Details

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 62.826797%

Results

9.0ms	31×	body	2560	valid
9.0ms	163×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	22×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	10×	body	80	invalid
0.0ms	9×	body	80	nan
0.0ms	3×	body	160	valid

simplify13.0ms

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

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: 37.2b

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)))))
26.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (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)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

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

prune181.0ms

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: 5.8b

Counts

90 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

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

prune154.0ms

Filtered

65 candidates to 97 candidates (-49.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Merged error: 5.8b

Counts

107 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
2.7b	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.4b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
26.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
52×	`times-frac`
51×	`add-exp-log`
30×	`add-cube-cbrt` `associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`difference-of-squares`
16×	`div-exp`
13×	`distribute-lft-out`
12×	`sqrt-prod`
9×	`distribute-lft-out--`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
12.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
45.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
62.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify123.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	758	2360
1	3752	2016
2	5001	1993

prune278.0ms

Filtered

102 candidates to 161 candidates (-57.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	162	11	173

Merged error: 5.7b

Counts

173 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.0b	(- (* b b) (* 4.0 (* a c)))
13.9b	(/ (* 4.0 (* a c)) (* 2.0 a))
26.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	399	575
1	2213	498
2	5003	498

prune93.0ms

Filtered

54 candidates to 79 candidates (-46.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	80	10	90

Merged error: 5.7b

Counts

90 → 10

regimes266.0ms

Accuracy

94.8% (1.2b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 29.5b

bsearch61.0ms

Steps

Iters	Range	Point
5	3.703875216598587e+124	9.699084025794829e+124	6.220885410238159e+124
8	1.863517854338852e-268	1.2283424063058854e-264	2.8000549201992103e-266
1	-5.4791059007034924e+75	-5.0848415215816745e+75	-5.380539805923038e+75

Iters

Range

Point

3.703875216598587e+124

9.699084025794829e+124

6.220885410238159e+124

1.863517854338852e-268

1.2283424063058854e-264

2.8000549201992103e-266

-5.4791059007034924e+75

-5.0848415215816745e+75

-5.380539805923038e+75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	24
1	44	24

end0.0ms

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 62.826797%

Results

327.0ms	1069×	body	2560	valid
269.0ms	5035×	body	80	valid
223.0ms	901×	body	1280	valid
97.0ms	506×	body	640	valid
46.0ms	127×	body	5120	valid
38.0ms	247×	body	320	valid
18.0ms	366×	body	80	nan
17.0ms	319×	body	80	invalid
13.0ms	115×	body	160	valid

Details

sample2.0s

simplify13.0ms

prune4.0ms

localize12.0ms

rewrite31.0ms

series58.0ms

simplify50.0ms

prune181.0ms

localize13.0ms

rewrite33.0ms

series60.0ms

simplify59.0ms

prune154.0ms

localize16.0ms

rewrite48.0ms

series130.0ms

simplify123.0ms

prune278.0ms

localize12.0ms

rewrite26.0ms

series40.0ms

simplify57.0ms

prune93.0ms

regimes266.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling