Details

sample296.0ms

Algorithm

intervals

Results

16.0ms	408×	body	80	nan
12.0ms	240×	body	80	valid
9.0ms	231×	body	80	overflowed
2.0ms	25×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	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: 5.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.5b	(- (exp (* 2.0 x)) 1.0)
5.6b	(- (exp x) 1.0)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

23.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune331.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	4	168

Merged error: 0b

Counts

168 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
5.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.5b	(- (exp (* 2.0 x)) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
108.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	805	3596
1	3551	3384
2	5003	3382

prune539.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	218	4	222

Merged error: 0b

Counts

222 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
0.1b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
5.6b	(- (exp x) 1.0)
5.6b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
31×	`times-frac`
30×	`add-cube-cbrt`
21×	`sqrt-prod`
9×	`prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `div-inv`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `clear-num` `fma-udef`

Counts

4 → 112

Calls

4 calls:

6.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
8.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series362.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
112.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)
84.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	356	1725
1	1097	1468
2	5001	1437

prune290.0ms

Filtered

124 candidates to 93 candidates (75.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	124	4	128

Merged error: 0b

Counts

128 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.6b	(- (exp x) 1.0)
5.6b	(- (exp x) 1.0)
5.6b	(- (exp x) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
63×	`prod-diff`
61×	`*-un-lft-identity`
51×	`add-cube-cbrt`
45×	`sqrt-prod`
15×	`fma-neg`
12×	`add-log-exp`
7×	`difference-of-squares`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 146

Calls

4 calls:

8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.0ms	(- (exp x) 1.0)
5.0ms	(- (exp x) 1.0)
5.0ms	(- (exp x) 1.0)

series90.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	325	1647
1	934	1117
2	5002	1054

prune376.0ms

Filtered

158 candidates to 83 candidates (52.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	158	4	162

Merged error: 0b

Counts

162 → 4

regimes29.0ms

Accuracy

69.3% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.5b

bsearch34.0ms

Steps

Iters	Range		Point
7	-8.122444927071721e-05	-1.7109189605450724e-06	-1.4065309123184993e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	16
1	22	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

475.0ms	12489×	body	80	nan
310.0ms	7435×	body	80	valid
236.0ms	6531×	body	80	overflowed
68.0ms	696×	body	160	valid