Details

Time bar (total: 15.8s)

sample116.0ms

Algorithm
intervals
Results
21.0ms43×body80valid
21.0ms163×body160valid
17.0ms267×body80nan
15.0ms523×pre80true
10.0ms50×body320valid

simplify143.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.6b

localize14.0ms

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))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite169.0ms

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:
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
96.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
57.0ms
(- (* b b) (* (* 4.0 a) c))
167.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
115.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14521588
221181361
done50011352

prune414.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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

rewrite301.0ms

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:
54.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
106.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series681.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(- (* b b) (* (* 4.0 a) c))
232.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
273.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify481.0ms

Counts
243 → 243
Iterations

Useful iterations: done (464.0ms)

IterNodesCost
033910026
18577622
done50006606

prune799.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize44.0ms

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))
0.1b
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(/ (+ 0 (* c (* 4.0 a))) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
132×add-sqr-sqrt *-un-lft-identity
124×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
9×pow1
7×associate-*r*
6×prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 285
Calls
4 calls:
58.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(- (* b b) (* (* 4.0 a) c))
142.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms
(/ (+ 0 (* c (* 4.0 a))) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(- (* b b) (* (* 4.0 a) c))
138.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
226.0ms
(/ (+ 0 (* c (* 4.0 a))) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify574.0ms

Counts
297 → 297
Iterations

Useful iterations: done (556.0ms)

IterNodesCost
036817588
1112711818
done50019508

prune686.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (- b) (* a 2.0)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0)))
0.1b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* c (* 4.0 a))) (+ (* (- b) (* a 2.0)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-*l*
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×distribute-lft-neg-out distribute-rgt-out
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×flip3-- sqrt-div associate-*l/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-mul-1 sub-neg distribute-neg-out fma-def frac-2neg fma-neg diff-log div-exp associate-*r* unsub-neg prod-diff clear-num sum-log *-commutative div-inv
Counts
4 → 107
Calls
4 calls:
20.0ms
(+ (* (- b) (* a 2.0)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0)))
90.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0))
18.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(/ (+ 0 (* c (* 4.0 a))) (+ (* (- b) (* a 2.0)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0))))

series687.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(+ (* (- b) (* a 2.0)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0)))
104.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0))
62.0ms
(- (* b b) (* (* 4.0 a) c))
358.0ms
(/ (+ 0 (* c (* 4.0 a))) (+ (* (- b) (* a 2.0)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a 2.0))))

simplify2.5s

Counts
119 → 119
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02183161
16312640
238952378
done50002376

prune961.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01929
12527
22927
33627
done3627

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.2s4892×body160valid
901.0ms8188×body80nan
725.0ms16188×pre80true
322.0ms1374×body320valid
129.0ms1734×body80valid