Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	201×	body	80	valid
6.0ms	31×	body	1280	valid
5.0ms	21×	body	2560	valid
4.0ms	103×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	5×	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: 29.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

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:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(+ (- 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))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune226.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

25.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	521	1588
1	2522	1375
2	5002	1308

prune255.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	145	511
1	528	483
2	2232	480
3	5002	474

prune287.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
14.8b	(- (pow b 2) (pow b 2))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
18×	`difference-of-squares`
15×	`add-cube-cbrt`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `distribute-lft-out--` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sqrt-prod`
3×	`flip3--` `times-frac` `diff-log` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `associate-+l-` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
143.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
10.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms	(- (pow b 2) (pow b 2))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify157.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	505	756
1	2990	603
2	5001	569

prune278.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.4b

regimes226.0ms

Accuracy

96.5% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 34.1b

bsearch194.0ms

Steps

Iters	Range	Point
8	4.989131466200188e+139	3.737025446948691e+142	3.369053057969164e+141
9	3.1425740402568386e-306	5.4379290726615864e-300	3.2001964328628576e-306
10	-1.5405955983178716e+163	-1.402598515452623e+153	-2.3044033969831823e+153

Iters

Range

Point

4.989131466200188e+139

3.737025446948691e+142

3.369053057969164e+141

3.1425740402568386e-306

5.4379290726615864e-300

3.2001964328628576e-306

-1.5405955983178716e+163

-1.402598515452623e+153

-2.3044033969831823e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

248.0ms	1101×	body	2560	valid
222.0ms	5850×	body	80	valid
177.0ms	921×	body	1280	valid
105.0ms	2888×	body	80	nan
66.0ms	450×	body	640	valid
29.0ms	103×	body	5120	valid
26.0ms	228×	body	320	valid
9.0ms	121×	body	160	valid