Details

sample311.0ms

Algorithm

intervals

Results

39.0ms	183×	body	10240	exit
10.0ms	323×	body	80	nan
8.0ms	238×	body	80	valid
2.0ms	19×	body	160	valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

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: 4.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp x) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify124.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune293.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	5	136

Merged error: 0.0b

Counts

136 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
4.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.8b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/r*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

20.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series364.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
182.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	481	1464
1	2401	1163
2	5003	1124

prune281.0ms

Filtered

117 candidates to 83 candidates (70.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 0.0b

Counts

122 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
0.1b	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
4.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.8b	(- (exp x) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`sqrt-prod`
24×	`cbrt-prod`
21×	`difference-of-squares`
18×	`unpow-prod-down` `cube-prod`
11×	`distribute-lft-out--`
10×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

10.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
8.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
53.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	357	1065
1	1371	995
2	5001	983

prune226.0ms

Filtered

116 candidates to 55 candidates (47.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	116	5	121

Merged error: 0.0b

Counts

121 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)
0.0b	(/ (+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0))) (- (exp x) 1.0))
4.7b	(+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)))
4.8b	(- (exp x) 1.0)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
30×	`times-frac`
25×	`add-log-exp`
21×	`distribute-lft-out`
17×	`add-cube-cbrt`
15×	`distribute-rgt-out`
12×	`sum-log`
11×	`flip3-+` `flip-+`
8×	`frac-add` `distribute-neg-frac` `distribute-lft-out--` `difference-of-squares`
7×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l/` `associate-/l*`
5×	`associate-/r*`
4×	`pow1` `neg-log`
3×	`div-sub`
2×	`+-commutative` `neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `associate-+l+` `associate-+r+` `distribute-neg-in` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

6.0ms	(+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)
19.0ms	(/ (+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0))) (- (exp x) 1.0))
14.0ms	(+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)))
4.0ms	(- (exp x) 1.0)

series165.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)
62.0ms	(/ (+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0))) (- (exp x) 1.0))
27.0ms	(+ (+ (exp (* 2.0 x)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (+ (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1.0)))
15.0ms	(- (exp x) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	559	2792
1	2423	2524
2	5003	2300

prune319.0ms

Filtered

130 candidates to 87 candidates (66.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	131	4	135

Merged error: 0.0b

Counts

135 → 4

regimes31.0ms

Accuracy

76.3% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 3.3b

bsearch17.0ms

Steps

Iters	Range		Point
3	-1.3488457936154646e-05	-1.0220710393840792e-05	-1.328422371476003e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	22
1	33	22

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	6682×	body	10240	exit
400.0ms	12570×	body	80	nan
256.0ms	7391×	body	80	valid
58.0ms	728×	body	160	valid