Details

sample5.0m (45.6%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66759×body1280valid
38.5s17648×body2560valid
25.1s41715×body640valid
13.3s94099×body80valid
12.9s12438×body10240exit
9.0s20948×body320valid
7.1s63993×body80nan
3.1s10800×body160valid
1.7s47361×pre80true
1.2s670×body1280nan
536.0ms706×body640nan
523.0ms434×body5120valid
174.0ms366×body320nan
62.0ms220×body160nan

simplify2.6m (23.7%)

prune2.3m (21.1%)

series37.4s (5.7%)

Calls

399 calls:

1.1s
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
840.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
624.0ms
(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
602.0ms
(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
583.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite15.1s (2.3%)

Algorithm
121×rewrite-expression-head
Calls

399 calls:

1.2s
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
457.0ms
(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))
437.0ms
(* x (- (* (* (* x x) 1/45) (* (* x x) 1/45)) (* 1/3 1/3)))
274.0ms
(* (* 1/6 x) (* (* (* a x) (* a x)) a))
234.0ms
(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
Rules
5373×*-un-lft-identity
4360×times-frac
4272×add-sqr-sqrt
2761×add-cube-cbrt
1940×sqrt-prod
1409×add-exp-log
1346×pow1
1269×add-cbrt-cube
1017×distribute-lft-out
739×associate-*r*
694×add-log-exp
604×associate-*l*
549×difference-of-squares
466×associate-/l*
420×prod-exp
405×distribute-lft-out--
392×insert-posit16
378×cbrt-unprod
365×pow-prod-down
317×associate-/r*
296×cbrt-prod
275×cbrt-div flip-+ flip3-+
274×div-inv
273×frac-times
254×tan-quot
253×div-exp
245×log-prod
240×associate-*l/
191×cbrt-undiv
190×associate-/r/
180×flip3-- flip--
175×unswap-sqr
166×associate-*r/
155×unpow-prod-down
147×log-pow
108×sqrt-div exp-prod
106×distribute-rgt-neg-in
103×pow-prod-up
96×diff-log
94×sub-neg
90×swap-sqr *-commutative
88×distribute-lft-neg-in
87×sqr-pow
71×pow-sqr
68×frac-2neg clear-num
66×pow1/3
65×associate-/l/
64×pow-plus
63×sum-log
49×frac-add
43×sqrt-pow1 pow1/2
42×log-div
39×pow-unpow
37×associate-+r+ pow2
36×associate-+l+
34×+-commutative
32×distribute-rgt-in distribute-lft-in
31×1-exp rec-exp
30×pow-flip
28×rem-sqrt-square
26×div-sub
21×difference-of-sqr-1
20×associate--l+
19×rem-log-exp
16×exp-sum
15×associate--r+ inv-pow
11×frac-sub
10×associate--l- cos-mult difference-of-sqr--1
9×pow-exp pow-to-exp
8×neg-sub0 pow3 distribute-neg-frac
7×neg-log sin-mult rem-exp-log
6×pow-div
5×exp-diff associate-+l- distribute-rgt1-in
4×distribute-lft-neg-out neg-mul-1 rem-cbrt-cube distribute-rgt-out
3×associate-+r- exp-to-pow pow-pow distribute-rgt-out-- sqr-sin
2×sin-sum distribute-lft1-in sqrt-unprod tan-sum exp-neg +.c-commutative cos-sum associate--r- count-2
1×remove-posit16 diff-atan frac-2neg.c sin-cos-mult sub-div un-div-inv diff-sin distribute-neg-in diff-cos

localize4.7s (0.7%)

regimes4.6s (0.7%)

Accuracy

Total 28.3b remaining (21.8%)

Threshold costs 5.1b (3.9%)

4.9b82.4%quadp (p42, positive)
4.9b82.2%quad2p (problem 3.2.1, positive)
4.7b82.4%quad2m (problem 3.2.1, negative)
4.5b83.7%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)

bsearch1.6s (0.2%)

end1.0ms (0.0%)