Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 25.512052%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

13.0ms	34×	body	2560	valid
9.0ms	169×	body	80	valid
6.0ms	27×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	14×	body	80	nan
1.0ms	12×	body	80	invalid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

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: 35.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
24.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

11.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune172.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 7.0b

Counts

90 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
24.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms	(- (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))))

simplify56.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	463	989
1	2033	868
2	5001	860

prune146.0ms

Filtered

64 candidates to 97 candidates (-51.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	97	10	107

Merged error: 7.0b

Counts

107 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
24.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

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

series53.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify74.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	144	505
1	524	483
2	2276	480
3	5002	477

prune207.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Merged error: 7.0b

Counts

79 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
25.7b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.7b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.7b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

15.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
28.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
27.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify230.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	363	1885
1	979	1835
2	4947	1803
3	5001	1803

prune192.0ms

Filtered

69 candidates to 101 candidates (-46.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	101	10	111

Merged error: 7.0b

Counts

111 → 10

regimes471.0ms

Accuracy

79.9% (5.7b remaining)

Error of 11.0b against oracle of 5.3b and baseline of 33.5b

bsearch74.0ms

Steps

Iters	Range		Point
7	1.0578608633919696e+41	2.8362434248328863e+42	2.785767790428005e+42
8	-2.5251096199815413e-148	-5.2278143631965466e-151	-2.497911152346715e-148

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 25.512052%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

318.0ms	1045×	body	2560	valid
274.0ms	5170×	body	80	valid
226.0ms	913×	body	1280	valid
87.0ms	445×	body	640	valid
47.0ms	116×	body	5120	valid
30.0ms	208×	body	320	valid
16.0ms	310×	body	80	invalid
16.0ms	311×	body	80	nan
10.0ms	103×	body	160	valid

Details

sample1.1s

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite27.0ms

series61.0ms

simplify45.0ms

prune172.0ms

localize14.0ms

rewrite30.0ms

series61.0ms

simplify56.0ms

prune146.0ms

localize17.0ms

rewrite15.0ms

series53.0ms

simplify74.0ms

prune207.0ms

localize15.0ms

rewrite29.0ms

series95.0ms

simplify230.0ms

prune192.0ms

regimes471.0ms

bsearch74.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling