Details

Time bar (total: 15.8s)

sample84.0ms

Algorithm
intervals
Results
40.0ms287×body80valid
14.0ms108×body80nan

simplify222.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize154.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.6s

Counts
163 → 163
Iterations

Useful iterations: 3 (2.5s)

IterNodesCost
01796238
14174208
211683343
347922690
done50002690

prune668.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize118.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
4.8b
(/ (* a c) b)
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
12×add-cube-cbrt
10×fma-def
8×add-log-exp
6×times-frac
5×pow1
4×cbrt-undiv expm1-log1p-u distribute-rgt-neg-in div-exp associate-/r* log1p-expm1-u associate-/l*
3×distribute-lft-neg-in sqrt-prod
2×frac-2neg sqrt-div prod-exp clear-num sum-log cbrt-unprod div-inv distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 90
Calls
4 calls:
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
11.0ms
(/ (* a c) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms
(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
23.0ms
(/ (* a c) b)
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
102 → 102
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01791375
14411282
215431112
done50001102

prune704.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize146.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite167.0ms

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-/r*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 89
Calls
4 calls:
68.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms
(- (* b b) (* (* 4.0 a) c))
53.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series577.0ms

Counts
4 → 12
Calls
4 calls:
280.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
78.0ms
(- (* b b) (* (* 4.0 a) c))
122.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
101 → 101
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01571641
13961523
213651304
done50011288

prune726.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize148.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (fma 2.0 (/ a (/ b c)) (* -2 b)) (* 2.0 a))
5.7b
(/ a (/ b c))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
56×*-un-lft-identity
53×add-sqr-sqrt
52×add-cube-cbrt
14×add-exp-log associate-/r* add-cbrt-cube
10×fma-def
8×add-log-exp
6×div-inv associate-/l*
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×frac-2neg sqrt-div clear-num sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp associate-/r/ flip-- cbrt-unprod flip-+
Counts
4 → 139
Calls
4 calls:
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (fma 2.0 (/ a (/ b c)) (* -2 b)) (* 2.0 a))
19.0ms
(/ a (/ b c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(/ (fma 2.0 (/ a (/ b c)) (* -2 b)) (* 2.0 a))
30.0ms
(/ a (/ b c))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
151 → 151
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02832069
16461916
220961736
done50001724

prune946.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes282.0ms

bsearch2.0ms