Details

simplify5.7m (45.2%)

sample4.4m (35.0%)

Algorithm
56×intervals
16×halfpoints
Results
50.6s66710×body1280valid
37.2s17577×body2560valid
19.5s42801×body640valid
11.5s12718×body10240exit
7.6s94377×body80valid
6.2s20173×body320valid
3.9s62982×body80nan
2.4s10324×body160valid
1.2s47457×pre80true
634.0ms652×body1280nan
429.0ms452×body5120valid
410.0ms667×body640nan
118.0ms349×body320nan
35.0ms179×body160nan

prune1.1m (9.0%)

series52.4s (6.9%)

Calls

382 calls:

1.0s
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
950.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
930.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
918.0ms
(* (cbrt (/ 1 (* (sqrt 2.0) 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
885.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (pow (* (tan x) (tan eps)) (* 2 3))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite19.2s (2.5%)

Algorithm
121×rewrite-expression-head
Calls

382 calls:

947.0ms
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
564.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
457.0ms
(- (sin (+ x eps)) (sin x))
391.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
341.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
Rules
11914×*-un-lft-identity
10729×times-frac
10025×add-sqr-sqrt
9123×sqrt-prod
8311×add-cube-cbrt
5695×prod-diff
1480×distribute-lft-out
1215×add-exp-log
950×add-cbrt-cube
826×unpow-prod-down
812×pow1
800×distribute-rgt-in distribute-lft-in
643×difference-of-squares
610×add-log-exp
601×div-inv
550×associate-*l*
536×associate-/l*
482×associate-/r/
476×fma-neg
419×distribute-lft-out--
393×log-prod
379×cbrt-prod
373×associate-*r*
371×expm1-log1p-u
369×log1p-expm1-u
364×distribute-rgt-neg-in
343×associate-/r*
333×distribute-lft-neg-in
303×sqr-pow
298×prod-exp
288×sqrt-div
259×div-exp
256×flip-+ flip3-+
248×associate-+l+
230×exp-sum
226×swap-sqr
225×log-pow
217×cube-prod
197×exp-prod
195×flip-- flip3--
191×cbrt-unprod
173×cbrt-undiv
146×unswap-sqr
131×pow-prod-down
121×associate-*l/
120×pow-unpow
111×neg-mul-1
108×sqrt-pow1
104×sub-neg
99×diff-log
87×associate-*r/
79×pow1/2
75×fma-def
74×frac-times
73×frac-2neg clear-num
71×tan-quot
62×associate-/l/
61×*-commutative pow-exp
60×pow-to-exp
58×unpow3 cube-mult
54×pow-prod-up
40×pow1/3
37×rem-sqrt-square
36×cbrt-div
35×log-div
31×div-sub
29×unpow2
27×fma-udef
26×1-exp rec-exp
24×pow-sqr
22×rem-log-exp
19×sum-log frac-sub
15×exp-diff pow-pow frac-add
14×pow-flip associate--l+
13×complex-mul-def +-commutative
12×neg-sub0
11×pow-plus
9×rem-exp-log
8×pow2
7×associate--l- associate--r+
6×sqrt-unprod sqrt-undiv neg-log associate-+l-
5×inv-pow
4×cube-div un-div-inv distribute-frac-neg hypot-def *.c-commutative exp-to-pow
3×rem-cube-cbrt log1p-udef exp-neg log1p-expm1 +.c-commutative rem-square-sqrt
2×cos-sum difference-cubes expm1-log1p complex-add-def sin-mult tan-sum rem-cbrt-cube expm1-udef frac-2neg.c sin-sum
1×associate-+l+.c sin-cos-mult diff-atan diff-cos cube-unmult hypot-udef associate-*l*.c distribute-rgt-neg-out diff-sin log-rec

regimes3.9s (0.5%)

Accuracy

Total 25.9b remaining (13.4%)

Threshold costs 7.9b (4.1%)

4.5b84.3%quadp (p42, positive)
3.7b86.5%quadm (p42, negative)
3.3b55.6%expq3 (problem 3.4.2)
3.1b87.1%expax (section 3.5)
2.1b77.2%2nthrt (problem 3.4.6)

localize3.0s (0.4%)

bsearch2.6s (0.4%)

end1.0ms (0.0%)