Details

sample2.1m (55.1%)

Algorithm
56×intervals
16×halfpoints
Results
31.1s66323×body1280valid
20.1s17425×body2560valid
12.2s42039×body640valid
6.7s94005×body80valid
4.1s20637×body320valid
3.9s63065×body80nan
1.5s10916×body160valid
991.0ms12736×body80overflowed
808.0ms47526×pre80true
396.0ms621×body1280nan
306.0ms667×body640nan
247.0ms427×body5120valid
100.0ms345×body320nan
42.0ms226×body160nan

series40.5s (17.5%)

Calls

401 calls:

1.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
1.2s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))
1.1s
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))) (pow x (/ 1.0 n)))
842.0ms
(/ (* (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (* (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0)))

prune36.0s (15.5%)

simplify10.7s (4.6%)

Algorithm
194×egg-herbie

rewrite10.6s (4.6%)

Algorithm
122×rewrite-expression-head
Calls

401 calls:

2.0s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))
1.2s
(- (+ (pow (* (cos x) (cos eps)) 3) (* 3 (* (cos x) (* (pow (sin x) 2) (* (pow (sin eps) 2) (cos eps)))))) (+ (+ (pow (cos x) 3) (* 3 (* (pow (cos x) 2) (* (sin x) (* (sin eps) (pow (cos eps) 2)))))) (pow (* (sin x) (sin eps)) 3)))
314.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
215.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
187.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
Rules
9913×times-frac
9104×*-un-lft-identity
7579×add-sqr-sqrt
5177×add-cube-cbrt
4237×sqrt-prod
1496×add-exp-log
1317×distribute-lft-out
1077×cbrt-prod
1058×add-cbrt-cube
971×unpow-prod-down
929×difference-of-squares
817×distribute-lft-out--
780×add-log-exp
774×pow1
767×associate-*r*
710×associate-*l*
703×associate-/l*
545×associate-/r*
475×cube-prod
378×div-exp
351×prod-exp
329×div-inv
325×associate-/r/
306×sqr-pow
283×unswap-sqr flip3-- flip--
234×flip-+ flip3-+
220×cbrt-undiv
205×sqrt-div
201×log-prod
189×log-pow
186×cbrt-unprod
172×unpow2
160×distribute-rgt-neg-in
146×pow-unpow
139×associate-*l/
128×diff-log
123×exp-prod
118×sub-neg
111×frac-times
104×associate-/l/ pow-exp
102×cbrt-div associate-*r/
101×pow-to-exp
98×pow-prod-down
84×frac-2neg clear-num
80×sum-log
72×*-commutative sqrt-pow1
59×unpow3 frac-add cube-mult
58×pow1/2 tan-quot
57×1-exp rec-exp
56×pow1/3
47×pow-pow
46×swap-sqr
43×frac-sub
35×distribute-rgt-in distribute-lft-in
33×pow-flip
30×rem-sqrt-square +-commutative div-sub
28×cube-div
27×log-div
24×complex-mul-def pow-prod-up
23×associate--l+
21×pow-sqr rem-log-exp
20×neg-sub0
19×associate-+l+
16×neg-log
15×rem-cube-cbrt distribute-rgt-out
14×associate--l- inv-pow associate--r+
11×associate-+l-
10×pow-div distribute-lft-neg-in distribute-rgt-out-- associate-+r+ pow-plus sin-mult exp-to-pow
rem-exp-log pow2
distribute-neg-frac
cos-mult
*.c-commutative
exp-diff associate-+r-
un-div-inv sqrt-unprod +.c-commutative complex-add-def exp-sum
sqrt-pow2 exp-neg difference-of-sqr-1 unsub-neg
cos-sum difference-cubes sqr-sin associate-+l+.c sqr-cos associate-*l*.c sub-div tan-sum rem-cbrt-cube sin-sum
sub-1-cos quot-tan distribute-lft-neg-out associate--r- diff-atan distribute-neg-in sin-cos-mult diff-cos rem-square-sqrt log-rec +-inverses neg-mul-1 diff-sin

regimes3.1s (1.4%)

Accuracy

Total 22.5b remaining (11%)

Threshold costs 4.8b (2.3%)

4.4b83.5%quadp (p42, positive)
3.4b0%expq3 (problem 3.4.2)
2.9b88.7%quad2m (problem 3.2.1, negative)
1.7b83.4%2cos (problem 3.3.5)
1.6b81.3%2nthrt (problem 3.4.6)

localize1.8s (0.8%)

bsearch1.3s (0.6%)

end1.0ms (0.0%)