Details

Time bar (total: 16.3s)

sample145.0ms

Algorithm
intervals
Results
54.0ms154×body160valid
22.0ms258×body80nan
19.0ms514×pre80true
9.0ms102×body80valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite187.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(- (* b b) (* (* 4.0 a) c))
131.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
56.0ms
(- (* b b) (* (* 4.0 a) c))
139.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
89.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01671697
14521588
221181361
done50011352

prune326.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

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

rewrite237.0ms

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:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
64.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series701.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(- (* b b) (* (* 4.0 a) c))
263.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
237.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify415.0ms

Counts
243 → 243
Iterations

Useful iterations: done (399.0ms)

IterNodesCost
033910026
18617622
done50006606

prune631.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
16×associate-/l*
7×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ fma-udef
Counts
4 → 105
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
1.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
42.0ms
(/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
403.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
226.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
432.0ms
(/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify2.3s

Counts
117 → 117
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02253857
16173557
238762714
done50002711

prune659.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite477.0ms

Algorithm
rewrite-expression-head
Rules
312×add-exp-log
142×div-exp
138×add-cbrt-cube
137×prod-exp
121×prod-diff
102×add-sqr-sqrt
100×*-un-lft-identity
96×add-cube-cbrt
62×distribute-rgt-in distribute-lft-in
61×sqrt-prod
57×cbrt-unprod
48×cbrt-undiv
40×1-exp
37×distribute-rgt-neg-in
36×distribute-lft-neg-in
33×times-frac
16×rec-exp
14×associate-/l*
12×neg-mul-1
7×associate-*r*
6×pow1 add-log-exp
5×flip3-- associate-*l* associate-/r/ flip-- div-inv
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×sub-neg
2×frac-2neg associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×fma-neg diff-log pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 327
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(/ (* 2.0 a) (* (* 4.0 a) c))
131.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
257.0ms
(* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(/ (* 2.0 a) (* (* 4.0 a) c))
241.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
176.0ms
(* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.1s

Counts
339 → 339
Iterations

Useful iterations: done (1.1s)

IterNodesCost
052818672
1178214116
done500011824

prune739.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02029
12327
done2327

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.3s16791×pre80true
1.2s8791×body80nan
707.0ms4436×body160valid
351.0ms3564×body80valid