Details

sample4.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.402832%

Guaranteed chance to sample good point: 74.783178%

Results

12.0ms	37×	body	2560	valid
9.0ms	35×	body	1280	valid
9.0ms	156×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	14×	body	80	nan
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	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: 35.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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))
6.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune170.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 6.9b

Counts

83 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
4.3b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.3b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

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) (* (* 3.0 a) c))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
53.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	634	2580
1	3161	2341
2	5001	2328

prune287.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	160	10	170

Merged error: 6.8b

Counts

170 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
4.0b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.3b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
16.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
43.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
55.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	679	1938
1	4478	1484
2	5001	1443

prune192.0ms

Filtered

81 candidates to 122 candidates (-50.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	121	11	132

Merged error: 6.8b

Counts

132 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
4.0b	(/ a (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
11.3b	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
29×	`add-cube-cbrt`
20×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
9×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`distribute-rgt-neg-in` `div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 130

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(/ a (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
10.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
25.0ms	(/ a (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
49.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	581	1944
1	2815	1719
2	5001	1702

prune216.0ms

Filtered

102 candidates to 142 candidates (-39.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	4	4	8
Picked	1	0	1
Done	1	1	2
Total	143	10	153

Merged error: 6.8b

Counts

153 → 10

regimes598.0ms

Accuracy

93.2% (1.6b remaining)

Error of 7.4b against oracle of 5.7b and baseline of 29.6b

bsearch162.0ms

Steps

Iters	Range		Point
7	850397597643135.8	2.0562449637825846e+17	2.011680736595535e+17
9	1.993411614932605e-308	2.3241379522823025e-299	2.0587072932184825e-308
9	-3.755435299728511e+89	-6.102210304194282e+82	-3.5878147758804023e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	43	26

end0.0ms

sample5.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.402832%

Guaranteed chance to sample good point: 74.783178%

Results

321.0ms	1022×	body	2560	valid
287.0ms	5148×	body	80	valid
233.0ms	893×	body	1280	valid
94.0ms	456×	body	640	valid
45.0ms	114×	body	5120	valid
37.0ms	244×	body	320	valid
18.0ms	352×	body	80	nan
17.0ms	304×	body	80	invalid
13.0ms	123×	body	160	valid

Details

sample4.2s

simplify11.0ms

prune4.0ms

localize11.0ms

rewrite30.0ms

series60.0ms

simplify47.0ms

prune170.0ms

localize16.0ms

rewrite41.0ms

series121.0ms

simplify119.0ms

prune287.0ms

localize16.0ms

rewrite41.0ms

series120.0ms

simplify128.0ms

prune192.0ms

localize14.0ms

rewrite36.0ms

series96.0ms

simplify78.0ms

prune216.0ms

regimes598.0ms

bsearch162.0ms

simplify2.0ms

end0.0ms

sample5.6s

Profiling