Details

sample312.0ms

Algorithm

intervals

Results

17.0ms	436×	body	80	nan
12.0ms	246×	body	80	valid
8.0ms	216×	body	80	overflowed
2.0ms	19×	body	160	valid

simplify75.0ms

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: 4.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite53.0ms

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:

24.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
96.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
26.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (42.0ms)

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

prune355.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	162	5	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	5	168

Merged error: 0.2b

Counts

168 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
0.2b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
4.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.1b	(- (exp (* 2.0 x)) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
155×	`*-un-lft-identity`
123×	`add-sqr-sqrt`
95×	`sqrt-prod`
79×	`add-cube-cbrt`
19×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
13×	`associate-/r/`
9×	`prod-diff`
7×	`div-inv`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`rem-sqrt-square` `fma-neg` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `clear-num` `flip--` `fma-udef`

Counts

4 → 183

Calls

4 calls:

16.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
10.0ms	(/ (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)

series298.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
69.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	836	3484
1	2947	3301
2	5001	3182

prune551.0ms

Filtered

195 candidates to 133 candidates (68.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	196	4	200

Merged error: 0.2b

Counts

200 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0)))
0.2b	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp (* 2 x)) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
11×	`sqrt-prod`
10×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/` `add-log-exp`
7×	`flip3--` `flip--`
6×	`fma-neg`
5×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `associate-/r/` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `div-inv`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`

Counts

4 → 117

Calls

4 calls:

10.0ms	(sqrt (/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0)))
15.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp (* 2 x)) 1.0)

series265.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0)))
89.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
30.0ms	(- (exp (* 2.0 x)) 1.0)
18.0ms	(- (exp (* 2 x)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	537	1392
1	2248	1153
2	5002	1144

prune282.0ms

Filtered

129 candidates to 89 candidates (69.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	129	4	133

Merged error: 0.2b

Counts

133 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

4.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.2b	(- (exp x) 1.0)
4.2b	(- (exp x) 1.0)
4.2b	(- (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)

series98.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)
14.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (35.0ms)

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

prune367.0ms

Filtered

158 candidates to 83 candidates (52.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Merged error: 0.2b

Counts

162 → 4

regimes30.0ms

Accuracy

75.6% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.8b

bsearch19.0ms

Steps

Iters	Range		Point
3	-7.102728357209251e-09	-5.857412215369722e-09	-7.0248960983442806e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	15
1	27	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

486.0ms	12530×	body	80	nan
313.0ms	7422×	body	80	valid
245.0ms	6612×	body	80	overflowed
69.0ms	706×	body	160	valid