Details

simplify10.9m (54.3%)

sample4.4m (21.8%)

Algorithm
56×intervals
16×halfpoints
Results
49.0s66642×body1280valid
33.1s17576×body2560valid
17.7s42571×body640valid
10.0s93739×body80valid
9.8s13021×body10240exit
7.1s20711×body320valid
4.5s63589×body80nan
2.1s47423×pre80true
1.8s10639×body160valid
815.0ms640×body1280nan
415.0ms646×body640nan
271.0ms478×body5120valid
139.0ms366×body320nan
30.0ms172×body160nan

prune2.9m (14.2%)

series1.2m (5.7%)

Calls

378 calls:

5.6s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma eps b (fma (* 1/2 (* eps eps)) (* b b) (* (* (* eps (* eps eps)) 1/6) (* (* b b) b))))))
1.9s
(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
1.3s
(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
1.1s
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
1.1s
(- (pow (+ 1.0 x) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite23.7s (2.0%)

Algorithm
122×rewrite-expression-head
Calls

378 calls:

690.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
466.0ms
(- (/ 1.0 (+ x 1.0)) (- (/ 2.0 x) (/ 1.0 (- x 1.0))))
404.0ms
(tan (+ x eps))
402.0ms
(* (* (* eps (* eps eps)) 1/6) (* (* b b) b))
341.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
Rules
10090×times-frac
9871×*-un-lft-identity
9600×add-sqr-sqrt
7457×add-cube-cbrt
4859×prod-diff
3134×sqrt-prod
1631×pow1
1140×add-exp-log
1066×add-cbrt-cube
652×div-inv
632×distribute-lft-out
608×add-log-exp
563×distribute-lft-out--
539×fma-neg
526×associate-*r*
525×difference-of-squares
485×associate-*l*
414×pow-prod-down
381×associate-/r/
379×cbrt-prod
377×swap-sqr
367×expm1-log1p-u
365×log1p-expm1-u insert-posit16
340×associate-/l*
338×prod-exp
316×cbrt-unprod
304×associate-/r*
296×pow-prod-up
280×associate--r+
277×associate-+l+
272×flip3-- flip--
212×unswap-sqr
191×distribute-rgt-neg-in
189×flip-+ flip3-+
178×log-prod
177×distribute-lft-neg-in
169×associate-*l/
160×sqrt-div
154×div-exp
134×associate-+r+
132×cbrt-undiv unpow-prod-down
130×pow-sqr
125×pow-unpow
108×distribute-rgt-in distribute-lft-in
102×sub-neg
97×fma-def
96×diff-log
94×pow-plus
89×log-pow
88×associate-*r/
86×associate-/l/
76×*-commutative
71×frac-times
70×pow2
69×frac-2neg clear-num
61×neg-mul-1
48×pow1/3
45×fma-udef
43×sqr-pow
38×frac-add
37×frac-sub
34×sqrt-pow1
32×div-sub
30×pow1/2
29×log-div
28×rem-sqrt-square
27×tan-quot
25×exp-prod
24×sum-log
20×rem-log-exp associate--l+
19×cube-unmult cbrt-div
18×+-commutative
15×complex-mul-def
11×1-exp pow-exp pow-to-exp
10×neg-sub0 exp-sum
9×rec-exp
8×associate--l- sqrt-undiv
7×cos-mult sin-mult exp-to-pow
6×neg-log rem-exp-log
5×distribute-frac-neg pow-pow
4×associate-+r- *.c-commutative un-div-inv associate-+l- hypot-def
3×expm1-log1p expm1-udef sin-sum sin-cos-mult sqrt-unprod +.c-commutative cos-sum
2×pow-flip associate-*l*.c frac-2neg.c log1p-expm1 sub-div complex-def-add inv-pow distribute-neg-frac complex-add-def rem-square-sqrt tan-sum log1p-udef
1×quot-tan diff-atan distribute-rgt-out-- distribute-lft-in.c distribute-rgt-in.c diff-sin sqr-cos associate-+l+.c diff-cos unsub-neg associate--r- +-inverses

regimes13.6s (1.1%)

Accuracy

Total 25.5b remaining (17.7%)

Threshold costs 7.0b (4.9%)

5.2b82.2%quadp (p42, positive)
5.0b82.7%quad2m (problem 3.2.1, negative)
4.7b83.9%quad2p (problem 3.2.1, positive)
1.8b90.6%2nthrt (problem 3.4.6)
1.8b92.9%quadm (p42, negative)

localize9.6s (0.8%)

bsearch1.8s (0.1%)

end1.0ms (0.0%)