Details

analyze463.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms

Algorithm

intervals

Results

10.0ms	34×	body	2560	valid
9.0ms	166×	body	80	valid
7.0ms	28×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	18×	body	80	nan
1.0ms	12×	body	80	invalid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	17
1	50	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 75

Calls

4 calls:

13.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5664	1454

prune164.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 4.1b

Counts

88 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
4.9b	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
8.6b	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
31×	`*-un-lft-identity`
26×	`times-frac`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-/l*`
11×	`add-cube-cbrt`
10×	`distribute-lft-out`
8×	`add-log-exp`
6×	`associate-/r*` `associate-/r/`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3-+` `flip-+` `div-inv`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `unsub-neg` `neg-log` `flip--` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
16.0ms	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
13.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
46.0ms	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
59.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5030	2415

prune174.0ms

Filtered

81 candidates to 122 candidates (-50.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Merged error: 4.0b

Counts

132 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.1b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `unsub-neg` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

12.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4970	1398
1	4970	1398

prune146.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 3.9b

Counts

99 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
1.1b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
4.9b	(/ (* 4.0 (* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))) (* 2.0 a))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log` `add-cbrt-cube`
31×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `associate-r`
17×	`times-frac`
16×	`prod-exp` `cbrt-unprod`
15×	`add-cube-cbrt`
11×	`cbrt-undiv` `div-exp`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1`
4×	`distribute-rgt-neg-in`
3×	`associate-r/` `associate-l*` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip-+` `div-inv` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `unsub-neg` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `associate-/l/` `associate-/l*`

Counts

4 → 101

Calls

4 calls:

15.0ms	(* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
16.0ms	(/ (* 4.0 (* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
56.0ms	(/ (* 4.0 (* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))) (* 2.0 a))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5398	1892

prune134.0ms

Filtered

74 candidates to 113 candidates (-52.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Merged error: 3.9b

Counts

122 → 10

regimes505.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 30.0b

bsearch528.0ms

Steps

Iters	Range	Point
7	3.992595040800578e+135	1.8924807240822056e+137	4.90748962395899e+136
6	4.392347151905198e-281	1.8688373648975135e-280	7.34590175634683e-281
5	-1.130439217872028e+121	-5.174635489623954e+120	-1.1128077792598092e+121

Iters

Range

Point

3.992595040800578e+135

1.8924807240822056e+137

4.90748962395899e+136

4.392347151905198e-281

1.8688373648975135e-280

7.34590175634683e-281

-1.130439217872028e+121

-5.174635489623954e+120

-1.1128077792598092e+121

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	72
1	55	72

end0.0ms

analyze457.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample1.3s

Algorithm

intervals

Results

320.0ms	1047×	body	2560	valid
281.0ms	5144×	body	80	valid
231.0ms	899×	body	1280	valid
94.0ms	460×	body	640	valid
43.0ms	111×	body	5120	valid
33.0ms	623×	body	80	nan
31.0ms	207×	body	320	valid
20.0ms	373×	body	80	invalid
13.0ms	132×	body	160	valid

Details

analyze463.0ms

sample44.0ms

simplify3.0ms

prune7.0ms

localize11.0ms

rewrite30.0ms

series57.0ms

simplify47.0ms

prune164.0ms

localize15.0ms

rewrite44.0ms

series133.0ms

simplify49.0ms

prune174.0ms

localize14.0ms

rewrite31.0ms

series86.0ms

simplify48.0ms

prune146.0ms

localize17.0ms

rewrite48.0ms

series137.0ms

simplify37.0ms

prune134.0ms

regimes505.0ms

bsearch528.0ms

simplify1.0ms

end0.0ms

analyze457.0ms

sample1.3s

Profiling