Details

sample310.0ms

Algorithm

intervals

Results

18.0ms	404×	body	80	nan
11.0ms	239×	body	80	valid
9.0ms	221×	body	80	overflowed
4.0ms	18×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 4.1b

Counts

2 → 1

localize13.0ms

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))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp x) 1.0)

rewrite47.0ms

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:

22.0ms	(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)

series202.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (112.0ms)

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

prune302.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0.0b

Counts

136 → 3

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))) (- (exp x) 1.0))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.4b	(- (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:

18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
16.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
9.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series355.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
113.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	481	1464
1	2403	1163
2	5002	1124

prune300.0ms

Filtered

117 candidates to 83 candidates (70.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

localize20.0ms

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))
4.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.4b	(- (exp x) 1.0)

rewrite31.0ms

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:

8.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
8.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series234.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
46.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
51.0ms	(- (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

prune240.0ms

Filtered

116 candidates to 55 candidates (47.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (exp x) 1.0))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp x) 1.0)
4.4b	(log (exp (- (exp x) 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-log-exp`
10×	`exp-prod`
7×	`add-cube-cbrt`
6×	`log-pow`
5×	`pow1` `log-prod`
4×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`flip3--` `exp-diff` `flip--` `rem-exp-log`
1×	`log-div` `rem-log-exp`

Counts

4 → 65

Calls

4 calls:

5.0ms	(exp (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
4.0ms	(- (exp x) 1.0)
5.0ms	(log (exp (- (exp x) 1.0)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)
18.0ms	(log (exp (- (exp x) 1.0)))

simplify127.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	190	331
1	474	302
2	1250	298
3	4156	298
4	5001	298

prune170.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	77	4	81

Merged error: 0.0b

Counts

81 → 4

regimes26.0ms

Accuracy

79.2% (0.6b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.2b

bsearch37.0ms

Steps

Iters	Range		Point
6	-6.594905655529368e-05	-1.244511409385973e-05	-1.5763013077646677e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

544.0ms	12641×	body	80	nan
348.0ms	7415×	body	80	valid
273.0ms	6671×	body	80	overflowed
74.0ms	697×	body	160	valid