Details

Time bar (total: 33.4s)

sample89.0ms

Algorithm
intervals
Results
21.0ms37×body2560valid
19.0ms186×body80valid
13.0ms27×body1280valid
9.0ms92×body80nan
5.0ms14×body640valid
3.0ms9×body320valid
1.0ms2×body5120valid
1.0ms4×body160valid

simplify542.0ms

Calls
1 calls:
Slowest
542.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize32.0ms

Local error

Found 3 expressions with local error:

21.1b
(sqrt (fma c (* -4 a) (* b b)))
1.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
134×add-sqr-sqrt
107×*-un-lft-identity
81×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
8×add-cbrt-cube add-exp-log
6×fma-neg
5×div-inv add-log-exp
4×pow1
3×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- associate-/l/
Calls
3 calls:
Slowest
42.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
14.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series347.0ms

Calls
3 calls:
Slowest
134.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
107.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
106.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify13.8s

Calls
222 calls:
Slowest
434.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
222.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
220.0ms
(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))
209.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
167.0ms
(/ (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 27.0b

localize21.0ms

Local error

Found 3 expressions with local error:

21.1b
(sqrt (fma c (* -4 a) (* b b)))
1.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
34×times-frac
25×add-exp-log
22×associate-*l*
19×sqrt-prod
18×prod-diff
15×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp difference-of-squares
6×pow1 fma-neg unswap-sqr
5×add-log-exp
4×cbrt-undiv cbrt-unprod distribute-lft-out--
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×rec-exp 1-exp div-inv
1×frac-times rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative flip--
Calls
3 calls:
Slowest
51.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series332.0ms

Calls
3 calls:
Slowest
116.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
115.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
100.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify7.3s

Calls
123 calls:
Slowest
291.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
266.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- 0 (log a)))
248.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))
229.0ms
(* (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
226.0ms
(* (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (/ (* (* 1 1) 1) (* (* a a) a)))

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 27.0b

localize25.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma c (* -4 a) (* b b)))
21.1b
(sqrt (fma c (* -4 a) (* b b)))
1.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Calls
4 calls:
Slowest
13.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series477.0ms

Calls
4 calls:
Slowest
123.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
122.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
119.0ms
(sqrt (fma c (* -4 a) (* b b)))
112.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify3.8s

Calls
116 calls:
Slowest
117.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (sqrt b) (sqrt b))))
99.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))
98.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
92.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
91.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 27.0b

localize46.0ms

Local error

Found 3 expressions with local error:

21.1b
(sqrt (fma c (* -4 a) (* b b)))
6.0b
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
10113×times-frac
5325×add-sqr-sqrt
5299×*-un-lft-identity
5273×add-cube-cbrt
3010×prod-diff
1230×sqrt-prod
469×div-inv
70×fma-neg
22×associate-/l*
13×distribute-lft-out--
12×difference-of-squares
8×add-cbrt-cube add-exp-log
5×add-log-exp
4×pow1 distribute-rgt-out--
3×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub flip-- sub-div associate-/l/
Calls
3 calls:
Slowest
34.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
11.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series408.0ms

Calls
3 calls:
Slowest
173.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
120.0ms
(sqrt (fma c (* -4 a) (* b b)))
114.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))