Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	154×	body	160	valid
10.0ms	522×	pre	80	true
9.0ms	266×	body	80	nan
4.0ms	102×	body	80	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite53.0ms

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))
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674

prune194.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series447.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
179.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify111.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5002	2388

prune436.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
0.4b	(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
0.5b	(* (* b b) (* b b))
0.7b	(pow (* (* 4.0 a) c) 3)

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

130×	`pow1`
49×	`add-sqr-sqrt`
36×	`pow-prod-up`
33×	`add-exp-log` `add-cbrt-cube`
32×	`pow-prod-down`
30×	`times-frac`
29×	`*-un-lft-identity`
24×	`difference-of-squares`
22×	`pow-sqr`
21×	`add-cube-cbrt` `sqr-pow`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
13×	`pow2`
10×	`associate-/l*`
9×	`unpow-prod-down`
4×	`associate-r` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `pow-pow` `pow-exp` `associate-/r*` `rem-cube-cbrt`
2×	`flip3-+` `associate-r/` `associate-l` `associate-/r/` `-commutative` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `flip3--` `frac-2neg` `distribute-lft-in` `unpow3` `div-sub` `cube-prod` `swap-sqr` `div-exp` `clear-num` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

79.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
43.0ms	(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
12.0ms	(* (* b b) (* b b))
6.0ms	(pow (* (* 4.0 a) c) 3)

series291.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
70.0ms	(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
36.0ms	(* (* b b) (* b b))
57.0ms	(pow (* (* 4.0 a) c) 3)

simplify145.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	702	2174
1	3841	2029
2	5001	2015

prune633.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`add-log-exp`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `sqrt-prod` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`pow1`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`diff-log` `div-inv` `associate-/l*`
2×	`sub-neg` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 146

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
147.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify136.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	735	2387
1	3947	2043
2	5002	2036

prune375.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

regimes181.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	12
1	30	12
2	30	12

end0.0ms

sample1.4s

Algorithm

intervals

Results

336.0ms	4518×	body	160	valid
317.0ms	16475×	pre	80	true
303.0ms	8475×	body	80	nan
131.0ms	3482×	body	80	valid