Details

analyze455.0ms

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

sample45.0ms

Algorithm

intervals

Results

12.0ms	34×	body	2560	valid
8.0ms	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 (1.0ms)

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

localize12.0ms

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))))

rewrite27.0ms

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:

11.0ms	(/ (- (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))))

series59.0ms

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)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

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

localize13.0ms

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))))

rewrite47.0ms

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))
16.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
44.0ms	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
60.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5030	2415

prune176.0ms

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))))

rewrite28.0ms

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:

10.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4970	1398
1	4970	1398

prune145.0ms

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

localize15.0ms

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))
18.0ms	(/ (* 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))))

series138.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* c (/ a (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
55.0ms	(/ (* 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))))

simplify35.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5398	1892

prune131.0ms

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

regimes311.0ms

Accuracy

95.4% (1.1b remaining)

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

bsearch532.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	72
1	55	72

end0.0ms

analyze455.0ms

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

sample1.2s

Algorithm

intervals

Results

326.0ms	1047×	body	2560	valid
265.0ms	5144×	body	80	valid
219.0ms	899×	body	1280	valid
93.0ms	460×	body	640	valid
40.0ms	111×	body	5120	valid
33.0ms	623×	body	80	nan
30.0ms	207×	body	320	valid
19.0ms	373×	body	80	invalid
13.0ms	132×	body	160	valid

Details

analyze455.0ms

sample45.0ms

simplify3.0ms

prune7.0ms

localize12.0ms

rewrite27.0ms

series59.0ms

simplify45.0ms

prune164.0ms

localize13.0ms

rewrite47.0ms

series133.0ms

simplify50.0ms

prune176.0ms

localize14.0ms

rewrite28.0ms

series87.0ms

simplify50.0ms

prune145.0ms

localize15.0ms

rewrite48.0ms

series138.0ms

simplify35.0ms

prune131.0ms

regimes311.0ms

bsearch532.0ms

simplify2.0ms

end0.0ms

analyze455.0ms

sample1.2s

Profiling