Details

Time bar (total: 36.9s)

sample279.0ms

Algorithm
intervals
Results
76.0ms527×pre80true
65.0ms111×body320valid
30.0ms271×body80nan
23.0ms97×body160valid
10.0ms20×body640valid
3.0ms28×body80valid

simplify170.0ms

Calls
1 calls:
Slowest
170.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.4b

localize48.0ms

Local error

Found 4 expressions with local error:

27.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(fma c (* -4 a) (* b b))
0.0b
(sqrt (fma c (* -4 a) (* b b)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
141×add-sqr-sqrt
138×times-frac
112×*-un-lft-identity
84×add-cube-cbrt
29×sqrt-prod
28×associate-/l* difference-of-squares
18×prod-diff
16×associate-/l/
14×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×associate-/r* fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp
2×clear-num frac-2neg flip3-- div-sub flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log fma-udef
Calls
4 calls:
Slowest
39.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
9.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series438.0ms

Calls
4 calls:
Slowest
145.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
114.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
110.0ms
(sqrt (fma c (* -4 a) (* b b)))
68.0ms
(fma c (* -4 a) (* b b))

simplify15.3s

Calls
235 calls:
Slowest
474.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
432.0ms
(/ (/ (* (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)))
371.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
209.0ms
(/ (* (* (/ (- (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))
186.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune2.8s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 49.1b

localize31.0ms

Local error

Found 4 expressions with local error:

51.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.1b
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.1b
(fma c (* -4 a) (* b b))
0.1b
(fma c (* -4 a) (* b b))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
48×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
9×add-cbrt-cube add-exp-log associate-/l/
6×associate-/r*
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp fma-udef
2×clear-num frac-2neg
Calls
4 calls:
Slowest
16.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
1.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma c (* -4 a) (* b b))
0.0ms
(fma c (* -4 a) (* b b))

series1.2s

Calls
4 calls:
Slowest
664.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
418.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
77.0ms
(fma c (* -4 a) (* b b))
57.0ms
(fma c (* -4 a) (* b b))

simplify9.8s

Calls
115 calls:
Slowest
444.0ms
(/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
391.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
297.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
234.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
217.0ms
(/ (/ (* (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune1.5s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 48.9b

localize52.0ms

Local error

Found 4 expressions with local error:

51.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
51.9b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.4b
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
46368×frac-times
40492×associate-/l*
25724×add-sqr-sqrt
25511×*-un-lft-identity
25451×add-cube-cbrt
24508×cbrt-div
23208×times-frac
22803×associate-/l/
15162×associate-/r*
5114×clear-num
5054×frac-2neg
2547×div-inv
1656×associate-*l/
840×associate-*r/
236×cbrt-prod
186×associate-*l*
120×un-div-inv
86×associate-*r*
81×unswap-sqr
52×swap-sqr
6×*-commutative
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
2×pow3 rem-cbrt-cube
1×pow1/3
Calls
4 calls:
Slowest
442.0ms
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series2.0s

Calls
4 calls:
Slowest
712.0ms
(cbrt (* (* (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)) (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)))
469.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
416.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
383.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))