Details

analyze461.0ms

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

sample41.0ms

Algorithm

intervals

Results

9.0ms	180×	body	80	valid
9.0ms	29×	body	1280	valid
6.0ms	21×	body	2560	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
0.0ms	5×	body	160	valid

simplify180.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (178.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune8.0ms

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)))

rewrite29.0ms

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))
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5899	1226

prune189.0ms

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)))

rewrite21.0ms

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))
4.0ms	(/ 1 (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
2.0ms	(/ 1 (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4889	824
1	4889	824

prune165.0ms

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))))

rewrite21.0ms

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))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
14.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4938	809
1	4938	809

prune142.0ms

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)))

rewrite35.0ms

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:

6.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(* (+ (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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
25.0ms	(* (+ (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)))

simplify62.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4973	1414
1	4973	1414

prune151.0ms

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

regimes514.0ms

Accuracy

87.7% (3.5b remaining)

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

bsearch103.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	140	75
1	140	75

end0.0ms

sample1.2s

Algorithm

intervals

Results

330.0ms	1115×	body	2560	valid
261.0ms	5136×	body	80	valid
210.0ms	887×	body	1280	valid
84.0ms	433×	body	640	valid
38.0ms	98×	body	5120	valid
35.0ms	714×	body	80	nan
31.0ms	224×	body	320	valid
19.0ms	345×	body	80	invalid
10.0ms	107×	body	160	valid

Details

analyze461.0ms

sample41.0ms

simplify180.0ms

prune8.0ms

localize11.0ms

rewrite29.0ms

series64.0ms

simplify43.0ms

prune189.0ms

localize12.0ms

rewrite21.0ms

series38.0ms

simplify65.0ms

prune165.0ms

localize11.0ms

rewrite21.0ms

series39.0ms

simplify41.0ms

prune142.0ms

localize12.0ms

rewrite35.0ms

series63.0ms

simplify62.0ms

prune151.0ms

regimes514.0ms

bsearch103.0ms

simplify2.0ms

end0.0ms

sample1.2s

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