Details

sample47.0ms

Algorithm

intervals

Results

11.0ms	189×	body	80	valid
8.0ms	33×	body	2560	valid
6.0ms	31×	body	1280	valid
4.0ms	104×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- 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)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune218.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune431.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.6b	(/ (* 2.0 a) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(- (- 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)))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune213.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
13×	`add-cube-cbrt` `associate-l`
10×	`times-frac` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`distribute-rgt-in` `frac-times` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

15.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	445	997
1	1857	906
2	5001	896

prune248.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes173.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.8b

bsearch208.0ms

Steps

Iters	Range	Point
9	1.846147638884188e+104	1.7844061428947563e+109	1.55563303224959e+106
9	-2.9188174999700146e-273	-1.0308405028667604e-278	-2.3730540219645598e-278
9	-3.3506371122085595e+158	-5.17073721832495e+150	-5.585435738628103e+150

Iters

Range

Point

1.846147638884188e+104

1.7844061428947563e+109

1.55563303224959e+106

-2.9188174999700146e-273

-1.0308405028667604e-278

-2.3730540219645598e-278

-3.3506371122085595e+158

-5.17073721832495e+150

-5.585435738628103e+150

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.3s

Algorithm

intervals

Results

281.0ms	1102×	body	2560	valid
255.0ms	5879×	body	80	valid
187.0ms	882×	body	1280	valid
127.0ms	2998×	body	80	nan
70.0ms	418×	body	640	valid
38.0ms	118×	body	5120	valid
30.0ms	236×	body	320	valid
10.0ms	124×	body	160	valid