Details

Time bar (total: 7.8s)

sample59.0ms

Algorithm
intervals
Results
15.0ms149×body160valid
10.0ms514×pre80true
9.0ms258×body80nan
5.0ms44×body320valid
2.0ms63×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

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))
38.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(- (* b b) (* (* 4.0 a) c))
33.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25002735

prune255.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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))
0.3b
(/ (/ (+ 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)))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u 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 → 231
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (/ (+ 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)))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify157.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08325099
139673830
250013828

prune571.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma 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)))) (fma b b (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite215.0ms

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
6×associate-/r/
5×div-inv associate-/l/
4×expm1-log1p-u unpow-prod-down flip3-- flip-- log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
1×pow2 flip3-+ div-sub swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 241
Calls
4 calls:
91.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
18.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
33.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
237.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
100.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
40.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify174.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09565111
149994590
250014590

prune753.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
0.3b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
524×add-sqr-sqrt
500×prod-diff
442×sqrt-prod
391×*-un-lft-identity
387×add-cube-cbrt
380×times-frac
252×distribute-rgt-in distribute-lft-in
195×difference-of-squares
151×distribute-rgt-neg-in
150×distribute-lft-neg-in
120×pow1
67×pow-prod-down
65×add-exp-log add-cbrt-cube
64×unpow-prod-down sqr-pow
50×neg-mul-1
37×prod-exp cbrt-unprod
22×div-inv
9×associate-*r* pow-sqr pow-prod-up
7×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u associate-*r/ associate-*l* associate-/r* log1p-expm1-u add-log-exp
3×flip3-- pow-plus flip--
2×sub-neg frac-2neg clear-num associate-/r/ *-commutative associate-/l/ distribute-lft-out--
1×pow2 div-sub swap-sqr unswap-sqr
Counts
4 → 666
Calls
4 calls:
153.0ms
(* a (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
35.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))))
18.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
29.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* a (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
184.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))))
95.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
35.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify336.0ms

Algorithm
egg-herbie
Counts
678 → 678
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0190943399
1500131708

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes120.0ms

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
04022
15322
25422
35422

end0.0ms

sample1.6s

Algorithm
intervals
Results
343.0ms4836×body160valid
300.0ms16280×pre80true
284.0ms1379×body320valid
280.0ms8280×body80nan
65.0ms1785×body80valid