Details

sample45.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	191×	body	80	valid
7.0ms	35×	body	1280	valid
4.0ms	115×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	3×	body	320	valid

simplify15.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite127.0ms

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:

74.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
27.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms	(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

prune538.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite99.0ms

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-/r*`
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-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 156

Calls

4 calls:

43.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
40.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	546	3279
1	2065	2181
2	5002	2098

prune321.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.8b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
62.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
59.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	375	3011
1	1273	1987
2	5001	1900

prune371.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

27.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
61.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	375	3008
1	1273	1987
2	5001	1900

prune368.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.8b

regimes343.0ms

Accuracy

84.5% (4.4b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 34.0b

bsearch102.0ms

Steps

Iters	Range		Point
9	1.7695728335377845e+74	3.738006738925262e+80	2.910803917041586e+80
8	-2.4986524154890664e-82	-7.620401823751653e-85	-2.4336717856540716e-82

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

260.0ms	1061×	body	2560	valid
228.0ms	5906×	body	80	valid
167.0ms	913×	body	1280	valid
107.0ms	2949×	body	80	nan
69.0ms	465×	body	640	valid
29.0ms	97×	body	5120	valid
21.0ms	196×	body	320	valid
9.0ms	119×	body	160	valid