Details

simplify5.2m (44.2%)

sample4.3m (36.7%)

Algorithm
56×intervals
16×halfpoints
Results
52.7s66914×body1280valid
32.7s17447×body2560valid
19.6s41775×body640valid
10.5s12457×body10240exit
8.9s93556×body80valid
5.7s21350×body320valid
5.4s63645×body80nan
1.8s10578×body160valid
1.3s47375×pre80true
875.0ms698×body640nan
850.0ms472×body5120valid
626.0ms692×body1280nan
175.0ms368×body320nan
37.0ms192×body160nan

series56.5s (8.0%)

Calls

406 calls:

2.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* eps b) 3)) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))))
704.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
624.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
589.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
562.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

prune47.5s (6.7%)

rewrite23.2s (3.3%)

Algorithm
123×rewrite-expression-head
Calls

406 calls:

972.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))
868.0ms
(* (/ (sqrt 2.0) 1) (+ (/ (sqrt 2.0) (pow x 5)) (/ (sqrt 2.0) (pow x 3))))
607.0ms
(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
501.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
470.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
Rules
4081×*-un-lft-identity
3966×add-sqr-sqrt
3234×times-frac
2400×add-cube-cbrt
1358×add-exp-log
1152×sqrt-prod
1065×add-cbrt-cube
753×pow1
692×associate-*l*
678×add-log-exp
621×difference-of-squares
545×unpow-prod-down
454×distribute-lft-out
444×associate-/r*
442×distribute-lft-out--
439×associate-*r*
405×cbrt-prod
398×associate-/l*
355×prod-exp
265×div-exp
246×sqr-pow
242×cube-prod
226×flip-- cbrt-unprod flip3--
204×log-prod
192×associate-/r/
186×cbrt-undiv
185×unswap-sqr
183×flip-+ flip3-+
178×div-inv
132×associate-*r/
117×pow-prod-down
114×log-pow
106×pow-unpow
104×diff-log sub-neg
97×cbrt-div
95×associate-*l/
89×frac-times
81×frac-2neg clear-num
79×sqrt-div
75×pow-exp
73×*-commutative swap-sqr
69×associate-/l/
67×pow-to-exp pow1/3
62×log-div
54×distribute-rgt-in distribute-lft-in
48×sqrt-pow1
47×sum-log
46×exp-prod
44×pow1/2
43×unpow3 cube-mult
38×unpow-prod-up
36×associate--l+
34×frac-add exp-sum
33×distribute-rgt-neg-in
32×+-commutative
31×div-sub
30×frac-sub
28×rem-sqrt-square tan-quot
24×pow-pow
23×1-exp
22×rec-exp
21×cube-div distribute-lft-neg-in neg-mul-1
20×pow-prod-up
18×associate-+l+
16×pow-sqr
15×associate-+r+ rem-log-exp
14×associate--r+
13×complex-mul-def associate-+l-
10×exp-diff rem-cube-cbrt unpow2 pow-sub neg-sub0
8×associate--l-
7×e-exp-1 pow-plus distribute-frac-neg pow2
6×difference-cubes pow-flip sin-mult
5×exp-neg rem-cbrt-cube
4×inv-pow distribute-neg-in *.c-commutative
3×sub0-neg un-div-inv rem-exp-log associate-+r- distribute-rgt-out-- +.c-commutative neg-log
2×cos-sum sqrt-unprod complex-add-def rem-square-sqrt cos-mult tan-sum exp-to-pow sin-sum
1×associate-+l+.c diff-atan sin-cos-mult diff-cos unsub-neg associate-*l*.c sub-div frac-2neg.c diff-sin

localize3.3s (0.5%)

regimes3.3s (0.5%)

Accuracy

Total 19.0b remaining (17.5%)

Threshold costs 7.5b (7%)

4.6b84.2%quadp (p42, positive)
3.1b0%expq3 (problem 3.4.2)
1.7b78.9%2nthrt (problem 3.4.6)
1.1b95.7%quadm (p42, negative)
1.0b95.8%quad2m (problem 3.2.1, negative)

bsearch2.1s (0.3%)

end1.0ms (0.0%)