Details

sample340.0ms

Algorithm

intervals

Results

42.0ms	207×	body	10240	exit
12.0ms	403×	body	80	nan
8.0ms	242×	body	80	valid
1.0ms	15×	body	160	valid

simplify89.0ms

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: 3.5b

Counts

2 → 1

localize12.0ms

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)))
3.3b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)

rewrite39.0ms

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))
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)

series212.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
36.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (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

prune344.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	3	168

Merged error: 0.5b

Counts

168 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.5b	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
3.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.3b	(- (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:

9.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series434.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
198.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5003	1028

prune318.0ms

Filtered

108 candidates to 81 candidates (75.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 0.5b

Counts

111 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
0.5b	(sqrt (/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0)))
3.3b	(- (exp (* 2.0 x)) 1.0)
3.3b	(- (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:

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
129.0ms	(sqrt (/ (* (+ (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)

simplify68.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (54.0ms)

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

prune277.0ms

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: 0.5b

Counts

133 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (exp x))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))))
3.3b	(- (exp (* 2.0 x)) 1.0)
3.4b	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt` `sqrt-prod`
16×	`times-frac`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
5×	`sqrt-pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`rem-sqrt-square` `exp-prod` `fma-neg`
2×	`pow1/2`
1×	`sub-neg` `flip3--` `sqrt-div` `diff-log` `flip--` `fma-udef` `div-inv`

Counts

4 → 89

Calls

4 calls:

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

series225.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
137.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))))
25.0ms	(- (exp (* 2.0 x)) 1.0)
51.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

simplify147.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	346	1014
1	929	876
2	4428	856
3	5001	841

prune247.0ms

Filtered

101 candidates to 75 candidates (74.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	101	4	105

Merged error: 0.5b

Counts

105 → 4

regimes30.0ms

Accuracy

98.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 3.2b

bsearch98.0ms

Steps

Iters	Range		Point
9	2.5055192714849007e-19	1.2000045585397406e-10	6.561572677279099e-15
7	-3.986979250504639e-11	-3.0624602319297156e-13	-8.351232208718257e-12

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	25
1	42	25

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	7003×	body	10240	exit
388.0ms	13033×	body	80	nan
235.0ms	7407×	body	80	valid
57.0ms	730×	body	160	valid