Details

Time bar (total: 6.8s)

sample66.0ms

Algorithm
intervals
Results
17.0ms127×body320valid
9.0ms527×pre80true
9.0ms271×body80nan
6.0ms90×body160valid
2.0ms15×body640valid
1.0ms24×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219
done1219

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
24.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite119.0ms

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)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
63.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25002735
done5002735

prune246.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- 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)))))

rewrite188.0ms

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))
84.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify151.0ms

Counts
243 → 243
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
08325099
139673830
250013828
done50013828

prune536.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
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
(/ (+ 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)))))

rewrite78.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
0.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
36.0ms
(/ (/ (+ 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))
29.0ms
(/ (+ 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)))))

series754.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt 1))))
246.0ms
(/ (/ (+ 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))
283.0ms
(/ (+ 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)))))

simplify131.0ms

Counts
123 → 123
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
07023991
136143486
250013478
done50013478

prune584.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* 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)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (* 4.0 (* a c)) a)

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
46×times-frac
40×*-un-lft-identity
27×add-exp-log add-cbrt-cube
24×add-sqr-sqrt add-cube-cbrt
10×cbrt-undiv div-exp
8×distribute-lft-out associate-/l* add-log-exp
7×associate-/r* div-inv
6×prod-exp associate-/r/ cbrt-unprod
4×pow1 expm1-log1p-u flip3-- sqrt-div associate-*l/ frac-add flip-- log1p-expm1-u distribute-neg-frac
3×flip3-+ flip-+
2×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num
1×associate-/l/
Counts
4 → 123
Calls
4 calls:
231.0ms
(/ (/ (* 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)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(/ (* 4.0 (* a c)) a)

series263.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (/ (* 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)))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (* 4.0 (* a c)) a)

simplify113.0ms

Counts
135 → 135
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07003101
139082682
250022637
done50022637

prune503.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes97.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03223
13423
23423
done3423

end0.0ms

sample1.8s

Algorithm
intervals
Results
386.0ms3616×body320valid
286.0ms16274×pre80true
281.0ms8274×body80nan
213.0ms2978×body160valid
73.0ms515×body640valid
33.0ms891×body80valid