Details

Time bar (total: 6.4s)

sample56.0ms

Algorithm
intervals
Results
11.0ms164×body160valid
11.0ms544×pre80true
9.0ms288×body80nan
3.0ms34×body320valid
2.0ms58×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite34.0ms

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)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674

prune194.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* 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)))))

rewrite49.0ms

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:
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(- (- 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)))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify121.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
06422664
131752400
250032388

prune435.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.5b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
31.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
11.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
12.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
230.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
94.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
44.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09935277
150014702

prune713.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
0.3b
(/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
105×*-un-lft-identity
85×add-sqr-sqrt
65×add-cube-cbrt
33×associate-/l*
24×sqrt-prod
22×add-exp-log add-cbrt-cube
20×distribute-lft-out--
19×associate-/r*
10×distribute-rgt-neg-in associate-/r/ difference-of-squares
9×cbrt-undiv div-exp
7×associate-/l/
6×div-inv
4×pow1 flip3-- frac-2neg flip3-+ sqrt-div clear-num flip-- flip-+ add-log-exp
2×prod-exp cbrt-unprod
1×div-sub
Counts
4 → 198
Calls
4 calls:
10.0ms
(/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))))) (* 2.0 a))
10.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
11.0ms
(/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))

series532.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
156.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (- (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
68.0ms
(/ (+ (pow b 2) (* 4.0 (* a c))) (sqrt (+ (* b b) (* (* 4.0 a) c))))

simplify170.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08626343
143945622
250015598

prune806.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes144.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03630
14030
24030

end0.0ms

sample1.5s

Algorithm
intervals
Results
334.0ms4870×body160valid
312.0ms16490×pre80true
280.0ms8490×body80nan
139.0ms1304×body320valid
67.0ms1826×body80valid