Details

sample86.0ms

Algorithm

intervals

Results

20.0ms	197×	body	80	valid
15.0ms	31×	body	2560	valid
11.0ms	32×	body	1280	valid
8.0ms	100×	body	80	nan
3.0ms	10×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	16
1	88	16

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: 32.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
23.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

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 → 70

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4953	1232
1	4953	1232

prune169.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 5.0b

Counts

83 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.3b	(* 3.0 (* a c))
0.8b	(- (* b b) (* 3.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite19.0ms

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 → 60

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4962	818
1	4962	818

prune117.0ms

Filtered

49 candidates to 72 candidates (-46.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	71	13	84

Merged error: 5.0b

Counts

84 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.3b	(* 3.0 (* a c))
0.8b	(- (* b b) (* 3.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite20.0ms

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 → 60

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4962	818
1	4962	818

prune121.0ms

Filtered

49 candidates to 72 candidates (-46.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	71	14	85

Merged error: 5.0b

Counts

85 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.3b	(* 3.0 (* a c))
0.8b	(- (* b b) (* 3.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite19.0ms

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 → 60

Calls

4 calls:

6.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
5.0ms	(* 3.0 (* a c))
3.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
3.0ms	(* 3.0 (* a c))
8.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4962	818
1	4962	818

prune82.0ms

Filtered

49 candidates to 72 candidates (-46.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	72	14	86

Merged error: 5.0b

Counts

86 → 14

regimes387.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 34.0b

bsearch78.0ms

Steps

Iters	Range		Point
7	5.816120864114621e-92	2.0250992463148254e-90	1.2655979455727147e-90
9	-1.6796181841493287e+154	-2.4052036288306873e+149	-1.8707267733210915e+150

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	44
1	34	44

end0.0ms

sample1.5s

Algorithm

intervals

Results

308.0ms	1068×	body	2560	valid
296.0ms	5901×	body	80	valid
207.0ms	889×	body	1280	valid
140.0ms	2906×	body	80	nan
86.0ms	457×	body	640	valid
34.0ms	99×	body	5120	valid
33.0ms	219×	body	320	valid
12.0ms	126×	body	160	valid

Details

sample86.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite27.0ms

series64.0ms

simplify57.0ms

prune169.0ms

localize10.0ms

rewrite19.0ms

series40.0ms

simplify51.0ms

prune117.0ms

localize12.0ms

rewrite20.0ms

series40.0ms

simplify40.0ms

prune121.0ms

localize11.0ms

rewrite19.0ms

series42.0ms

simplify39.0ms

prune82.0ms

regimes387.0ms

bsearch78.0ms

simplify1.0ms

end0.0ms

sample1.5s

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