Details

Time bar (total: 15.5s)

sample56.0ms

Algorithm
intervals
Results
25.0ms287×body80valid
8.0ms108×body80nan

simplify288.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize110.0ms

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)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in 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 → 63
Calls
4 calls:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
117.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
75 → 75
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01001330
12461186
27801089
327401070
done50011066

prune418.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize148.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac
5×pow1
4×cbrt-undiv div-exp associate-/r* associate-/l*
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 div-sub neg-log flip-+
Counts
4 → 75
Calls
4 calls:
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
20.0ms
(/ (* a c) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
32.0ms
(/ (* a c) b)
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
87 → 87
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01781385
14841293
217951117
done50001071

prune585.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize132.0ms

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)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/r*
3×distribute-rgt-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- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 69
Calls
4 calls:
67.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series630.0ms

Counts
4 → 12
Calls
4 calls:
308.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
80.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts
81 → 81
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
01441509
13651401
212401188
349701172
done50011172

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize134.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
53×*-un-lft-identity
50×add-sqr-sqrt
49×add-cube-cbrt
14×add-exp-log associate-/r* add-cbrt-cube
8×add-log-exp
6×div-inv associate-/l*
5×pow1 cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div clear-num sum-log flip-- associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 div-sub neg-log prod-exp associate-/r/ cbrt-unprod flip-+
Counts
4 → 124
Calls
4 calls:
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(/ (- (* 2.0 (/ a (/ b c))) (* 2 b)) (* 2.0 a))
18.0ms
(/ a (/ b c))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(/ (- (* 2.0 (/ a (/ b c))) (* 2 b)) (* 2.0 a))
38.0ms
(/ a (/ b c))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
136 → 136
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02842079
16911927
223731741
done50011693

prune888.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes407.0ms

bsearch4.0ms