Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	38×	body	2560	valid
7.0ms	177×	body	80	valid
5.0ms	26×	body	1280	valid
4.0ms	112×	body	80	nan
3.0ms	20×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

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

prune295.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.8b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

18.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
174.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify144.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	829	5119
1	3763	3863
2	5001	3860

prune555.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.1b	(/ (* 2.0 a) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-exp-log`
63×	`add-cbrt-cube`
60×	`prod-diff`
57×	`prod-exp`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`div-exp`
34×	`sqrt-prod`
25×	`cbrt-unprod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
20×	`cbrt-undiv`
10×	`fma-neg`
8×	`pow1` `rec-exp` `1-exp` `add-log-exp`
7×	`neg-mul-1`
5×	`associate-/r/`
4×	`expm1-log1p-u` `flip3--` `times-frac` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `diff-log` `associate-r/` `clear-num` `associate-/r` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-*l/` `inv-pow`

Counts

4 → 193

Calls

4 calls:

66.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify136.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	915	3955
1	4836	2570
2	5001	2570

prune365.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

1901×	`times-frac`
856×	`add-sqr-sqrt`
855×	`*-un-lft-identity`
851×	`add-cube-cbrt`
102×	`div-inv`
87×	`add-exp-log`
70×	`div-exp`
61×	`prod-diff`
44×	`associate-/l*`
34×	`sqrt-prod`
25×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r/`
13×	`associate-/r*`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
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` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 800

Calls

4 calls:

30.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
44.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify168.0ms

Algorithm

egg-herbie

Counts

812 → 812

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	4141	11665
1	5001	9903

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

regimes143.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 30.4b

bsearch180.0ms

Steps

Iters	Range	Point
9	2.6683347110001497e+63	3.895668027475672e+69	6.6664567809045535e+68
6	-8.36501767772797e-260	-8.1135434350231975e-261	-2.3757722518657493e-260
9	-1.2294333374423815e+100	-1.4471431684397531e+91	-4.301018409236461e+98

Iters

Range

Point

2.6683347110001497e+63

3.895668027475672e+69

6.6664567809045535e+68

-8.36501767772797e-260

-8.1135434350231975e-261

-2.3757722518657493e-260

-1.2294333374423815e+100

-1.4471431684397531e+91

-4.301018409236461e+98

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	28
1	51	28
2	51	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

260.0ms	1085×	body	2560	valid
234.0ms	5822×	body	80	valid
165.0ms	888×	body	1280	valid
111.0ms	2903×	body	80	nan
73.0ms	453×	body	640	valid
28.0ms	99×	body	5120	valid
27.0ms	244×	body	320	valid
9.0ms	123×	body	160	valid