Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	30×	body	2560	valid
7.0ms	173×	body	80	valid
7.0ms	35×	body	1280	valid
4.0ms	103×	body	80	nan
3.0ms	18×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:

35.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune256.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.2b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.8b	(- (pow b 2) (pow b 2))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
78×	`times-frac`
68×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`difference-of-squares`
27×	`associate-/l*`
22×	`unpow-prod-down`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`sqrt-prod`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`div-sub` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

184.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
168.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
144.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify176.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (149.0ms)

Iter	Nodes	Cost
0	761	2839
1	3905	2393
2	5002	2366

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
13.1b	(/ (* 4.0 (* a c)) a)
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(/ (* 4.0 (* a c)) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
45.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(/ (* 4.0 (* a c)) a)
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	344	518
1	1520	468
2	5001	450

prune206.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

20.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
46.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	346	764
1	1376	681
2	5001	678

prune197.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes143.0ms

Accuracy

95.7% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 30.2b

bsearch135.0ms

Steps

Iters	Range	Point
6	2.6216430800597077e+98	1.6496650416179864e+99	8.293479107059485e+98
9	-8.084947448317929e-241	-9.625818304957947e-248	-9.7864508816149e-248
5	-6.921878941686949e+150	-3.374237180858152e+150	-4.4767676629755074e+150

Iters

Range

Point

2.6216430800597077e+98

1.6496650416179864e+99

8.293479107059485e+98

-8.084947448317929e-241

-9.625818304957947e-248

-9.7864508816149e-248

-6.921878941686949e+150

-3.374237180858152e+150

-4.4767676629755074e+150

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

245.0ms	1041×	body	2560	valid
228.0ms	5853×	body	80	valid
170.0ms	876×	body	1280	valid
107.0ms	2872×	body	80	nan
72.0ms	489×	body	640	valid
33.0ms	117×	body	5120	valid
25.0ms	229×	body	320	valid
8.0ms	106×	body	160	valid