Details

sample71.0ms

Algorithm

intervals

Results

18.0ms	47×	body	2560	valid
12.0ms	167×	body	80	valid
10.0ms	32×	body	1280	valid
7.0ms	107×	body	80	nan
4.0ms	16×	body	640	valid
2.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize13.0ms

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))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune339.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
4.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
31.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4.0 a) c))
175.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
210.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify142.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	674	2663
1	3462	2412
2	5001	2406

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
4.6b	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
9.2b	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

609×	`times-frac`
256×	`add-sqr-sqrt`
255×	`*-un-lft-identity`
159×	`add-cube-cbrt`
154×	`add-exp-log`
117×	`associate-/l*`
94×	`div-exp`
72×	`add-cbrt-cube`
48×	`distribute-lft-out--` `difference-of-squares`
40×	`cbrt-undiv`
30×	`prod-exp`
27×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
18×	`div-inv`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `associate-/r*` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 348

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
43.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
125.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1762	6116
1	5002	5495

prune928.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
13.0b	(/ (* a c) a)
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`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`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `times-frac` `diff-log` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `distribute-lft-out--` `difference-of-squares`
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 → 146

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(/ (* a c) a)
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* a c) a)
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	504	2930
1	1997	1883
2	5002	1788

prune371.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

regimes198.0ms

Accuracy

94.3% (1.4b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 29.2b

bsearch184.0ms

Steps

Iters	Range	Point
6	5.779436182351587e+124	6.964873849469576e+125	3.6708609126801744e+125
4	-1.3699538778299852e-160	-8.754296253605712e-161	-8.908835082502404e-161
7	-2.3860448187824777e+68	-1.0929352752278947e+66	-2.3202538172935113e+68

Iters

Range

Point

5.779436182351587e+124

6.964873849469576e+125

3.6708609126801744e+125

-1.3699538778299852e-160

-8.754296253605712e-161

-8.908835082502404e-161

-2.3860448187824777e+68

-1.0929352752278947e+66

-2.3202538172935113e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	29
1	49	29

end0.0ms

sample1.9s

Algorithm

intervals

Results

435.0ms	5747×	body	80	valid
428.0ms	1108×	body	2560	valid
290.0ms	926×	body	1280	valid
199.0ms	2804×	body	80	nan
128.0ms	481×	body	640	valid
48.0ms	106×	body	5120	valid
40.0ms	215×	body	320	valid
16.0ms	117×	body	160	valid