Details

analyze476.0ms

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms

Algorithm

intervals

Results

10.0ms	180×	body	80	valid
9.0ms	21×	body	2560	valid
8.0ms	29×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	23×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	invalid
1.0ms	5×	body	160	valid

simplify201.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (199.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune10.0ms

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: 29.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.5b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.9b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5899	1226

prune173.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	10	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	10	82

Merged error: 5.0b

Counts

82 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ 1 (* 3.0 a))
1.9b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(/ 1 (* 3.0 a))
9.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
2.0ms	(/ 1 (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4889	824
1	4889	824

prune143.0ms

Filtered

57 candidates to 81 candidates (-42.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 5.0b

Counts

91 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.2b	(* 3.0 (* a c))
1.9b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
19.9b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
7.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
16.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4938	809
1	4938	809

prune128.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	69	12	81

Merged error: 5.0b

Counts

81 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 0.3333333333333333 a))
1.9b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `associate-r`
10×	`times-frac` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/` `prod-exp` `sum-log` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `neg-log` `-commutative` `div-inv`

Counts

4 → 79

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(* (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 0.3333333333333333 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
28.0ms	(* (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 0.3333333333333333 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4973	1414
1	4973	1414

prune136.0ms

Filtered

74 candidates to 91 candidates (-23.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	92	11	103

Merged error: 5.0b

Counts

103 → 11

regimes554.0ms

Accuracy

87.7% (3.5b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 34.0b

bsearch107.0ms

Steps

Iters	Range	Point
9	3.941840907108429e+21	5.2616773805123306e+26	1.6062084660570117e+25
11	1.421928872855589e-225	3.3149207510730995e-205	9.589091698821888e-216
8	-6.283062771645217e+155	-4.3224285963270155e+152	-2.7824475285260255e+153

Iters

Range

Point

3.941840907108429e+21

5.2616773805123306e+26

1.6062084660570117e+25

1.421928872855589e-225

3.3149207510730995e-205

9.589091698821888e-216

-6.283062771645217e+155

-4.3224285963270155e+152

-2.7824475285260255e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	140	75
1	140	75

end0.0ms

sample1.3s

Algorithm

intervals

Results

355.0ms	1115×	body	2560	valid
283.0ms	5136×	body	80	valid
223.0ms	887×	body	1280	valid
88.0ms	433×	body	640	valid
39.0ms	98×	body	5120	valid
36.0ms	714×	body	80	nan
33.0ms	224×	body	320	valid
19.0ms	345×	body	80	invalid
11.0ms	107×	body	160	valid

Details

analyze476.0ms

sample44.0ms

simplify201.0ms

prune10.0ms

localize11.0ms

rewrite32.0ms

series67.0ms

simplify47.0ms

prune173.0ms

localize12.0ms

rewrite26.0ms

series40.0ms

simplify70.0ms

prune143.0ms

localize11.0ms

rewrite22.0ms

series43.0ms

simplify50.0ms

prune128.0ms

localize12.0ms

rewrite33.0ms

series66.0ms

simplify65.0ms

prune136.0ms

regimes554.0ms

bsearch107.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling