Details

Time bar (total: 18.8s)

sample213.0ms

Algorithm
intervals
Results
54.0ms267×body80nan
24.0ms108×body320valid
15.0ms523×pre80true
12.0ms96×body160valid
8.0ms25×body640valid
2.0ms27×body80valid

simplify120.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize35.0ms

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))
25.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite172.0ms

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:
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series504.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
85.0ms
(- (* b b) (* (* 4.0 a) c))
170.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
141.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.7s

Counts
102 → 102
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01671697
14521588
221181361
done50011352

prune407.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

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))

rewrite329.0ms

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:
49.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
159.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series722.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(- (* b b) (* (* 4.0 a) c))
281.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
266.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify590.0ms

Counts
243 → 243
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
033910026
18577622
done50006606

prune844.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite497.0ms

Algorithm
rewrite-expression-head
Rules
338×times-frac
263×add-sqr-sqrt
252×*-un-lft-identity
151×add-cube-cbrt
107×add-exp-log
85×associate-*r*
65×add-cbrt-cube
50×distribute-lft-out-- difference-of-squares
47×div-exp
35×prod-exp
30×associate-/l*
25×cbrt-undiv distribute-rgt-neg-in sqrt-prod
21×cbrt-unprod
16×associate-/r/
11×div-inv
10×associate-/r*
9×flip3-- flip--
7×pow1 associate-*l*
6×rec-exp 1-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
2×frac-2neg clear-num
1×frac-times sub-neg pow-flip fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 339
Calls
4 calls:
57.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
301.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series585.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
59.0ms
(- (* b b) (* (* 4.0 a) c))
168.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
218.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify810.0ms

Counts
351 → 351
Iterations

Useful iterations: done (784.0ms)

IterNodesCost
044610240
114379321
done50008431

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize30.0ms

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)))))
0.3b
(/ (+ 0 (* c (* 4.0 a))) (+ (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ -1 1))))
0.3b
(/ (/ (+ 0 (* c (* 4.0 a))) (+ (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ -1 1)))) (* 2.0 a))

rewrite101.0ms

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)))))
47.0ms
(/ (+ 0 (* c (* 4.0 a))) (+ (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ -1 1))))
40.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (+ (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ -1 1)))) (* 2.0 a))

series1.1s

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* b b) (* (* 4.0 a) c))
232.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
344.0ms
(/ (+ 0 (* c (* 4.0 a))) (+ (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ -1 1))))
416.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (+ (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ -1 1)))) (* 2.0 a))

simplify3.1s

Counts
123 → 123
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02526092
17165460
245773123
done50003122

prune875.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.4b 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
02027
12925
23825
done3825

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.5s3658×body320valid
997.0ms8320×body80nan
640.0ms16320×pre80true
522.0ms2954×body160valid
198.0ms515×body640valid
58.0ms873×body80valid