Details

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 69.504911%

Results

15.0ms	44×	body	2560	valid
9.0ms	152×	body	80	valid
7.0ms	26×	body	1280	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
1.0ms	5×	body	160	valid

simplify10.0ms

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))))

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 → 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)))
10.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (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)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune156.0ms

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))))

rewrite42.0ms

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:

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

series125.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* 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))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	626	2580
1	2991	2341
2	5003	2328

prune270.0ms

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

localize17.0ms

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))))

rewrite24.0ms

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:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
2.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	410	626
1	2230	543
2	5001	535

prune119.0ms

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

localize15.0ms

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))))

rewrite29.0ms

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:

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

series89.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms	(- (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))))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	437	925
1	1833	796
2	5002	783

prune109.0ms

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

regimes366.0ms

Accuracy

95% (1.2b remaining)

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

bsearch130.0ms

Steps

Iters	Range	Point
9	6.998369980341823e+52	3.884464804506573e+61	3.228017031988626e+61
10	-1.98310207619125e-258	-7.853937664262267e-274	-1.409134108000268e-273
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

-1.409134108000268e-273

-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

sample3.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 69.504911%

Results

364.0ms	1077×	body	2560	valid
300.0ms	5154×	body	80	valid
239.0ms	876×	body	1280	valid
98.0ms	453×	body	640	valid
47.0ms	111×	body	5120	valid
37.0ms	232×	body	320	valid
30.0ms	480×	body	80	invalid
22.0ms	393×	body	80	nan
11.0ms	97×	body	160	valid

Details

sample1.7s

simplify10.0ms

prune4.0ms

localize12.0ms

rewrite29.0ms

series65.0ms

simplify45.0ms

prune156.0ms

localize16.0ms

rewrite42.0ms

series125.0ms

simplify99.0ms

prune270.0ms

localize17.0ms

rewrite24.0ms

series40.0ms

simplify56.0ms

prune119.0ms

localize15.0ms

rewrite29.0ms

series89.0ms

simplify49.0ms

prune109.0ms

regimes366.0ms

bsearch130.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling