Details

Time bar (total: 16.8s)

sample103.0ms

Algorithm
intervals
Results
40.0ms283×body80valid
13.0ms106×body80nan

simplify252.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize181.0ms

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

rewrite114.0ms

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:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
135.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
75 → 75
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01001330
12461186
27801089
327401070
done50011066

prune463.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize160.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.8b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

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 associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
11.0ms
(/ (* a c) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
36.0ms
(/ (* a c) b)
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
86 → 86
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01731340
14581252
217401078
done50011070

prune486.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize171.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 b)))
1.3b
(* (/ a (sqrt b)) (/ c (sqrt b)))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
51×times-frac
37×*-un-lft-identity
33×add-cube-cbrt
27×sqrt-prod
22×associate-*r* associate-*l*
21×add-exp-log add-cbrt-cube
9×unswap-sqr
8×add-log-exp
7×pow1
6×cbrt-undiv div-exp
5×prod-exp cbrt-unprod
3×associate-/r* div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 126
Calls
4 calls:
177.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 b)))
75.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
45.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 b)))
55.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
112.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
138 → 138
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02792356
17962205
229101787
done50021755

prune926.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize156.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (/ a (sqrt b)) (* (cbrt c) (cbrt c)))
1.2b
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (sqrt b)) (* (cbrt c) (cbrt c))) (/ (cbrt c) (sqrt b)))) (* 2 b)))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite878.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×*-un-lft-identity
23×times-frac
22×associate-*l*
21×add-exp-log
20×add-cube-cbrt
17×add-cbrt-cube
13×sqrt-prod
10×pow1
8×add-log-exp
7×prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×pow-prod-down associate-/r* unswap-sqr
2×flip3-- sqrt-div sum-log associate-/r/ flip-- div-inv distribute-lft-out
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r* neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 98
Calls
4 calls:
58.0ms
(* (/ a (sqrt b)) (* (cbrt c) (cbrt c)))
773.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (sqrt b)) (* (cbrt c) (cbrt c))) (/ (cbrt c) (sqrt b)))) (* 2 b)))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series692.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(* (/ a (sqrt b)) (* (cbrt c) (cbrt c)))
207.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (sqrt b)) (* (cbrt c) (cbrt c))) (/ (cbrt c) (sqrt b)))) (* 2 b)))
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
110 → 110
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02662256
17492146
226901739
done50001637

prune874.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

regimes428.0ms

bsearch4.0ms