Details

Time bar (total: 8.1s)

sample102.0ms

Algorithm
intervals
Results
25.0ms154×body160valid
22.0ms261×body80nan
21.0ms517×pre80true
10.0ms42×body320valid
6.0ms60×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.5b

localize11.0ms

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))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

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)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms
(+ (- 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

prune251.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

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)))))

rewrite101.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- 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))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08325099
139673830
250013828

prune563.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize21.0ms

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)))) (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)))
0.6b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite220.0ms

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:
93.0ms
(/ (/ (+ 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))
62.0ms
(/ (+ 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))))))
19.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
32.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (/ (+ 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))
231.0ms
(/ (+ 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))))))
97.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
36.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify67.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09565104
150004587

prune773.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (fma b b (* (* 4.0 a) c)))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (fma b b (* (* 4.0 a) c)))))))
0.6b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
0.6b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
232×pow1
132×pow-prod-down
80×add-exp-log add-cbrt-cube
54×prod-exp cbrt-unprod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
33×add-cube-cbrt
24×sqrt-prod
18×pow-sqr pow-prod-up
16×difference-of-squares
12×associate-/l*
9×associate-/r*
8×distribute-lft-out--
6×pow-plus
4×expm1-log1p-u unpow-prod-down distribute-rgt-neg-in log1p-expm1-u associate-/l/ add-log-exp sqr-pow
2×cbrt-undiv pow2 flip3-- frac-2neg sqrt-div swap-sqr div-exp associate-*r* associate-*l* clear-num associate-/r/ *-commutative flip-- div-inv
1×flip3-+ flip-+
Counts
4 → 224
Calls
4 calls:
13.0ms
(/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (fma b b (* (* 4.0 a) c)))
16.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (fma b b (* (* 4.0 a) c)))))))
32.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
30.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (fma b b (* (* 4.0 a) c)))
235.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (fma b b (* (* 4.0 a) c)))))))
36.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
40.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify127.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
06173545
131143099
250023079

prune618.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes152.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03120
13120

end0.0ms

sample3.0s

Algorithm
intervals
Results
813.0ms4874×body160valid
724.0ms8522×body80nan
571.0ms16522×pre80true
308.0ms1295×body320valid
170.0ms1831×body80valid