Details

analyze644.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample114.0ms

Algorithm

intervals

Results

28.0ms	79×	body	1280	valid
11.0ms	45×	body	640	valid
5.0ms	31×	body	320	valid
4.0ms	95×	body	80	valid
1.0ms	6×	body	160	valid

simplify482.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5131	12

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 40.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
0.0b	(pow (exp x) 2.0)
38.2b	(- (pow (exp x) 2.0) 1.0)
38.3b	(- (exp x) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
41×	`sqrt-prod`
36×	`times-frac`
26×	`difference-of-squares`
20×	`add-cube-cbrt`
14×	`distribute-lft-out--`
9×	`unpow-prod-down`
8×	`add-log-exp`
7×	`sqr-pow`
6×	`pow1`
4×	`add-exp-log` `pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `exp-prod` `flip3--` `flip--`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `associate-/r/`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `div-inv`

Counts

4 → 101

Calls

4 calls:

11.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
3.0ms	(pow (exp x) 2.0)
5.0ms	(- (pow (exp x) 2.0) 1.0)
6.0ms	(- (exp x) 1.0)

series54.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
16.0ms	(pow (exp x) 2.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	1624
1	4984	1624

prune206.0ms

Filtered

82 candidates to 113 candidates (-37.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 0.0b

Counts

114 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (sqrt 2)) x)
0.2b	(* (* (/ x (sqrt 2)) x) 3/16)
0.4b	(/ x (sqrt 2))
0.4b	(/ x (sqrt 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
23×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `add-log-exp`
3×	`associate-*l/` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 141

Calls

4 calls:

8.0ms	(* (/ x (sqrt 2)) x)
8.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
7.0ms	(/ x (sqrt 2))
4.0ms	(/ x (sqrt 2))

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ x (sqrt 2)) x)
6.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
5.0ms	(/ x (sqrt 2))
5.0ms	(/ x (sqrt 2))

simplify55.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5135	1163

prune249.0ms

Filtered

98 candidates to 153 candidates (-56.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	153	2	155

Merged error: 0.0b

Counts

155 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2)
0.0b	(+ (exp x) 1.0)
38.2b	(- (pow (exp x) 2.0) 1.0)
38.2b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
5×	`pow1` `unpow-prod-down`
4×	`add-exp-log` `pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `exp-prod` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `unpow2`
1×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

3.0ms	(pow (exp x) 2)
4.0ms	(+ (exp x) 1.0)
6.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series12.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (exp x) 2)
2.0ms	(+ (exp x) 1.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5112	578

prune133.0ms

Filtered

55 candidates to 75 candidates (-36.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Merged error: 0b

Counts

77 → 3

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (exp x) 2.0) 1.0) 3)
26.3b	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
38.2b	(- (pow (exp x) 2) (* 1.0 1.0))
38.2b	(- (pow (exp x) 2.0) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
20×	`cbrt-prod` `unpow-prod-down` `*-un-lft-identity`
19×	`difference-of-squares`
14×	`cube-prod`
10×	`add-cube-cbrt`
8×	`add-log-exp` `sqr-pow`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `unpow2` `rem-cube-cbrt`

Counts

4 → 94

Calls

4 calls:

7.0ms	(pow (- (pow (exp x) 2.0) 1.0) 3)
7.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
6.0ms	(- (pow (exp x) 2.0) 1.0)

series22.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow (- (pow (exp x) 2.0) 1.0) 3)
4.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(- (pow (exp x) 2.0) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4945	1210
1	4945	1210

prune188.0ms

Filtered

64 candidates to 106 candidates (-65.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	106	3	109

Merged error: 0b

Counts

109 → 3

regimes41.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.4b

bsearch30.0ms

Steps

Iters	Range		Point
8	-0.010362335511986289	-1.5877884991823088e-06	-7.3062666099573845e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	43
1	52	43

end0.0ms

sample3.0s

Algorithm

intervals

Results

815.0ms	2287×	body	1280	valid
368.0ms	1663×	body	640	valid
121.0ms	833×	body	320	valid
115.0ms	2847×	body	80	valid
35.0ms	370×	body	160	valid

Details

analyze644.0ms

sample114.0ms

simplify482.0ms

prune11.0ms

localize22.0ms

rewrite31.0ms

series54.0ms

simplify68.0ms

prune206.0ms

localize9.0ms

rewrite31.0ms

series22.0ms

simplify55.0ms

prune249.0ms

localize35.0ms

rewrite20.0ms

series12.0ms

simplify49.0ms

prune133.0ms

localize39.0ms

rewrite28.0ms

series22.0ms

simplify44.0ms

prune188.0ms

regimes41.0ms

bsearch30.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling