Details

Time bar (total: 6.7s)

sample59.0ms

Algorithm
intervals
Results
12.0ms124×body320valid
9.0ms512×pre80true
8.0ms256×body80nan
6.0ms89×body160valid
2.0ms16×body640valid
1.0ms27×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: 52.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
25.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite109.0ms

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:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series277.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438854
11702750
25001735

prune238.0ms

Pruning

4 alts after pruning (4 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))
0.3b
(/ (+ 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))

rewrite193.0ms

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:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
86.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series420.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
169.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
134.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify151.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08325099
139673830
250013828

prune538.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
0.3b
(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
120×pow1
68×add-exp-log add-cbrt-cube
67×pow-prod-down
34×prod-exp cbrt-unprod
28×times-frac
25×flip3-- flip--
24×associate-/r/
20×add-sqr-sqrt associate-/l*
18×*-un-lft-identity
16×frac-times
14×add-cube-cbrt
12×cbrt-undiv div-exp
9×pow-sqr pow-prod-up
8×associate-*r/ associate-*l* associate-*l/
6×prod-diff difference-of-squares
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*r* log1p-expm1-u div-inv add-log-exp
3×pow-plus div-sub associate-/l/
2×sub-neg frac-2neg clear-num associate-/r* *-commutative distribute-lft-out--
1×pow2 distribute-rgt-neg-in sub0-neg swap-sqr sqrt-prod distribute-rgt-neg-out unswap-sqr
Counts
4 → 200
Calls
4 calls:
95.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
66.0ms
(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
48.0ms
(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
82.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
136.0ms
(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
176.0ms
(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
39.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09713659
150013032

prune589.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c))))))
0.4b
(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))))) (* (/ a 4.0) (/ 2.0 (* a c))))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
232×pow1
189×add-exp-log add-cbrt-cube
132×pow-prod-down
86×prod-exp cbrt-unprod
58×cbrt-undiv div-exp
28×times-frac
27×associate-/r/
20×associate-/l*
19×flip3-- flip--
18×pow-sqr pow-prod-up
13×frac-times
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*r/ associate-*l/
6×pow-plus
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp difference-of-squares
3×div-sub associate-/l/
2×pow2 frac-2neg swap-sqr associate-*r* associate-*l* clear-num associate-/r* *-commutative
Counts
4 → 252
Calls
4 calls:
55.0ms
(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c))))))
94.0ms
(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))))) (* (/ a 4.0) (/ 2.0 (* a c))))
78.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
79.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c))))))
138.0ms
(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))))) (* (/ a 4.0) (/ 2.0 (* a c))))
37.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
33.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012125363
150024070

prune535.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
12714

end0.0ms

sample1.7s

Algorithm
intervals
Results
366.0ms3626×body320valid
287.0ms16342×pre80true
262.0ms8342×body80nan
193.0ms2922×body160valid
70.0ms512×body640valid
31.0ms940×body80valid