Details

Time bar (total: 6.5s)

sample70.0ms

Algorithm
intervals
Results
13.0ms305×body80nan
12.0ms116×body320valid
10.0ms561×pre80true
7.0ms99×body160valid
2.0ms17×body640valid
1.0ms24×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: 52.9b

localize11.0ms

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))
27.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite112.0ms

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)))
67.0ms
(/ (+ (- 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))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25001735

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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))
0.2b
(/ (/ (+ 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)))))

rewrite196.0ms

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:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify152.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08325099
139673830
250013828

prune529.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.1b
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×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
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 230
Calls
4 calls:
1.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
18.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
60.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
43.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
90.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
157.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
191.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify119.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07675082
131663826
250013733

prune504.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.1b
(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
28×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
16×associate-/l*
7×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv add-log-exp
3×sqrt-prod associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef
Counts
4 → 104
Calls
4 calls:
1.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
32.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
170.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
235.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))) (* 2.0 a))
278.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
05382130
123521803
250011752

prune381.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes81.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
13413
24013
34013

end0.0ms

sample1.7s

Algorithm
intervals
Results
367.0ms3590×body320valid
280.0ms15933×pre80true
266.0ms7933×body80nan
206.0ms3001×body160valid
70.0ms504×body640valid
33.0ms905×body80valid