Details

simplify5.2m (43.9%)

sample4.4m (37.4%)

Algorithm
56×intervals
16×halfpoints
Results
53.9s66823×body1280valid
31.2s16913×body2560valid
17.7s42623×body640valid
9.7s12526×body10240exit
9.1s93843×body80valid
6.2s20586×body320valid
5.3s63900×body80nan
2.6s47359×pre80true
2.1s10767×body160valid
624.0ms649×body1280nan
469.0ms683×body640nan
318.0ms458×body5120valid
115.0ms348×body320nan
38.0ms192×body160nan

series51.3s (7.2%)

Calls

395 calls:

1.4s
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow (pow x 1.0) (/ 1 n)))
1.2s
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
675.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
660.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
616.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))

prune49.1s (6.9%)

rewrite22.7s (3.2%)

Algorithm
123×rewrite-expression-head
Calls

395 calls:

550.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (cbrt (+ x 1.0))))) (cbrt (cbrt (cbrt (+ x 1.0)))))) (cbrt x))
548.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
490.0ms
(- (sin (+ x eps)) (sin x))
488.0ms
(log (* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2))))))
464.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
7771×times-frac
6364×add-sqr-sqrt
5988×*-un-lft-identity
4082×add-cube-cbrt
1547×add-exp-log
1074×add-cbrt-cube
1007×sqrt-prod
858×difference-of-squares
852×associate-*r*
733×pow1
647×add-log-exp
590×distribute-lft-out--
583×unpow-prod-down
522×associate-/l*
488×associate-*l*
482×associate-/r*
399×distribute-lft-out div-exp
397×prod-exp
365×div-inv
298×flip-- flip3--
296×associate-/r/
272×cbrt-prod
257×unswap-sqr
231×sqr-pow
221×cbrt-undiv
213×cbrt-unprod
200×associate-*l/
194×flip-+ flip3-+
152×unpow2
145×associate-*r/
138×log-pow
133×log-prod
131×cbrt-div
125×frac-times
118×pow-exp
115×pow-to-exp sub-neg
107×diff-log
100×pow-prod-down
96×pow-unpow sqrt-pow1
94×associate-/l/
89×distribute-rgt-neg-in
88×frac-2neg clear-num
85×swap-sqr
80×exp-prod
79×cube-prod
77×*-commutative
75×sqrt-div
66×distribute-lft-neg-in
65×pow1/3
57×pow1/2
56×frac-add
54×distribute-rgt-in distribute-lft-in
39×neg-mul-1
34×div-sub pow-prod-up
33×rec-exp 1-exp
32×tan-quot
30×sum-log frac-sub
27×log-div
26×pow-sqr
25×rem-sqrt-square
22×unpow3
20×exp-sum associate--l+
19×distribute-rgt-out-- cube-mult
16×pow-pow +-commutative
15×associate--r+ neg-sub0 rem-log-exp
13×complex-mul-def
12×associate-+l+ un-div-inv
11×cube-div
9×associate--l- pow-flip
8×sub-div pow2 pow-plus
7×inv-pow distribute-frac-neg
6×exp-diff neg-log
5×associate-+l-
4×sqrt-unprod associate--r- *.c-commutative
3×rem-exp-log +.c-commutative rem-square-sqrt cos-mult
2×pow-div cos-sum rem-cube-cbrt exp-neg associate-+r+ complex-add-def sin-mult tan-sum rem-cbrt-cube sin-sum
1×sub0-neg sin-cos-mult associate-+r- associate-+l+.c distribute-lft-neg-out diff-atan diff-cos associate-*l*.c sqrt-undiv frac-2neg.c diff-sin

regimes4.0s (0.6%)

Accuracy

Total 24.2b remaining (13.8%)

Threshold costs 6.8b (3.8%)

4.7b41.9%expq3 (problem 3.4.2)
4.6b83.9%quadp (p42, positive)
3.0b87.4%expax (section 3.5)
1.7b81.1%2nthrt (problem 3.4.6)
1.2b95%quad2m (problem 3.2.1, negative)

localize3.5s (0.5%)

bsearch2.7s (0.4%)

end1.0ms (0.0%)