Details

sample1.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 69.504911%

Results

14.0ms	44×	body	2560	valid
8.0ms	152×	body	80	valid
7.0ms	26×	body	1280	valid
4.0ms	5×	body	160	valid
3.0ms	14×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	17×	body	80	nan
1.0ms	14×	body	80	invalid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 36.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune148.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.2b

Counts

83 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.8b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	637	2580
1	3184	2341
2	5001	2328

prune324.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	160	8	168

Merged error: 5.2b

Counts

168 → 8

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
16.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	426	636
1	2470	542
2	5003	534

prune112.0ms

Filtered

55 candidates to 82 candidates (-49.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 5.2b

Counts

90 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

13.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	439	925
1	1879	796
2	5003	783

prune107.0ms

Filtered

61 candidates to 94 candidates (-54.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	94	7	101

Merged error: 5.2b

Counts

101 → 7

regimes365.0ms

Accuracy

95% (1.2b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 30.2b

bsearch125.0ms

Steps

Iters	Range	Point
9	6.998369980341823e+52	3.884464804506573e+61	3.228017031988626e+61
10	-1.98310207619125e-258	-7.853937664262267e-274	-7.969484042382057e-274
10	-3.2251985257956323e+159	-1.6184271943407125e+144	-2.4657553073520727e+153

Iters

Range

Point

6.998369980341823e+52

3.884464804506573e+61

3.228017031988626e+61

-1.98310207619125e-258

-7.853937664262267e-274

-7.969484042382057e-274

-3.2251985257956323e+159

-1.6184271943407125e+144

-2.4657553073520727e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 69.504911%

Results

333.0ms	1077×	body	2560	valid
293.0ms	5154×	body	80	valid
229.0ms	876×	body	1280	valid
92.0ms	453×	body	640	valid
43.0ms	111×	body	5120	valid
35.0ms	232×	body	320	valid
27.0ms	480×	body	80	invalid
21.0ms	393×	body	80	nan
10.0ms	97×	body	160	valid

Details

sample1.6s

simplify11.0ms

prune4.0ms

localize12.0ms

rewrite28.0ms

series64.0ms

simplify46.0ms

prune148.0ms

localize16.0ms

rewrite44.0ms

series124.0ms

simplify112.0ms

prune324.0ms

localize34.0ms

rewrite43.0ms

series70.0ms

simplify95.0ms

prune112.0ms

localize13.0ms

rewrite30.0ms

series86.0ms

simplify52.0ms

prune107.0ms

regimes365.0ms

bsearch125.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling