Details

Time bar (total: 15.7s)

sample103.0ms

Algorithm
intervals
Results
40.0ms283×body80valid
13.0ms106×body80nan

simplify230.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize151.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
52.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
177 → 177
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02086992
14584570
212263570
done50002949

prune644.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize133.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
4.8b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
32×add-sqr-sqrt
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
9×times-frac associate-/r*
6×fma-neg add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 112
Calls
4 calls:
69.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
17.0ms
(/ (* a c) b)
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
254.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
23.0ms
(/ (* a c) b)
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
124 → 124
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02122318
15142017
218571714
done50001619

prune745.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize160.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
30×add-exp-log
23×add-cbrt-cube
22×associate-*r*
18×prod-diff
16×sqrt-prod
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×fma-neg associate-/r* add-log-exp unswap-sqr
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 150
Calls
4 calls:
72.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
89.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
51.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series613.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
87.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
303.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
162 → 162
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02963451
17893097
229492275
done50002162

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize166.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (cbrt b)) (* (/ (cbrt a) (cbrt b)) (/ c (cbrt b))))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
30×add-sqr-sqrt
21×add-cube-cbrt
19×prod-diff
16×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/r*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u difference-of-squares
2×cbrt-undiv sub-neg distribute-rgt-neg-in sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
87.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
44.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (cbrt b)) (* (/ (cbrt a) (cbrt b)) (/ c (cbrt b))))))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
281.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (cbrt b)) (* (/ (cbrt a) (cbrt b)) (/ c (cbrt b))))))))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
117 → 117
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02022960
14802657
216802268
done50002141

prune868.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

regimes282.0ms

bsearch2.0ms