Details

simplify5.3m (43.9%)

sample4.5m (37.2%)

Algorithm
56×intervals
16×halfpoints
Results
50.9s66914×body1280valid
34.1s17447×body2560valid
21.0s41775×body640valid
10.6s12457×body10240exit
9.2s93556×body80valid
5.5s21350×body320valid
4.4s63645×body80nan
1.9s10578×body160valid
1.2s47375×pre80true
1.1s692×body1280nan
509.0ms698×body640nan
385.0ms472×body5120valid
123.0ms368×body320nan
36.0ms192×body160nan

series56.7s (7.8%)

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))))))
1.1s
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
850.0ms
(- (sqrt (pow (pow (+ x 1.0) 1.0) (/ 1 n))) (pow x (/ (/ 1.0 n) 2)))
696.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
679.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))

prune48.6s (6.7%)

rewrite23.5s (3.2%)

Algorithm
123×rewrite-expression-head
Calls

406 calls:

818.0ms
(- (+ (/ (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)))
794.0ms
(* (/ (sqrt 2.0) 1) (+ (/ (sqrt 2.0) (pow x 5)) (/ (sqrt 2.0) (pow x 3))))
543.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* (- (* 1.0 x) (log 1.0)) (- (* (pow 1.0 2) (+ (* 1.0 x) (log 1.0))) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
505.0ms
(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
428.0ms
(- (tan (+ x eps)) (tan x))
Rules
4770×*-un-lft-identity
4672×add-sqr-sqrt
4552×times-frac
3022×add-cube-cbrt
2278×sqrt-prod
1505×add-exp-log
1138×add-cbrt-cube
950×associate-*l*
732×pow1
686×add-log-exp
644×difference-of-squares
526×unpow-prod-down
510×associate-*r*
483×distribute-lft-out--
461×associate-/r*
455×associate-/l*
422×distribute-lft-out
393×prod-exp
348×cbrt-prod
345×div-exp
243×cbrt-unprod
239×flip-- flip3--
230×sqr-pow
219×cbrt-undiv
215×associate-/r/
209×div-inv
203×cube-prod
193×log-prod
189×unswap-sqr
160×flip-+ flip3-+
128×associate-*r/
113×pow-prod-down
109×pow-unpow
107×diff-log
103×sub-neg
89×associate-*l/
85×frac-2neg clear-num
80×log-pow
79×frac-times
77×sqrt-div
72×*-commutative pow-exp
69×associate-/l/
68×distribute-rgt-neg-in
67×sqrt-pow1
64×pow-to-exp swap-sqr
61×cbrt-div
54×distribute-rgt-in distribute-lft-in
53×pow1/2
48×log-div
47×pow1/3
46×exp-prod
45×sum-log
44×1-exp
43×rec-exp
42×unpow3 cube-mult
38×unpow-prod-up
34×frac-add exp-sum
30×frac-sub
29×+-commutative
28×div-sub tan-quot
27×rem-sqrt-square
25×pow-pow
23×cube-div
22×pow-flip associate--l+
21×distribute-lft-neg-in neg-mul-1
18×neg-sub0
17×associate-+l+
15×pow-prod-up rem-log-exp
14×associate--r+
13×complex-mul-def
11×pow-sqr
10×pow-div exp-diff rem-cube-cbrt associate--l- unpow2 pow-sub
9×neg-log associate-+l-
8×inv-pow
7×e-exp-1
6×associate-+r+ sin-mult
5×un-div-inv exp-neg pow-plus rem-cbrt-cube pow2
4×distribute-neg-in distribute-frac-neg *.c-commutative
3×difference-cubes rem-exp-log distribute-rgt-out-- +.c-commutative
2×cos-sum associate-+r- sqrt-unprod complex-add-def rem-square-sqrt cos-mult tan-sum exp-to-pow sin-sum
1×sub0-neg associate-+l+.c diff-atan sin-cos-mult diff-cos unsub-neg associate-*l*.c sub-div frac-2neg.c diff-sin

regimes3.5s (0.5%)

Accuracy

Total 21.4b remaining (19.3%)

Threshold costs 6.6b (6%)

4.6b83.5%quadp (p42, positive)
3.3b86.8%quad2p (problem 3.2.1, positive)
3.1b0%expq3 (problem 3.4.2)
1.7b79%2nthrt (problem 3.4.6)
1.1b95.7%quadm (p42, negative)

localize3.4s (0.5%)

bsearch2.1s (0.3%)

end1.0ms (0.0%)