Details

sample35.0ms

Algorithm

intervals

Results

16.0ms	83×	body	1280	valid
6.0ms	47×	body	640	valid
4.0ms	157×	body	80	valid
2.0ms	30×	body	320	valid
0.0ms	9×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	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: 40.9b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.7b	(- (exp x) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

9.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series52.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune96.0ms

Filtered

58 candidates to 43 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.1b

Counts

59 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

7.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
5.0ms	(* 1/6 (pow x 2))

series45.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
23.0ms	(* 1/6 (pow x 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune68.0ms

Filtered

46 candidates to 29 candidates (63.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	44	6	50

Merged error: 0.1b

Counts

50 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow x 2))
0.2b	(* 1/6 (pow x 2))
9.6b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
9.6b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`pow1` `associate-l` `prod-exp` `sqrt-prod`
4×	`sqrt-div` `unpow2` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 84

Calls

4 calls:

6.0ms	(* 1/6 (pow x 2))
5.0ms	(* 1/6 (pow x 2))
6.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
6.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/6 (pow x 2))
24.0ms	(* 1/6 (pow x 2))
61.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
62.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	241	550
1	976	510
2	5002	500

prune200.0ms

Filtered

96 candidates to 66 candidates (68.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	97	5	102

Merged error: 0.1b

Counts

102 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))) (+ (* 5/96 (pow x 2)) (+ (* 1/4 x) 1)))
0.1b	(* 5/96 (pow x 2))
0.2b	(* 1/6 (pow x 2))
9.6b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
10×	`add-cbrt-cube` `unswap-sqr`
8×	`unpow-prod-down` `sqrt-div`
7×	`pow1` `flip3-+` `prod-exp` `sqrt-prod` `flip-+`
4×	`frac-times` `unpow2` `add-log-exp` `sqr-pow`
3×	`*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `associate-r/` `associate-l/` `pow-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down`

Counts

4 → 101

Calls

4 calls:

15.0ms	(* (sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))) (+ (* 5/96 (pow x 2)) (+ (* 1/4 x) 1)))
5.0ms	(* 5/96 (pow x 2))
5.0ms	(* 1/6 (pow x 2))
6.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))) (+ (* 5/96 (pow x 2)) (+ (* 1/4 x) 1)))
24.0ms	(* 5/96 (pow x 2))
24.0ms	(* 1/6 (pow x 2))
62.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify81.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	567	1043
1	2628	978
2	5003	978

prune259.0ms

Filtered

113 candidates to 77 candidates (68.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	3	3
Picked	1	0	1
Done	1	0	1
Total	113	5	118

Merged error: 0.0b

Counts

118 → 5

regimes31.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.8b

bsearch54.0ms

Steps

Iters	Range		Point
8	-6.238959787773506	-0.00010711273713490883	-0.00017128650325012662

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	53
1	62	53

end0.0ms

sample992.0ms

Algorithm

intervals

Results

427.0ms	2230×	body	1280	valid
206.0ms	1665×	body	640	valid
130.0ms	5466×	body	80	valid
68.0ms	805×	body	320	valid
23.0ms	427×	body	160	valid

Details

sample35.0ms

simplify7.0ms

prune2.0ms

localize4.0ms

rewrite15.0ms

series52.0ms

simplify76.0ms

prune96.0ms

localize8.0ms

rewrite13.0ms

series45.0ms

simplify35.0ms

prune68.0ms

localize10.0ms

rewrite26.0ms

series171.0ms

simplify43.0ms

prune200.0ms

localize17.0ms

rewrite36.0ms

series225.0ms

simplify81.0ms

prune259.0ms

regimes31.0ms

bsearch54.0ms

simplify2.0ms

end0.0ms

sample992.0ms

Profiling