Details

sample103.0ms

Algorithm

intervals

Results

30.0ms	77×	body	10240	exit
20.0ms	51×	body	1280	valid
18.0ms	348×	body	80	valid
16.0ms	51×	body	640	valid
2.0ms	15×	body	320	valid
0.0ms	3×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
81×	`add-sqr-sqrt`
26×	`distribute-lft-out--`
25×	`add-cube-cbrt`
17×	`difference-of-squares`
14×	`add-log-exp`
6×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`div-sub` `associate-/r*` `div-inv`
2×	`exp-prod` `flip3--` `diff-log` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `sub-div` `associate--r-`

Counts

4 → 105

Calls

4 calls:

12.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
3.0ms	(exp (* (- 1.0 eps) x))
3.0ms	(exp (* (+ 1.0 eps) x))
164.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series262.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
20.0ms	(exp (* (- 1.0 eps) x))
18.0ms	(exp (* (+ 1.0 eps) x))
177.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	506	1621
1	1440	1536
2	5002	1520

prune342.0ms

Filtered

117 candidates to 85 candidates (72.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	3	118

Merged error: 0.6b

Counts

118 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

8.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series80.0ms

Counts

1 → 3

Calls

1 calls:

79.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify164.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	158	214
1	638	189
2	4553	189
3	5001	189

prune70.0ms

Filtered

36 candidates to 22 candidates (61.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	35	4	39

Merged error: 0.6b

Counts

39 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow x 2)) (cbrt (pow x 2)))
29.2b	(cbrt (pow x 2))
29.2b	(cbrt (pow x 2))
29.2b	(cbrt (pow x 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
52×	`add-sqr-sqrt`
31×	`unpow-prod-down`
25×	`unswap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
17×	`unpow2` `sqr-pow`
11×	`pow1` `swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

10.0ms	(* (cbrt (pow x 2)) (cbrt (pow x 2)))
2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))

series722.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cbrt (pow x 2)) (cbrt (pow x 2)))
176.0ms	(cbrt (pow x 2))
172.0ms	(cbrt (pow x 2))
177.0ms	(cbrt (pow x 2))

simplify82.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	168	785
1	552	648
2	2672	604
3	5001	600

prune313.0ms

Filtered

136 candidates to 83 candidates (61.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	136	4	140

Merged error: 0.6b

Counts

140 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

29.2b	(cbrt (pow x 2))
29.2b	(cbrt (pow x 2))
29.2b	(cbrt (pow x 2))
29.2b	(cbrt (pow x 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))

series717.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (pow x 2))
179.0ms	(cbrt (pow x 2))
183.0ms	(cbrt (pow x 2))
176.0ms	(cbrt (pow x 2))

simplify195.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	66	296
1	162	260
2	607	244
3	3985	244
4	5002	244

prune247.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Merged error: 0.6b

Counts

80 → 4

regimes92.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.3b

bsearch132.0ms

Steps

Iters	Range		Point
9	0.08433677106829839	715934.3120435103	282.8047645330818

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	32
1	46	32

end0.0ms

sample2.8s

Algorithm

intervals

Results

792.0ms	1990×	body	10240	exit
748.0ms	1778×	body	1280	valid
511.0ms	9707×	body	80	valid
304.0ms	1274×	body	640	valid
99.0ms	630×	body	320	valid
38.0ms	379×	body	160	valid