Details

sample100.0ms

Algorithm

intervals

Results

24.0ms	61×	body	10240	exit
23.0ms	57×	body	1280	valid
21.0ms	316×	body	80	valid
11.0ms	45×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	8×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

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

prune17.0ms

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: 31.4b

Counts

2 → 2

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (+ 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
0.5b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
5.8b	(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

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`add-exp-log`
7×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod`
4×	`pow1` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*`
3×	`rem-exp-log`
2×	`cbrt-undiv` `exp-to-pow` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `neg-mul-1` `distribute-rgt-neg-in` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`

Counts

4 → 69

Calls

4 calls:

3.0ms	(exp (- (* (+ 1.0 eps) x)))
3.0ms	(exp (* (- 1.0 eps) x))
21.0ms	(/ (+ 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)))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (- (* (+ 1.0 eps) x)))
20.0ms	(exp (* (- 1.0 eps) x))
47.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
233.0ms	(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)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	365	706
1	1230	610
2	5001	590

prune273.0ms

Filtered

81 candidates to 62 candidates (76.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 6.5b

Counts

83 → 9

localize11.0ms

Local error

Found 2 expressions with local error:

2.6b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.3b	(/ (pow x 3) eps)

rewrite10.0ms

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)

series73.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms	(/ (pow x 3) eps)

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (7.0ms)

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

prune198.0ms

Filtered

83 candidates to 49 candidates (59.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 6.5b

Counts

92 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
2.6b	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
41.4b	(cbrt (pow x 3))
41.4b	(cbrt (pow x 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

12.0ms	(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
1.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
2.0ms	(cbrt (pow x 3))
3.0ms	(cbrt (pow x 3))

series171.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
85.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
19.0ms	(cbrt (pow x 3))
17.0ms	(cbrt (pow x 3))

simplify85.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	388	603
1	2652	494
2	5002	480

prune297.0ms

Filtered

116 candidates to 80 candidates (69.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 2.5b

Counts

129 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
2.2b	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.8b	(log (exp x))
41.4b	(cbrt (pow x 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

11.0ms	(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
1.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
2.0ms	(log (exp x))
2.0ms	(cbrt (pow x 3))

series144.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x))
73.0ms	(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (log (exp x))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
8.0ms	(log (exp x))
16.0ms	(cbrt (pow x 3))

simplify85.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	432	605
1	2783	478
2	5002	464

prune283.0ms

Filtered

110 candidates to 81 candidates (73.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 2.5b

Counts

118 → 9

regimes144.0ms

Accuracy

96.5% (0.6b remaining)

Error of 2.1b against oracle of 1.5b and baseline of 18.1b

bsearch115.0ms

Steps

Iters	Range		Point
7	0.00999808388340962	0.475758948552502	0.020502406150930446

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	32
1	49	32

end0.0ms

sample2.8s

Algorithm

intervals

Results

752.0ms	1741×	body	1280	valid
729.0ms	1825×	body	10240	exit
532.0ms	9883×	body	80	valid
332.0ms	1271×	body	640	valid
109.0ms	671×	body	320	valid
33.0ms	308×	body	160	valid