Details

sample5.1m (42.9%)

Algorithm
56×intervals
16×halfpoints
Results
1.2m67113×body1280valid
39.3s17237×body2560valid
27.1s42016×body640valid
14.1s12757×body10240exit
11.0s93998×body80valid
8.6s20566×body320valid
6.7s62518×body80nan
3.2s10871×body160valid
1.8s47509×pre80true
813.0ms647×body1280nan
642.0ms708×body640nan
526.0ms438×body5120valid
171.0ms362×body320nan
54.0ms187×body160nan

simplify4.8m (40.5%)

prune52.4s (7.4%)

series39.5s (5.6%)

Calls

361 calls:

1.8s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.1s
(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x)))
527.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
492.0ms
(* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))

rewrite14.4s (2.0%)

Algorithm
115×rewrite-expression-head
Calls

361 calls:

1.1s
(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
500.0ms
(* (/ (+ (* (pow x 5) 1/60) (+ (* (* (* x x) 1/3) x) (* 2 x))) 2) (sin y))
494.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
423.0ms
(/ (tan (/ x 2)) x)
376.0ms
(/ (* x (+ 1/27 (* (* (* (* x x) x) 1/91125) (* (* x x) x)))) (+ (* 1/3 1/3) (- (* (* x (* x 1/45)) (* x (* x 1/45))) (* 1/3 (* x (* x 1/45))))))
Rules
3501×*-un-lft-identity
3357×add-sqr-sqrt
2705×times-frac
1922×add-cube-cbrt
1281×add-exp-log
1275×pow1
1176×add-cbrt-cube
963×sqrt-prod
612×add-log-exp
501×difference-of-squares
482×associate-*l*
451×associate-*r*
426×distribute-lft-out
388×prod-exp
368×pow-prod-down
367×cbrt-unprod
364×distribute-lft-out--
354×insert-posit16
324×associate-/l*
294×log-prod
230×associate-/r*
202×flip-+ flip3-+
193×div-exp
189×div-inv
181×flip3-- flip--
175×associate-*l/
170×associate-/r/
163×tan-quot
161×swap-sqr
156×cbrt-undiv
150×unswap-sqr
147×frac-times
144×cbrt-prod associate-*r/
136×sqrt-div
132×unpow-prod-down
121×sqrt-pow1
120×pow-prod-up
99×*-commutative
97×pow1/2
95×log-pow
92×diff-log
90×sub-neg
83×associate-/l/
69×sqr-pow pow-unpow
66×pow-sqr
59×exp-prod
56×frac-add
55×frac-2neg clear-num
52×pow-plus
47×difference-of-sqr-1
46×sum-log
39×associate-+r+
37×distribute-rgt-out log-div
34×cbrt-div
33×associate-+l+ pow1/3 distribute-rgt-in distribute-lft-in rem-sqrt-square
31×pow2
29×+-commutative
25×frac-sub div-sub
24×associate--l+
21×1-exp rem-log-exp
19×exp-sum
17×distribute-rgt-neg-in
16×associate--r+
14×rec-exp
12×exp-diff pow-flip
10×neg-sub0 associate--l- pow-exp pow-to-exp
8×pow-pow inv-pow
7×sqrt-unprod
6×distribute-rgt-out--
5×sin-sum associate-+r- exp-neg
4×unpow-prod-up neg-log sin-mult sub-div rem-exp-log distribute-rgt1-in
3×sqr-sin associate-+l- pow-div
2×sin-cos-mult distribute-frac-neg +.c-commutative rem-square-sqrt cos-sum tan-sum pow-sub
1×remove-posit16 diff-atan sqrt-undiv frac-2neg.c cube-unmult sub0-neg pow3 sqrt-pow2 un-div-inv diff-sin diff-cos

localize4.6s (0.7%)

regimes4.2s (0.6%)

Accuracy

Total 40.2b remaining (27.7%)

Threshold costs 5.3b (3.6%)

13.5b36.4%expax (section 3.5)
4.8b83%quadm (p42, negative)
4.6b83.4%quadp (p42, positive)
4.6b83.5%quad2p (problem 3.2.1, positive)
3.4b87.8%quad2m (problem 3.2.1, negative)

bsearch2.3s (0.3%)

end1.0ms (0.0%)