Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	186×	body	80	valid
8.0ms	34×	body	2560	valid
5.0ms	25×	body	1280	valid
3.0ms	88×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

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:

17.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

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

prune347.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

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:

14.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (67.0ms)

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

prune373.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

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:

15.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	566	3514
1	1966	2446
2	5001	2363

prune361.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 257

Calls

4 calls:

14.0ms	(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify112.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	782	5140
1	3327	3846
2	5002	3657

prune616.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

regimes252.0ms

Accuracy

83.6% (4.7b remaining)

Error of 10.5b against oracle of 5.8b and baseline of 34.3b

bsearch100.0ms

Steps

Iters	Range		Point
5	1.1874868645648804e+84	3.824179182553312e+84	2.4992282662840617e+84
9	-6.219842315709727e-116	-4.3103875869831393e-125	-4.4270058556435274e-117

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

270.0ms	1089×	body	2560	valid
239.0ms	5868×	body	80	valid
173.0ms	894×	body	1280	valid
105.0ms	2862×	body	80	nan
69.0ms	441×	body	640	valid
30.0ms	105×	body	5120	valid
24.0ms	212×	body	320	valid
9.0ms	116×	body	160	valid