Details

simplify6.5m (44.7%)

sample5.0m (34.1%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67223×body1280valid
36.5s17247×body2560valid
27.1s42743×body640valid
15.1s12792×body10240exit
12.1s94155×body80valid
8.1s20240×body320valid
6.4s63595×body80nan
2.9s10190×body160valid
2.0s47494×pre80true
827.0ms660×body1280nan
550.0ms647×body640nan
522.0ms452×body5120valid
257.0ms434×body320nan
83.0ms184×body160nan

prune2.2m (14.9%)

series31.6s (3.6%)

Calls

360 calls:

456.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
439.0ms
(- (cos (+ x eps)) (cos x))
418.0ms
(/ (* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125))) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))
390.0ms
(- (sin (+ x eps)) (sin x))
364.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite12.9s (1.5%)

Algorithm
119×rewrite-expression-head
Calls

360 calls:

613.0ms
(+ (- (exp (- (log (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
449.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
414.0ms
(+ (+ (* (* a x) (* (* a x) 1/2)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
340.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))
338.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))
Rules
4944×*-un-lft-identity
4801×times-frac
4686×add-sqr-sqrt
3114×sqrt-prod
2740×add-cube-cbrt
1283×pow1
1262×add-exp-log
1107×add-cbrt-cube
708×difference-of-squares
652×log-prod
615×add-log-exp
507×distribute-lft-out--
481×distribute-lft-out
420×associate-*l*
406×associate-/l*
374×prod-exp
352×insert-posit16
349×associate-*r*
339×pow-prod-down
323×cbrt-unprod
290×div-inv
266×swap-sqr
262×associate-/r*
238×flip3-- flip--
224×frac-sub
213×div-exp
200×associate-+r+
178×frac-times
165×cbrt-undiv
158×cbrt-prod
152×flip-+ flip3-+
151×associate-*l/
149×sqrt-div
139×associate-/l/
132×pow-prod-up
128×associate-*r/
119×sqrt-pow1
114×unswap-sqr
108×associate-+l+
98×cbrt-div
89×sub-neg
88×diff-log pow-sqr
86×associate-/r/
83×pow1/2
78×log-pow
77×*-commutative
69×frac-2neg clear-num
61×pow1/3
59×pow-plus
56×unpow-prod-down
52×pow-unpow
47×sum-log
45×log-div
42×pow2
38×difference-of-sqr-1 sin-mult
36×associate--l+
35×pow-flip
34×rem-sqrt-square
33×un-div-inv
32×sqr-pow
31×1-exp rec-exp distribute-rgt-in distribute-lft-in
30×+-commutative
29×exp-prod
27×associate--r+
25×frac-add
23×rem-log-exp
21×inv-pow
19×distribute-rgt-neg-in
17×associate--l-
16×tan-quot div-sub
12×neg-sub0
10×rem-exp-log
9×cos-mult
8×neg-log
7×pow-exp exp-to-pow pow-to-exp associate--r-
6×exp-sum distribute-neg-in
5×exp-diff sin-sum difference-of-sqr--1 exp-neg sqr-sin associate-+l-
4×distribute-lft-neg-in pow-pow distribute-rgt-out distribute-rgt1-in
3×sin-cos-mult sqrt-unprod rem-square-sqrt cos-sum
2×frac-2neg.c pow3 sub-div +.c-commutative tan-sum e-exp-1
1×quot-tan diff-atan associate-+r- sqrt-undiv neg-mul-1 diff-sin diff-cos exp-lft-cube rem-cbrt-cube

regimes4.7s (0.5%)

Accuracy

Total 26.5b remaining (18.1%)

Threshold costs 5.3b (3.6%)

5.2b81.1%quadm (p42, negative)
4.3b84.8%quad2p (problem 3.2.1, positive)
4.2b85.1%quadp (p42, positive)
3.2b88.6%quad2m (problem 3.2.1, negative)
3.1b0%expq3 (problem 3.4.2)

localize4.4s (0.5%)

bsearch2.4s (0.3%)

end1.0ms (0.0%)