Details

sample4.5m (41.1%)

Algorithm
56×intervals
16×halfpoints
Results
49.7s67101×body1280valid
33.0s17627×body2560valid
18.3s41943×body640valid
12.2s12665×body10240exit
8.6s93568×body80valid
6.2s20624×body320valid
5.1s63583×body80nan
1.8s10562×body160valid
1.1s47456×pre80true
632.0ms677×body1280nan
456.0ms699×body640nan
309.0ms425×body5120valid
113.0ms349×body320nan
33.0ms172×body160nan

simplify3.8m (35.0%)

series1.2m (10.9%)

Calls

386 calls:

2.0s
(- (+ (fma (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin eps) 3) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (* (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))
1.8s
(cbrt (cbrt (fma x 0.3333333333333333 (* 0.0021164021164021165 (pow x 5)))))
1.5s
(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)))
1.5s
(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.5s
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

prune58.2s (9.0%)

rewrite15.9s (2.4%)

Algorithm
121×rewrite-expression-head
Calls

386 calls:

514.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
270.0ms
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (* x x))))
268.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
216.0ms
(* (sin (* 1/2 eps)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))
216.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
Rules
7069×*-un-lft-identity
6343×add-sqr-sqrt
5025×add-cube-cbrt
4868×times-frac
3752×prod-diff
1678×sqrt-prod
1085×add-exp-log
1066×unpow-prod-down
877×add-cbrt-cube
799×pow1
796×cbrt-prod
712×log-prod
668×distribute-lft-out
609×add-log-exp
464×difference-of-squares
446×fma-neg
426×distribute-lft-out--
424×associate-*r*
423×associate-*l*
405×div-inv
390×exp-sum
376×log1p-expm1-u
374×expm1-log1p-u
354×distribute-rgt-neg-in
335×sqr-pow
316×associate-/l*
311×associate-+l+
308×associate-/r*
273×distribute-lft-neg-in
272×associate-/r/
222×div-exp
217×cube-prod
214×prod-exp
183×flip-- flip3--
169×unswap-sqr
160×flip-+ flip3-+
157×cbrt-unprod
149×cbrt-undiv
140×sqrt-div
124×pow-prod-down
119×log-pow
103×sqrt-pow1
97×fma-def
95×distribute-rgt-in distribute-lft-in
92×diff-log
91×neg-mul-1
89×sub-neg
78×associate-*r/
72×pow-unpow pow1/2
67×tan-quot
65×pow1/3
64×log-div
61×associate-/l/ clear-num swap-sqr frac-2neg
56×*-commutative
51×associate-*l/
47×unpow3 cube-mult
44×frac-times
43×exp-prod
42×pow-exp
39×cbrt-div
38×rem-sqrt-square
36×fma-udef pow-to-exp
31×pow-prod-up sum-log
30×rem-log-exp
29×associate--l+
28×unpow2
25×unpow-prod-up
24×pow-sqr
22×exp-diff
21×neg-sub0
20×pow-pow 1-exp
19×frac-add +-commutative div-sub
17×rec-exp associate--r+
16×associate--l-
14×sum-cubes
13×complex-mul-def neg-log frac-sub
11×pow-plus
9×rem-cube-cbrt
8×pow2 associate-+l-
6×cube-div associate-+r+ exp-neg
5×rem-exp-log sqrt-unprod
4×*.c-commutative pow-sub un-div-inv hypot-def
3×inv-pow +.c-commutative pow-flip cos-mult sin-sum
2×cos-sum sin-cos-mult e-exp-1 log1p-udef associate--r- log1p-expm1 expm1-log1p complex-add-def rem-square-sqrt sin-mult tan-sum expm1-udef
1×associate-+l+.c sqrt-pow2 associate-+r- diff-atan diff-cos associate-*l*.c frac-2neg.c exp-to-pow diff-sin

regimes4.1s (0.6%)

Accuracy

Total 27.7b remaining (21.4%)

Threshold costs 5.9b (4.6%)

4.5b83.3%quad2p (problem 3.2.1, positive)
4.5b83.4%quadp (p42, positive)
4.0b85.9%quad2m (problem 3.2.1, negative)
4.0b86%quadm (p42, negative)
3.2b0%expq3 (problem 3.4.2)

localize3.8s (0.6%)

bsearch2.2s (0.3%)

end1.0ms (0.0%)