Details

sample346.0ms

Algorithm

intervals

Results

43.0ms	204×	body	10240	exit
15.0ms	422×	body	80	nan
8.0ms	229×	body	80	valid
2.0ms	27×	body	160	valid

simplify87.0ms

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: 5.8b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite38.0ms

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:

10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
9.0ms	(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)

series199.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
87.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
33.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (42.0ms)

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

prune336.0ms

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: 0.5b

Counts

168 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
0.5b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
5.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.7b	(- (exp (* 2.0 x)) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
10.0ms	(sqrt (* (/ (- (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)

series411.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
155.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5001	1028

prune290.0ms

Filtered

108 candidates to 81 candidates (75.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Merged error: 0.5b

Counts

113 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (- (exp (* 2.0 x)) 1.0))
0.5b	(sqrt (/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (- (exp x) 1.0)))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
27×	`add-cube-cbrt`
21×	`sqrt-prod`
18×	`prod-diff`
16×	`times-frac`
8×	`add-log-exp`
6×	`fma-neg`
5×	`pow1` `expm1-log1p-u` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `associate-/r/`
1×	`log1p-udef` `sqrt-pow1` `pow1/2` `sqrt-div` `log1p-expm1` `div-inv`

Counts

4 → 102

Calls

4 calls:

1.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
7.0ms	(sqrt (/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (- (exp x) 1.0)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp x) 1.0)

series675.0ms

Counts

4 → 12

Calls

4 calls:

420.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
213.0ms	(sqrt (/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (- (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
17.0ms	(- (exp x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	375	1080
1	1014	875
2	5001	847

prune259.0ms

Filtered

114 candidates to 78 candidates (68.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	114	5	119

Merged error: 0.5b

Counts

119 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)
6.2b	(log (exp (- (exp x) 1.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`add-cube-cbrt`
45×	`times-frac`
42×	`log-pow`
35×	`exp-prod`
27×	`prod-diff`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`log-prod`
11×	`pow1` `exp-sum`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`diff-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-sub` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 163

Calls

4 calls:

11.0ms	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
5.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp x) 1.0)
7.0ms	(log (exp (- (exp x) 1.0)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
24.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)
19.0ms	(log (exp (- (exp x) 1.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	497	1684
1	1459	1368
2	5001	1247

prune320.0ms

Filtered

175 candidates to 106 candidates (60.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	175	5	180

Merged error: 0.5b

Counts

180 → 5

regimes39.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 3.0b

bsearch123.0ms

Steps

Iters	Range		Point
6	54.48611989218426	719.5386143167987	356.5832744964275
9	1.300586776622768e-14	1.3201210546183864e-08	8.959964813264309e-14
6	-8.463887753721946e-05	-1.2089635435907877e-05	-1.4928955228485282e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	42
1	45	42

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6577×	body	10240	exit
413.0ms	12798×	body	80	nan
252.0ms	7346×	body	80	valid
63.0ms	766×	body	160	valid