Details

sample44.0ms

Algorithm

intervals

Results

11.0ms	187×	body	80	valid
9.0ms	36×	body	2560	valid
4.0ms	22×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	5×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`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 → 157

Calls

4 calls:

16.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune412.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 205

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify96.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	718	4221
1	3099	2976
2	5001	2863

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

14.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
4.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify85.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	566	3514
1	1966	2446
2	5001	2361

prune366.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
291×	`add-sqr-sqrt`
290×	`*-un-lft-identity`
190×	`add-cube-cbrt`
87×	`add-exp-log`
61×	`prod-diff`
58×	`div-exp` `sqrt-prod`
50×	`distribute-lft-out--` `difference-of-squares`
46×	`distribute-rgt-neg-in`
37×	`div-inv`
27×	`associate-/r*`
25×	`add-cbrt-cube`
21×	`distribute-lft-neg-in`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `fma-neg` `flip--`
10×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 394

Calls

4 calls:

20.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify95.0ms

Algorithm

egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1416	8436
1	5002	6798

prune606.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.0b

regimes180.0ms

Accuracy

84.6% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.7b

bsearch100.0ms

Steps

Iters	Range		Point
6	1.7071993853452014e+98	1.0593861995340862e+99	1.0479007947857462e+99
8	-2.0898868129100636e-78	-1.06178241226232e-82	-4.653701756906352e-82

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	21
1	42	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

275.0ms	1068×	body	2560	valid
243.0ms	5772×	body	80	valid
190.0ms	919×	body	1280	valid
112.0ms	2858×	body	80	nan
73.0ms	466×	body	640	valid
41.0ms	127×	body	5120	valid
27.0ms	228×	body	320	valid
10.0ms	128×	body	160	valid