Details

Time bar (total: 9.8s)

sample57.0ms

Algorithm
intervals
Results
11.0ms146×body160valid
11.0ms543×pre80true
10.0ms287×body80nan
7.0ms110×body80valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

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))
29.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

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)))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify723.0ms

Counts
102 → 102
Iterations

Useful iterations: done (720.0ms)

IterNodesCost
01671697
14361584
214861361
done50001351

prune269.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

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
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite113.0ms

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:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
33.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
132.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
171.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.1s

Counts
243 → 243
Iterations

Useful iterations: done (1.1s)

IterNodesCost
034510784
18528200
228786674
done50006672

prune627.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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 (- (* c (* 4.0 a)))))
17.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* c (* 4.0 a)))))))) (* 2.0 a))
0.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* c (* 4.0 a)))))))
14.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* c (* 4.0 a))))))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))
195.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* c (* 4.0 a)))))))) (* 2.0 a))
183.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* c (* 4.0 a)))))))
226.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* c (* 4.0 a))))))))

simplify839.0ms

Counts
116 → 116
Iterations

Useful iterations: done (829.0ms)

IterNodesCost
02344374
16233966
221742854
done50002851

prune481.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1
6×flip3-- flip-- div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×frac-2neg diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 280
Calls
4 calls:
1.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))
11.0ms
(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
25.0ms
(/ (/ (fma 4.0 (* a c) 0) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) a)
17.0ms
(/ (fma 4.0 (* a c) 0) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))
82.0ms
(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
231.0ms
(/ (/ (fma 4.0 (* a c) 0) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) a)
213.0ms
(/ (fma 4.0 (* a c) 0) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))

simplify900.0ms

Counts
292 → 292
Iterations

Useful iterations: done (882.0ms)

IterNodesCost
037012150
18229953
223008660
done50008658

prune774.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes173.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13333
24133
done4133

end0.0ms

sample1.4s

Algorithm
intervals
Results
324.0ms16822×pre80true
322.0ms4417×body160valid
312.0ms8822×body80nan
134.0ms3583×body80valid