Details

Time bar (total: 6.2s)

sample54.0ms

Algorithm
intervals
Results
12.0ms269×body80nan
10.0ms525×pre80true
9.0ms136×body160valid
4.0ms120×body80valid

simplify12.0ms

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: 27.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
27.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite31.0ms

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)))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438854
11702750
25001735

prune253.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* 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)))))

rewrite61.0ms

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:
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
20.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
14.0ms
(/ (+ 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)))))

simplify160.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
08325099
139673830
250013828

prune554.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube associate-/l*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
4×pow1 expm1-log1p-u flip3-+ associate-/r* flip-+ log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- fma-udef
Counts
4 → 111
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))))) (* 2.0 a))
1.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
7.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))

series733.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
232.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))))) (* 2.0 a))
177.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
274.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1)))))

simplify132.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
07023991
136143486
250013478

prune597.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))) (- b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
0.2b
(/ (/ (* 4.0 (* a c)) a) (+ (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))) (- b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (* b b) (* (* 4.0 a) c))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
41×*-un-lft-identity
24×add-log-exp
23×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube
10×sum-log
9×distribute-lft-out
8×sqrt-div associate-*l/ frac-add distribute-neg-frac
7×cbrt-undiv div-exp associate-/l*
6×flip3-- flip3-+ associate-/r/ flip-- flip-+ div-inv
5×neg-log
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u
3×associate-+l- fma-def prod-exp cbrt-unprod
2×neg-sub0 associate-+r- sub-neg fma-neg diff-log unsub-neg prod-diff
1×+-commutative associate-+l+ frac-2neg clear-num associate-/l/
Counts
4 → 131
Calls
4 calls:
24.0ms
(+ (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))) (- b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
35.0ms
(/ (/ (* 4.0 (* a c)) a) (+ (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))) (- b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))

series341.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))) (- b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
158.0ms
(/ (/ (* 4.0 (* a c)) a) (+ (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- (sqrt 1)) (sqrt 1))) (- b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1)))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(- (* b b) (* (* 4.0 a) c))

simplify124.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07943981
142843571
250013533

prune573.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes163.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14327
24327

end0.0ms

sample1.4s

Algorithm
intervals
Results
325.0ms4500×body160valid
307.0ms16533×pre80true
285.0ms8533×body80nan
126.0ms3500×body80valid