Details

sample52.0ms

Algorithm

intervals

Results

14.0ms	36×	body	2560	valid
10.0ms	176×	body	80	valid
7.0ms	28×	body	1280	valid
3.0ms	70×	body	80	nan
3.0ms	18×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify14.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 32.5b

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))
0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b	(- (* b b) (* 4.0 (* a c)))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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

series305.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune236.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	11	90

Merged error: 4.5b

Counts

90 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b	(- (* b b) (* 4.0 (* a c)))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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)))
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))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
78.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (45.0ms)

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

prune236.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 4.5b

Counts

108 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* 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))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

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)))
24.0ms	(* (/ (+ 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))))

series614.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* 4.0 (* a c)))
220.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
269.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify119.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (98.0ms)

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

prune349.0ms

Filtered

161 candidates to 102 candidates (63.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	160	10	170

Merged error: 4.5b

Counts

170 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b	(- (* b b) (* 4.0 (* a c)))
12.9b	(/ (* 4.0 (* a c)) (* 2.0 a))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
44.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

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

prune153.0ms

Filtered

79 candidates to 54 candidates (68.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	80	9	89

Merged error: 4.5b

Counts

89 → 9

regimes197.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 29.7b

bsearch171.0ms

Steps

Iters	Range	Point
5	2.4830732657334904e+107	7.560458574844312e+107	7.414038599441506e+107
8	-1.4157471845133372e-251	-1.0118265238578241e-254	-1.0292006029626433e-254
9	-1.269270905055957e+156	-1.2401372487940452e+151	-3.149142078055873e+153

Iters

Range

Point

2.4830732657334904e+107

7.560458574844312e+107

7.414038599441506e+107

-1.4157471845133372e-251

-1.0118265238578241e-254

-1.0292006029626433e-254

-1.269270905055957e+156

-1.2401372487940452e+151

-3.149142078055873e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	24
1	44	24

end0.0ms

sample1.4s

Algorithm

intervals

Results

331.0ms	1120×	body	2560	valid
302.0ms	5827×	body	80	valid
214.0ms	883×	body	1280	valid
141.0ms	2877×	body	80	nan
95.0ms	475×	body	640	valid
33.0ms	93×	body	5120	valid
31.0ms	216×	body	320	valid
12.0ms	120×	body	160	valid

Details

sample52.0ms

simplify14.0ms

prune3.0ms

localize11.0ms

rewrite28.0ms

series305.0ms

simplify46.0ms

prune236.0ms

localize12.0ms

rewrite32.0ms

series313.0ms

simplify55.0ms

prune236.0ms

localize15.0ms

rewrite49.0ms

series614.0ms

simplify119.0ms

prune349.0ms

localize17.0ms

rewrite23.0ms

series213.0ms

simplify56.0ms

prune153.0ms

regimes197.0ms

bsearch171.0ms

simplify1.0ms

end0.0ms

sample1.4s

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