Details

sample4.5m (45.1%)

Algorithm
56×intervals
16×halfpoints
Results
49.9s67398×body1280valid
33.0s16865×body2560valid
18.5s42563×body640valid
10.0s13183×body10240exit
9.3s93544×body80valid
6.6s63024×body80nan
5.6s20713×body320valid
1.9s47478×pre80true
1.9s10683×body160valid
607.0ms643×body1280nan
363.0ms643×body640nan
251.0ms442×body5120valid
97.0ms304×body320nan
37.0ms190×body160nan

simplify3.3m (33.2%)

series54.1s (9.1%)

Calls

389 calls:

2.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
1.6s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))
1.5s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))
1.1s
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
742.0ms
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))

prune48.5s (8.1%)

rewrite17.9s (3.0%)

Algorithm
121×rewrite-expression-head
Calls

389 calls:

408.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
351.0ms
(/ (- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3)) (+ (+ (pow 1.0 8) (pow (exp (* a x)) 8)) (* (exp (* (* a x) 4)) (pow 1.0 4))))
306.0ms
(log (exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
292.0ms
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))
272.0ms
(exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
Rules
4985×*-un-lft-identity
4977×add-sqr-sqrt
4715×times-frac
2890×add-cube-cbrt
1265×add-exp-log
1015×add-cbrt-cube
982×sqrt-prod
842×difference-of-squares
770×pow1
767×associate-*r*
760×unpow-prod-down
651×add-log-exp
611×distribute-lft-out
558×associate-/l*
489×distribute-lft-out--
443×associate-*l*
407×sqr-pow
354×associate-/r*
336×log-prod
325×prod-exp
301×unswap-sqr
284×cube-prod
236×div-exp
219×flip-- flip3--
209×associate-/r/
204×cbrt-unprod
200×distribute-rgt-neg-in
192×distribute-lft-neg-in
183×cbrt-undiv
181×div-inv
169×cbrt-prod
163×log-pow
145×flip-+ flip3-+
130×associate-*l/
129×unpow2
124×sqrt-div
123×exp-prod
117×pow-prod-down
100×sub-neg
99×pow-unpow
95×diff-log
87×associate-*r/
86×sqrt-pow1
84×pow-to-exp *-commutative pow-exp
78×associate-/l/
76×swap-sqr
74×associate-+r+
72×pow1/2 frac-2neg clear-num
70×tan-quot
68×frac-times
64×neg-mul-1
44×sum-log
41×log-div
37×pow1/3
34×rem-sqrt-square div-sub
30×cbrt-div
29×distribute-rgt-in rem-log-exp distribute-lft-in
28×pow-prod-up
26×+-commutative
25×frac-add
24×associate-+l+
23×pow-pow
22×frac-sub
20×pow-sqr
17×unpow3 cube-mult
16×associate--l+
13×complex-mul-def
12×difference-cubes
11×associate--r+
10×exp-diff exp-sum
9×1-exp exp-to-pow
8×pow-plus
7×pow2
6×sqrt-unprod rec-exp associate-+l-
5×rem-cube-cbrt rem-exp-log associate--l- sin-sum
4×distribute-rgt-out-- neg-sub0 *.c-commutative
3×associate-+r- inv-pow sin-cos-mult +.c-commutative pow-flip rem-square-sqrt
2×cos-sum exp-neg complex-add-def sub-div neg-log sin-mult tan-sum
1×associate-+l+.c diff-atan diff-cos associate-*l*.c rem-cbrt-cube diff-sin

regimes4.4s (0.7%)

Accuracy

Total 30.1b remaining (21.1%)

Threshold costs 6.6b (4.7%)

4.8b82.2%quadm (p42, negative)
4.2b85.2%quad2p (problem 3.2.1, positive)
4.2b85.2%quadp (p42, positive)
3.7b86.1%quad2m (problem 3.2.1, negative)
3.3b0%expq3 (problem 3.4.2)

localize3.6s (0.6%)

bsearch1.6s (0.3%)

end0.0ms (0.0%)