Details

sample1.8m (55.0%)

Algorithm
56×intervals
16×halfpoints
Results
24.4s67861×body1280valid
16.7s17317×body2560valid
8.4s42520×body640valid
4.0s13292×body10240exit
2.7s91993×body80valid
2.5s20821×body320valid
1.7s64849×body80nan
1.3s2270×body1280nan
854.0ms10544×body160valid
764.0ms1942×body640nan
551.0ms47526×pre80true
223.0ms939×body320nan
122.0ms427×body5120valid
71.0ms503×body160nan

series35.2s (17.5%)

Calls

384 calls:

1.4s
(/ (* 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)))))
627.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
605.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
493.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
493.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

prune32.6s (16.2%)

simplify9.9s (4.9%)

Algorithm
192×egg-herbie

rewrite6.7s (3.3%)

Algorithm
120×rewrite-expression-head
Calls

384 calls:

246.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))
245.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))
192.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
105.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
101.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
Rules
7181×times-frac
6086×add-sqr-sqrt
5868×*-un-lft-identity
3799×add-cube-cbrt
1425×add-exp-log
1029×add-cbrt-cube
903×difference-of-squares
889×sqrt-prod
724×associate-*r*
700×add-log-exp
679×distribute-lft-out--
657×pow1
648×associate-/l*
571×unpow-prod-down
549×associate-*l*
412×cbrt-prod
390×distribute-lft-out
381×associate-/r*
365×div-exp
349×prod-exp
279×unswap-sqr
273×sqr-pow
269×flip-- flip3--
259×div-inv
221×log-prod
217×cbrt-undiv
207×associate-/r/
199×flip-+ flip3-+
198×cbrt-unprod
190×associate-*l/
168×unpow2
164×log-pow
143×cbrt-div
133×sub-neg
122×exp-prod
119×diff-log
110×associate-*r/
102×frac-times
100×sqrt-div
96×associate-/l/
88×pow-prod-down
84×pow-exp
83×pow-to-exp
81×sqrt-pow1
73×clear-num frac-2neg
71×pow-unpow
69×*-commutative
66×frac-add
60×cube-prod distribute-rgt-neg-in
54×sum-log
51×pow1/3 swap-sqr
49×pow1/2 1-exp
46×rec-exp
39×distribute-rgt-in distribute-lft-in
35×exp-sum
34×log-div
32×+-commutative
27×rem-sqrt-square
24×associate-+l+ complex-mul-def
22×div-sub frac-sub
21×rem-log-exp
18×associate--l+
15×pow-pow
14×pow-prod-up sin-mult tan-quot
13×exp-diff
12×cube-div unpow3 pow-sqr pow-flip cube-mult neg-sub0 cos-mult
11×associate--r+
10×inv-pow
9×neg-log associate-+r+ associate-+l-
8×associate--l-
6×rem-cube-cbrt un-div-inv *.c-commutative
5×sqrt-unprod pow2 pow-plus
4×pow-div +.c-commutative difference-of-sqr-1 complex-add-def associate-+r-
3×rem-exp-log rem-cbrt-cube
2×associate-+l+.c exp-neg sub-div rem-square-sqrt associate-*l*.c cos-sum tan-sum frac-2neg.c exp-to-pow sin-sum
1×difference-cubes diff-atan diff-cos sin-cos-mult diff-sin

regimes2.9s (1.4%)

Accuracy

Total 28.5b remaining (13.1%)

Threshold costs 8.2b (3.8%)

5.2b81.3%quadp (p42, positive)
5.2b81.3%quad2p (problem 3.2.1, positive)
3.2b0%expq3 (problem 3.4.2)
3.0b88.6%quad2m (problem 3.2.1, negative)
1.9b81.8%2nthrt (problem 3.4.6)

localize1.8s (0.9%)

bsearch1.6s (0.8%)

end1.0ms (0.0%)