Details

sample4.6m (40.2%)

Algorithm
56×intervals
16×halfpoints
Results
52.7s66982×body1280valid
34.7s17531×body2560valid
20.2s42033×body640valid
10.9s12945×body10240exit
9.4s93711×body80valid
6.9s20423×body320valid
5.8s63822×body80nan
2.0s10943×body160valid
1.4s47413×pre80true
544.0ms638×body1280nan
497.0ms635×body640nan
340.0ms408×body5120valid
172.0ms363×body320nan
46.0ms211×body160nan

simplify4.1m (36.0%)

series1.1m (9.8%)

Calls

395 calls:

2.0s
(- (fma (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (+ (fma (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (/ (sin eps) (* (cos eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))
1.9s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.7s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.6s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.5s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

prune1.1m (9.8%)

rewrite18.4s (2.7%)

Algorithm
124×rewrite-expression-head
Calls

395 calls:

670.0ms
(+ (+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3))) (/ 2.0 (pow x 7)))
409.0ms
(pow (* (cos x) (cos eps)) 3)
357.0ms
(* (/ (sqrt (+ (exp x) (exp (- x)))) 1) (* (/ 1 (sqrt 2.0)) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y))))
349.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))
307.0ms
(* (/ (/ 1 (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (cbrt a)))
Rules
8730×add-sqr-sqrt
8573×*-un-lft-identity
6954×times-frac
5981×add-cube-cbrt
4749×prod-diff
1622×add-exp-log
1413×sqrt-prod
1242×unpow-prod-down
1147×add-cbrt-cube
1065×difference-of-squares
785×pow1
758×distribute-lft-out--
648×add-log-exp
639×cube-prod
559×associate-*r*
542×distribute-lft-out
534×associate-*l*
480×fma-neg
479×sqr-pow prod-exp
446×div-inv
436×associate-/r/
412×associate-/l*
405×log-prod
404×cbrt-prod
402×div-exp
385×expm1-log1p-u
384×log1p-expm1-u
334×flip-- flip3--
322×exp-sum
300×associate-/r*
276×associate--r+
267×cbrt-unprod
261×distribute-rgt-neg-in
251×cbrt-undiv
236×associate-*r/
228×unswap-sqr
204×fma-def
203×flip-+ flip3-+
190×distribute-lft-neg-in
182×unpow3 cube-mult
155×log-pow
146×sqrt-pow1
145×sqrt-div
137×pow-unpow
117×pow-prod-down
113×associate-/l/
110×sub-neg
105×diff-log
102×exp-prod
98×associate-*l/
96×pow1/2
95×associate-+r+
90×frac-times
88×unpow2
82×frac-sub
78×distribute-rgt-in distribute-lft-in
72×pow-exp
71×associate--l+
70×frac-2neg clear-num
66×pow-to-exp
64×*-commutative neg-mul-1
56×1-exp
48×pow-prod-up
43×pow1/3
40×rec-exp swap-sqr
38×rem-sqrt-square tan-quot
34×sum-log
33×div-sub
29×fma-udef
28×log-div
24×pow-pow
21×+-commutative
18×pow-sqr
17×neg-sub0
16×rem-cube-cbrt associate-+l+
14×rem-log-exp
13×frac-add complex-mul-def
12×cube-div
11×associate--l-
9×exp-diff pow-flip cbrt-div
8×neg-log
7×sqrt-unprod
6×difference-cubes un-div-inv hypot-def
5×inv-pow associate-+l-
4×exp-neg pow2 *.c-commutative pow-plus distribute-frac-neg distribute-rgt-out associate--r- rem-cbrt-cube
3×rem-exp-log log1p-udef log1p-expm1 +.c-commutative expm1-log1p cos-mult distribute-rgt-out-- expm1-udef
2×distribute-lft1-in complex-add-def rem-square-sqrt cos-sum sin-mult sin-sum tan-sum
1×associate-+l+.c sin-cos-mult pow3 diff-atan sub-div diff-cos associate-+r- associate-*l*.c quot-tan frac-2neg.c diff-sin

regimes4.4s (0.6%)

Accuracy

Total 25.1b remaining (20.6%)

Threshold costs 5.1b (4.2%)

5.2b82.2%quadm (p42, negative)
3.2b0%expq3 (problem 3.4.2)
3.2b88.1%quad2p (problem 3.2.1, positive)
3.2b88.6%quad2m (problem 3.2.1, negative)
2.5b90.4%quadp (p42, positive)

localize4.0s (0.6%)

bsearch2.3s (0.3%)

end1.0ms (0.0%)