Details

sample864.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 20.645142%

Guaranteed chance to sample good point: 86.566935%

Results

8.0ms	168×	body	80	valid
7.0ms	30×	body	2560	valid
4.0ms	21×	body	1280	valid
3.0ms	20×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	25×	body	80	invalid
1.0ms	3×	body	5120	valid
1.0ms	14×	body	80	nan
0.0ms	3×	body	160	valid

simplify377.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune5.0ms

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: 32.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune146.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	81	11	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 4.9b

Counts

93 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	428	816
1	1923	721
2	5001	680

prune118.0ms

Filtered

71 candidates to 96 candidates (-35.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	97	10	107

Merged error: 4.9b

Counts

107 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.9b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.7b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 200

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	708	3365
1	3231	3197
2	5001	3171

prune226.0ms

Filtered

141 candidates to 212 candidates (-50.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	212	10	222

Merged error: 4.9b

Counts

222 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.7b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.9b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 485

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
24.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
49.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
46.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1525	8627
1	5002	7984

prune281.0ms

Filtered

298 candidates to 497 candidates (-66.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	495	2	497
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	497	10	507

Merged error: 4.9b

Counts

507 → 10

regimes385.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.8b

bsearch91.0ms

Steps

Iters	Range	Point
8	1.4124388747746146e+74	5.427444901772608e+77	1.0805933203349935e+77
9	4.43786811160581e-304	1.1944347498966476e-295	1.0458040096969713e-301
7	-9.631271020185472e+143	-3.7800962504590556e+141	-4.065691323206844e+141

Iters

Range

Point

1.4124388747746146e+74

5.427444901772608e+77

1.0805933203349935e+77

4.43786811160581e-304

1.1944347498966476e-295

1.0458040096969713e-301

-9.631271020185472e+143

-3.7800962504590556e+141

-4.065691323206844e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 20.645142%

Guaranteed chance to sample good point: 86.566935%

Results

277.0ms	1070×	body	2560	valid
222.0ms	5140×	body	80	valid
173.0ms	872×	body	1280	valid
72.0ms	455×	body	640	valid
35.0ms	118×	body	5120	valid
32.0ms	734×	body	80	invalid
27.0ms	227×	body	320	valid
22.0ms	537×	body	80	nan
9.0ms	118×	body	160	valid

Details

sample864.0ms

simplify377.0ms

prune5.0ms

localize12.0ms

rewrite40.0ms

series62.0ms

simplify141.0ms

prune146.0ms

localize10.0ms

rewrite31.0ms

series53.0ms

simplify52.0ms

prune118.0ms

localize11.0ms

rewrite46.0ms

series113.0ms

simplify111.0ms

prune226.0ms

localize11.0ms

rewrite83.0ms

series115.0ms

simplify105.0ms

prune281.0ms

regimes385.0ms

bsearch91.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling