Details

sample5.1m (46.7%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66750×body1280valid
39.2s16915×body2560valid
27.8s42952×body640valid
13.2s12723×body10240exit
12.7s93370×body80valid
9.4s20720×body320valid
6.7s63553×body80nan
3.1s10923×body160valid
1.9s47339×pre80true
676.0ms622×body1280nan
532.0ms655×body640nan
520.0ms520×body5120valid
222.0ms358×body320nan
86.0ms187×body160nan

simplify3.6m (33.4%)

prune1.0m (9.5%)

series38.9s (6.0%)

Calls

393 calls:

1.9s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)) (* (* (* (* (* eps eps) eps) b) (* b b)) 1/6))))
488.0ms
(log (+ 1 (* (* x x) x)))
482.0ms
(* (+ 1/27 (* (* x (* x x)) (* (* x (* x x)) 1/91125))) (/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9)))
450.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
390.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite18.3s (2.8%)

Algorithm
122×rewrite-expression-head
Calls

393 calls:

875.0ms
(* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x)
604.0ms
(- (- (+ 1 (/ 1/2 n)) (- (/ 1/6 (* n n)) (log n))) 1)
544.0ms
(/ (* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x) (+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x))))))
532.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* (* (* eps b) (* eps b)) 1/2) (* eps b)) (* (* (* (* (* eps eps) eps) b) (* b b)) 1/6))))
374.0ms
(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* x (* (* 1/6 a) (* (* a x) (* a x)))))
Rules
7435×*-un-lft-identity
7413×times-frac
5528×add-sqr-sqrt
3968×add-cube-cbrt
3105×sqrt-prod
1825×add-exp-log
1618×distribute-lft-out
1466×add-cbrt-cube
1352×pow1
841×associate-*r*
720×add-log-exp
639×prod-exp
623×associate-*l*
526×div-inv
517×associate-/l*
481×difference-of-squares
471×cbrt-unprod
386×insert-posit16
368×pow-prod-down
364×div-exp
353×associate-/r*
335×distribute-lft-out--
242×associate-*l/
239×cbrt-undiv
224×log-pow
216×log-prod flip3-- flip--
214×unswap-sqr
211×swap-sqr
206×associate-/r/
202×unpow-prod-down
191×flip-+ flip3-+
129×cbrt-prod
124×frac-times
113×diff-log
110×sub-neg
106×sqrt-div exp-prod
105×sqrt-pow1 associate-*r/
101×pow1/2
100×*-commutative
99×associate-/l/
97×pow-prod-up
91×pow-flip
79×frac-2neg clear-num
78×sqr-pow
68×1-exp rec-exp
59×sum-log pow-sqr
58×pow-unpow
54×cbrt-div
51×frac-sub
50×frac-add distribute-rgt-out
42×rem-sqrt-square
39×pow-plus
38×difference-of-sqr-1
37×distribute-rgt-in distribute-lft-in log-div
33×inv-pow
31×+-commutative
30×pow2 rem-log-exp
29×associate--l+
26×pow1/3 div-sub
22×associate--r-
20×un-div-inv
18×associate--r+
17×exp-to-pow tan-quot
15×neg-sub0
14×pow-div distribute-frac-neg
13×exp-sum sin-mult distribute-rgt-neg-in
11×associate-+l+ pow-exp distribute-lft1-in pow-to-exp
10×associate--l- distribute-rgt1-in
8×pow-pow
7×exp-diff cube-prod associate-+r- unsub-neg
6×neg-log rem-exp-log
5×cos-mult associate-+r+ count-2
4×cube-unmult associate-+l-
3×sin-sum sin-cos-mult sqr-sin cos-sum
2×quot-tan sub-div exp-neg +.c-commutative tan-sum
1×remove-posit16 diff-atan rem-cube-cbrt pow3 unpow3 frac-2neg.c sum-cubes diff-sin cube-mult rem-cbrt-cube diff-cos

localize4.7s (0.7%)

regimes4.3s (0.7%)

Accuracy

Total 24.8b remaining (19.7%)

Threshold costs 5.5b (4.4%)

4.1b85.5%quadp (p42, positive)
4.1b85.6%quad2p (problem 3.2.1, positive)
3.3b0%expq3 (problem 3.4.2)
3.1b88.8%quad2m (problem 3.2.1, negative)
3.0b89.1%quadm (p42, negative)

bsearch1.2s (0.2%)

end1.0ms (0.0%)