Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	188×	body	80	valid
8.0ms	33×	body	2560	valid
5.0ms	97×	body	80	nan
5.0ms	26×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

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:

32.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- 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:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune246.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

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:

50.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
2.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
35.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	881
1	1823	791
2	5003	771

prune246.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.3b	(* (/ 1 a) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`add-sqr-sqrt` `associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `neg-log` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 79

Calls

4 calls:

2.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(* (/ 1 a) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(* (/ 1 a) (* a c))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	416	490
1	1971	383
2	5002	371

prune231.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) (* (/ (sqrt 1) 1) c)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
1.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+` `associate-/l/` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-*l/` `sum-log` `associate-/r/` `flip--`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `frac-add` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

33.0ms	(/ (+ (* (/ 1 a) 0) (* (/ (sqrt 1) 1) c)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
2.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (+ (* (/ 1 a) 0) (* (/ (sqrt 1) 1) c)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
33.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	418	1137
1	1780	984
2	5002	918

prune267.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.5b

regimes162.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.4b

bsearch189.0ms

Steps

Iters	Range	Point
11	3.0336165705843857e+124	3.3022304128508224e+146	6.18485615157459e+127
10	-5.101983181585387e-291	-7.022503022848276e-302	-7.104724366101806e-302
7	-8.769455893714235e+71	-4.6413401405224465e+69	-2.3088264856711725e+71

Iters

Range

Point

3.0336165705843857e+124

3.3022304128508224e+146

6.18485615157459e+127

-5.101983181585387e-291

-7.022503022848276e-302

-7.104724366101806e-302

-8.769455893714235e+71

-4.6413401405224465e+69

-2.3088264856711725e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	28
1	48	28

end0.0ms

sample1.3s

Algorithm

intervals

Results

334.0ms	5757×	body	80	valid
252.0ms	1061×	body	2560	valid
181.0ms	968×	body	1280	valid
156.0ms	2883×	body	80	nan
70.0ms	459×	body	640	valid
32.0ms	103×	body	5120	valid
27.0ms	220×	body	320	valid
12.0ms	118×	body	160	valid