Details

sample328.0ms

Algorithm

intervals

Results

16.0ms	382×	body	80	nan
10.0ms	235×	body	80	valid
7.0ms	196×	body	80	overflowed
2.0ms	25×	body	160	valid

simplify73.0ms

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

prune24.0ms

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: 4.2b

Counts

2 → 1

localize12.0ms

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))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.3b	(- (exp x) 1.0)

rewrite37.0ms

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:

10.0ms	(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)

series198.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify123.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune286.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (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))
5.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`sqrt-prod`
7×	`pow1`
5×	`sqrt-div` `difference-of-squares`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `distribute-lft-out--`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*l/` `flip--` `distribute-lft-out`
1×	`+-commutative` `pow1/2` `associate-*r/` `pow-prod-down` `sum-log`

Counts

4 → 61

Calls

4 calls:

18.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
6.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series431.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
45.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	423	784
1	1662	727
2	5002	716

prune200.0ms

Filtered

73 candidates to 53 candidates (72.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	73	4	77

Merged error: 0.0b

Counts

77 → 4

localize15.0ms

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))
5.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite30.0ms

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))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
51.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	357	1065
1	1371	995
2	5001	983

prune224.0ms

Filtered

116 candidates to 54 candidates (46.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0.0b

Counts

120 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3)
0.1b	(cbrt (* (pow (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3) (pow (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3)))
5.3b	(- (exp x) 1.0)
5.4b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

36×	`sqrt-prod`
27×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`cube-div`
10×	`difference-of-squares`
8×	`cbrt-div` `add-log-exp`
7×	`add-cube-cbrt`
6×	`unpow-prod-down` `cube-prod` `distribute-lft-out`
5×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
4×	`frac-times` `flip3-+` `flip-+` `distribute-lft-out--`
3×	`pow-unpow`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/`
1×	`cbrt-prod` `cube-mult` `pow-to-exp` `pow-pow` `pow1/3` `unpow3` `pow-prod-down` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

11.0ms	(pow (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3)
24.0ms	(cbrt (* (pow (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3) (pow (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3)))
4.0ms	(- (exp x) 1.0)
10.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(pow (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3)
325.0ms	(cbrt (* (pow (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3) (pow (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) 3)))
14.0ms	(- (exp x) 1.0)
152.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	442	1426
1	1795	1312
2	5001	1284

prune333.0ms

Filtered

99 candidates to 62 candidates (62.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	99	4	103

Merged error: 0b

Counts

103 → 4

regimes34.0ms

Accuracy

80.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 3.3b

bsearch42.0ms

Steps

Iters	Range		Point
8	-2.7295025598725334e-05	-9.206870428625285e-10	-6.3972092504398615e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	22
1	33	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

479.0ms	12635×	body	80	nan
297.0ms	7412×	body	80	valid
247.0ms	6682×	body	80	overflowed
67.0ms	717×	body	160	valid

Details

sample328.0ms

simplify73.0ms

prune24.0ms

localize12.0ms

rewrite37.0ms

series198.0ms

simplify123.0ms

prune286.0ms

localize13.0ms

rewrite36.0ms

series431.0ms

simplify51.0ms

prune200.0ms

localize15.0ms

rewrite30.0ms

series233.0ms

simplify47.0ms

prune224.0ms

localize26.0ms

rewrite52.0ms

series725.0ms

simplify61.0ms

prune333.0ms

regimes34.0ms

bsearch42.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling