Details

simplify6.6m (46.5%)

sample5.0m (35.8%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67063×body1280valid
40.9s17671×body2560valid
28.8s41322×body640valid
13.6s12541×body10240exit
11.3s93881×body80valid
9.0s20662×body320valid
7.8s64155×body80nan
3.8s10837×body160valid
2.1s47390×pre80true
846.0ms724×body1280nan
681.0ms478×body5120valid
545.0ms689×body640nan
216.0ms388×body320nan
45.0ms169×body160nan

prune1.4m (9.9%)

series37.7s (4.5%)

Calls

357 calls:

3.2s
(log (- (* 1 1) (* (* (* x x) x) (* (* x x) x))))
978.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
870.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (+ (* 1/60 (pow x 5)) (* x (+ (* x (* 1/3 x)) 2))) (sqrt 2)) (sin y)))
684.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
550.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (- (/ (sin x) (cos x)) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))))))

rewrite17.3s (2.1%)

Algorithm
116×rewrite-expression-head
Calls

357 calls:

3.5s
(* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1))
991.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
767.0ms
(- (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))) b)
340.0ms
(- (* (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b)))) (sqrt (sqrt (+ (* (* (* -4 a) (* (cbrt c) (cbrt c))) (cbrt c)) (* b b))))) b)
301.0ms
(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))
Rules
3688×add-sqr-sqrt
3640×*-un-lft-identity
3007×times-frac
2077×add-cube-cbrt
1563×pow1
1291×add-exp-log
1144×add-cbrt-cube
789×sqrt-prod
629×difference-of-squares
606×add-log-exp
598×cbrt-prod
526×associate-*l*
455×pow-prod-down
411×distribute-lft-out
405×prod-exp
385×cbrt-unprod
375×associate-*r*
351×insert-posit16
330×distribute-lft-out--
288×associate-/l*
275×associate-/r*
239×log-prod
206×pow-prod-up
201×div-inv
188×div-exp
187×associate-/r/
183×flip-+ flip3-+
182×flip3-- flip--
168×unswap-sqr unpow-prod-down
163×swap-sqr
135×associate-*l/
134×cbrt-div
131×cbrt-undiv
122×pow-sqr
104×sqr-pow
97×*-commutative
95×sub-neg
94×sqrt-pow1
93×pow-plus
87×diff-log
85×sqrt-div
80×log-pow
68×pow-unpow
66×frac-times
65×pow1/3
64×associate-*r/
61×pow2
59×frac-2neg clear-num
56×exp-prod pow1/2
47×associate-/l/
40×sum-log distribute-rgt-in distribute-lft-in
39×log-div
33×pow-flip
30×difference-of-sqr-1
29×rem-sqrt-square
28×1-exp rec-exp
27×+-commutative
26×frac-add
25×rem-log-exp
23×difference-of-sqr--1 inv-pow
19×exp-sum associate--l+
18×tan-quot
17×associate--r+
15×distribute-rgt-neg-in
14×exp-to-pow
13×frac-sub
12×div-sub
10×associate--l- pow-exp pow-to-exp
9×associate-+l+ pow3
6×neg-sub0 exp-diff pow-pow distribute-rgt-out
5×sin-sum rem-exp-log distribute-rgt1-in
4×associate-+r+ neg-log sin-mult
3×quot-tan sin-cos-mult sqr-sin
2×cube-unmult exp-neg sqrt-unprod difference-cubes tan-sum +.c-commutative associate-+l- rem-square-sqrt cos-sum associate--r-
1×diff-atan cos-mult diff-sin exp-lft-cube rem-cbrt-cube diff-cos

localize4.4s (0.5%)

regimes4.1s (0.5%)

Accuracy

Total 23.0b remaining (15.4%)

Threshold costs 4.7b (3.2%)

4.9b82.3%quad2p (problem 3.2.1, positive)
3.5b86.7%quadm (p42, negative)
3.4b0%expq3 (problem 3.4.2)
3.0b86.7%quadp (p42, positive)
1.9b92%quad2m (problem 3.2.1, negative)

bsearch1.7s (0.2%)

end2.0ms (0.0%)