Details

sample58.0ms

Algorithm

intervals

Results

16.0ms	120×	body	320	valid
9.0ms	475×	pre	80	true
7.0ms	219×	body	80	nan
6.0ms	91×	body	160	valid
1.0ms	10×	body	640	valid
1.0ms	35×	body	80	valid

simplify12.0ms

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: 51.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms	(- (* b b) (* (* 4.0 a) c))
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (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	5002	674

prune183.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
177.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify113.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5003	2388

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
35.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
106.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms	(- (* b b) (* (* 4.0 a) c))
151.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify123.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	522	1156
1	3447	949
2	5002	944

prune255.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ 1 (* (/ 2.0 4.0) (/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))))
0.3b	(/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
71×	`add-cbrt-cube`
65×	`div-exp`
59×	`prod-exp`
28×	`cbrt-undiv`
23×	`cbrt-unprod`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`rec-exp` `1-exp`
9×	`pow1`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`associate-*r/`
4×	`times-frac` `associate-/l*`
3×	`sub-neg` `flip3--` `associate-l` `associate-/r/` `flip--`
2×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `distribute-rgt-neg-in` `diff-log` `associate-l/` `sqrt-prod` `-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

41.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(/ 1 (* (/ 2.0 4.0) (/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))))
21.0ms	(/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))

series435.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
164.0ms	(/ 1 (* (/ 2.0 4.0) (/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))))
121.0ms	(/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))

simplify126.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	802	1962
1	4603	1471
2	5002	1401

prune253.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes97.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

380.0ms	3628×	body	320	valid
304.0ms	16249×	pre	80	true
280.0ms	8249×	body	80	nan
208.0ms	2984×	body	160	valid
72.0ms	506×	body	640	valid
31.0ms	882×	body	80	valid