Details

simplify5.6m (46.2%)

sample4.4m (36.4%)

Algorithm
56×intervals
16×halfpoints
Results
49.4s66599×body1280valid
34.2s17327×body2560valid
18.3s41902×body640valid
10.9s12868×body10240exit
8.5s93800×body80valid
7.8s21104×body320valid
5.1s64266×body80nan
2.5s47408×pre80true
1.8s10710×body160valid
618.0ms654×body1280nan
515.0ms674×body640nan
373.0ms510×body5120valid
117.0ms374×body320nan
39.0ms207×body160nan

prune55.0s (7.5%)

series48.7s (6.6%)

Calls

351 calls:

1.8s
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))
1.2s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
868.0ms
(+ (fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* 2.0 1))) (- (exp (- x)) 0))
766.0ms
(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
721.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite15.0s (2.0%)

Algorithm
123×rewrite-expression-head
Calls

351 calls:

543.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
426.0ms
(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (+ 1.0 (exp x)) (fma 1.0 1.0 (exp (* 2 x)))))
247.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
238.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
226.0ms
(- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0)))
Rules
9185×times-frac
8870×*-un-lft-identity
8104×add-sqr-sqrt
6599×add-cube-cbrt
3127×prod-diff
2932×sqrt-prod
1153×add-exp-log
931×add-cbrt-cube
754×associate-*l*
708×pow1
682×distribute-lft-out
636×unpow-prod-down
602×difference-of-squares
550×add-log-exp
530×div-inv
529×associate-/l*
510×cbrt-prod
492×distribute-lft-out--
437×pow-unpow
403×associate-/r*
392×fma-neg
358×associate-*r*
340×log1p-expm1-u
339×expm1-log1p-u
321×associate-/r/
295×distribute-rgt-neg-in
287×distribute-lft-neg-in
276×div-exp
249×prod-exp
248×associate-+l+
209×sqr-pow
208×cube-prod
202×flip-- flip3--
193×cbrt-undiv
177×cbrt-unprod
152×flip-+ flip3-+
144×log-prod
130×unswap-sqr
103×pow-prod-down fma-def
99×sqrt-div
98×sub-neg
97×neg-mul-1
96×sqrt-pow1
94×associate-*l/
90×diff-log
82×swap-sqr
81×log-pow
75×distribute-rgt-in distribute-lft-in
71×frac-2neg clear-num
70×associate-*r/
66×tan-quot
65×pow1/2
64×associate-/l/
60×frac-times
58×pow1/3 exp-sum
52×cbrt-div
50×*-commutative unpow2
48×unpow3 cube-mult
43×associate--l+
40×pow-exp
37×pow-to-exp
31×div-sub
30×log-div 1-exp rec-exp
28×fma-udef
27×pow-prod-up
25×frac-add
24×rem-sqrt-square pow-flip
23×pow-pow
21×pow-sqr
18×sum-log
16×exp-prod
14×+-commutative
13×complex-mul-def
11×rem-cube-cbrt associate-+r+
10×pow-div associate--r+ rem-log-exp
inv-pow pow-plus frac-sub
pow2
associate--l-
cube-div exp-diff neg-sub0
sqrt-unprod
*.c-commutative associate-+l-
sin-cos-mult +.c-commutative distribute-frac-neg sin-sum
rem-exp-log associate--r- exp-neg complex-add-def rem-square-sqrt neg-log cos-sum sin-mult tan-sum rem-cbrt-cube sqrt-undiv distribute-neg-frac exp-to-pow
associate-+l+.c difference-cubes sqrt-pow2 un-div-inv log1p-udef associate-+r- diff-atan log1p-expm1 diff-cos expm1-log1p associate-*l*.c expm1-udef frac-2neg.c diff-sin

regimes3.7s (0.5%)

Accuracy

Total 34.5b remaining (24%)

Threshold costs 5.9b (4.1%)

6.0b82.2%quadp (p42, positive)
5.9b82.7%quad2p (problem 3.2.1, positive)
5.5b77.2%quad2m (problem 3.2.1, negative)
5.5b77.2%quadm (p42, negative)
3.2b0%expq3 (problem 3.4.2)

localize3.1s (0.4%)

bsearch1.9s (0.3%)

end2.0ms (0.0%)