates (68.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	126	2	128

Merged error: 4.8b

Counts

128 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (pow x 3) eps)
4.5b	(/ (pow x 3) eps)
9.7b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
9.7b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod` `associate-/l*`
14×	`add-exp-log`
8×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
6×	`cbrt-prod` `div-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `div-inv`

Counts

4 → 160

Calls

4 calls:

6.0ms	(/ (pow x 3) eps)
6.0ms	(/ (pow x 3) eps)
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)))))

series808.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (pow x 3) eps)
28.0ms	(/ (pow x 3) eps)
382.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
377.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	271	926
1	1222	878
2	5002	872

prune593.0ms

Filtered

172 candidates to 106 candidates (61.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	166	6	172
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	167	7	174

Merged error: 4.7b

Counts

174 → 7

regimes138.0ms

Accuracy

96.3% (0.6b remaining)

Error of 5.5b against oracle of 4.9b and baseline of 21.5b

bsearch196.0ms

Steps

Iters	Range		Point
10	8.159003009805276e-07	18724.121991280714	0.00010098764690112613

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	42
1	71	42
2	71	42

end0.0ms

sample2.7s

Algorithm

intervals

Results

880.0ms	1708×	body	1280	valid
729.0ms	10224×	body	80	valid
395.0ms	1243×	body	640	valid
137.0ms	615×	body	320	valid
135.0ms	1850×	body	80	overflowed
48.0ms	333×	body	160	valid