Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	204×	body	80	valid
7.0ms	29×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	104×	body	80	nan
1.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

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: 30.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

13.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune222.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 5.9b

Counts

104 → 9

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	(- (* b_2 b_2) (* a c))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

17.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	428	881
1	1823	791
2	5002	771

prune202.0ms

Filtered

101 candidates to 70 candidates (69.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	101	9	110

Merged error: 5.9b

Counts

110 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
35.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	591	2456
1	2706	2224
2	5001	2069

prune238.0ms

Filtered

189 candidates to 86 candidates (45.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	189	9	198

Merged error: 5.9b

Counts

198 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
8.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
52×	`times-frac`
51×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
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 → 141

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
154.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
195.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	700	1778
1	3170	1574
2	5001	1556

prune302.0ms

Filtered

153 candidates to 112 candidates (73.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	3	2	5
Picked	0	1	1
Done	0	3	3
Total	153	9	162

Merged error: 5.9b

Counts

162 → 9

regimes252.0ms

Accuracy

90% (2.9b remaining)

Error of 8.3b against oracle of 5.4b and baseline of 34.3b

bsearch154.0ms

Steps

Iters	Range	Point
8	4.1433580792185867e+68	2.4413096282015733e+73	2.397673767055932e+73
8	-3.835192842819844e-306	1.0596325554755924e-307	-1.5747579267209835e-308
10	-1.779583628235151e+73	-1.8574760383643568e+59	-2.9600705709081314e+66

Iters

Range

Point

4.1433580792185867e+68

2.4413096282015733e+73

2.397673767055932e+73

-3.835192842819844e-306

1.0596325554755924e-307

-1.5747579267209835e-308

-1.779583628235151e+73

-1.8574760383643568e+59

-2.9600705709081314e+66

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	32
1	45	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

251.0ms	1086×	body	2560	valid
237.0ms	5784×	body	80	valid
170.0ms	874×	body	1280	valid
117.0ms	2970×	body	80	nan
73.0ms	480×	body	640	valid
30.0ms	105×	body	5120	valid
28.0ms	231×	body	320	valid
9.0ms	126×	body	160	valid

Details

sample39.0ms

simplify8.0ms

prune2.0ms

localize9.0ms

rewrite31.0ms

series254.0ms

simplify47.0ms

prune222.0ms

localize10.0ms

rewrite35.0ms

series253.0ms

simplify55.0ms

prune202.0ms

localize10.0ms

rewrite38.0ms

series273.0ms

simplify75.0ms

prune238.0ms

localize12.0ms

rewrite49.0ms

series489.0ms

simplify108.0ms

prune302.0ms

regimes252.0ms

bsearch154.0ms

simplify2.0ms

end0.0ms

sample1.2s

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