Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	209×	body	80	valid
8.0ms	34×	body	2560	valid
4.0ms	22×	body	1280	valid
3.0ms	79×	body	80	nan
3.0ms	18×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 34.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

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

prune310.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

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))
40.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
158.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify129.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (101.0ms)

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

prune503.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
14.1b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	610	3042
1	3078	1945
2	5002	1857

prune354.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
166×	`div-exp`
119×	`prod-exp`
65×	`add-sqr-sqrt`
64×	`*-un-lft-identity` `1-exp`
61×	`prod-diff`
60×	`add-cube-cbrt` `add-cbrt-cube`
34×	`rec-exp` `sqrt-prod`
31×	`times-frac`
26×	`cbrt-undiv`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`cbrt-unprod`
14×	`associate-/r/`
13×	`associate-/l*`
11×	`frac-times` `fma-neg`
10×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`neg-mul-1` `associate-*l/`
5×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log` `un-div-inv` `div-inv`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 259

Calls

4 calls:

38.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1354	4924
1	5002	3462

prune402.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes259.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.3b

bsearch205.0ms

Steps

Iters	Range	Point
8	1.9559514031553493e+101	2.0413668072230428e+104	9.373511171447418e+103
9	1.0311906074547519e-259	1.091011630730822e-254	1.0417939395900796e-259
9	-2.3467190644739184e+107	-3.2019781887028674e+101	-1.7431685240570133e+102

Iters

Range

Point

1.9559514031553493e+101

2.0413668072230428e+104

9.373511171447418e+103

1.0311906074547519e-259

1.091011630730822e-254

1.0417939395900796e-259

-2.3467190644739184e+107

-3.2019781887028674e+101

-1.7431685240570133e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	33
1	51	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

263.0ms	1070×	body	2560	valid
228.0ms	5839×	body	80	valid
166.0ms	884×	body	1280	valid
102.0ms	2849×	body	80	nan
72.0ms	496×	body	640	valid
31.0ms	102×	body	5120	valid
24.0ms	220×	body	320	valid
8.0ms	103×	body	160	valid