Details

Time bar (total: 14.4s)

sample103.0ms

Algorithm
intervals
Results
41.0ms186×body80valid
18.0ms41×body2560valid
8.0ms28×body1280valid
7.0ms108×body80nan
4.0ms17×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify174.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
79.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms
(- (* b b) (* 4.0 (* a c)))
26.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
90.0ms
(- (* b b) (* 4.0 (* a c)))
132.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.2s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01571750
14021650
213171474
349661459
done50001459

prune369.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.1b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 141
Calls
4 calls:
68.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
131.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
94.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
235.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
314.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
110.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
153 → 153
Iterations

Useful iterations: 2 (666.0ms)

IterNodesCost
02534579
16194057
224603753
done50003753

prune635.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize50.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×add-exp-log
44×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp difference-of-squares
11×sqrt-prod
8×cbrt-undiv cbrt-unprod distribute-lft-out--
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 139
Calls
4 calls:
57.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
182.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
111.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series1.2s

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
230.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
761.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
105.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
151 → 151
Iterations

Useful iterations: 2 (580.0ms)

IterNodesCost
02584293
16783713
226683279
done50003279

prune620.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize35.0ms

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)
14.5b
(/ (* (* 4.0 a) c) (* 2.0 a))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
10.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
50.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* 4.0 (* a c)))
123.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
108.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
79 → 79
Iterations

Useful iterations: 2 (405.0ms)

IterNodesCost
01501246
13931128
21989964
done5000964

prune267.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

regimes252.0ms

bsearch3.0ms