Details

simplify10.2m (46.3%)

sample7.0m (31.5%)

Algorithm
56×intervals
16×halfpoints
Results
1.4m66703×body1280valid
53.2s17280×body2560valid
31.6s41844×body640valid
25.1s12698×body10240exit
17.0s93548×body80valid
9.4s62434×body80nan
9.0s20935×body320valid
3.9s11237×body160valid
3.5s47470×pre80true
768.0ms653×body1280nan
513.0ms659×body640nan
303.0ms414×body5120valid
130.0ms324×body320nan
50.0ms210×body160nan

prune2.7m (12.4%)

series1.3m (6.0%)

Calls

371 calls:

9.2s
(expm1 (expm1 (log1p (log1p (fma 1/12 x 1/2)))))
2.7s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (* eps b) (* eps b)) (* eps b))))
1.7s
(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
1.3s
(- (/ (sin x) (cos x)) (/ (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos x)))
1.3s
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

rewrite29.7s (2.2%)

Algorithm
120×rewrite-expression-head
Calls

371 calls:

1.8s
(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
1.2s
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
917.0ms
(- (tan (+ x eps)) (tan x))
907.0ms
(/ (* x (fma 0.3333333333333333 (* 0.3333333333333333 0.3333333333333333) (* (* 0.022222222222222223 (* x x)) (* (* 0.022222222222222223 (* x x)) (* 0.022222222222222223 (* x x)))))) (+ (* 0.3333333333333333 0.3333333333333333) (- (* (* (* 0.022222222222222223 x) x) (* (* 0.022222222222222223 x) x)) (* 0.3333333333333333 (* (* 0.022222222222222223 x) x)))))
695.0ms
(* (/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0))) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt (sqrt 2.0)) (sin y))))
Rules
11048×*-un-lft-identity
11010×times-frac
10025×add-sqr-sqrt
7692×add-cube-cbrt
4989×prod-diff
2398×sqrt-prod
2123×pow1
1228×add-exp-log
1107×add-cbrt-cube
901×distribute-lft-out
845×difference-of-squares
831×distribute-lft-out--
665×div-inv
606×add-log-exp
549×associate-*l*
527×pow-prod-up
522×associate-/r/
483×cbrt-prod
459×pow-prod-down
452×fma-neg
436×associate-*r*
405×associate-/l*
376×unpow-prod-down
374×flip--
365×associate-*l/
361×log1p-expm1-u expm1-log1p-u
359×flip3--
344×prod-exp
318×cbrt-unprod
280×flip-+
274×associate-/r*
265×flip3-+
249×associate-+l+
248×pow-sqr
237×associate-+r+
224×div-exp
221×distribute-rgt-neg-in
213×log-pow
205×unswap-sqr
200×pow-plus
197×distribute-lft-neg-in
185×log-prod
184×exp-prod
176×cbrt-undiv
168×associate-*r/
140×pow2
132×fma-def
124×sqrt-pow1
123×sqrt-div
115×swap-sqr
113×sqr-pow frac-sub
109×associate-/l/
105×pow-unpow diff-log
103×sub-neg
101×frac-times
89×pow1/2
83×frac-add
70×exp-sum
67×neg-mul-1
66×frac-2neg clear-num
62×*-commutative
50×rem-sqrt-square
38×div-sub
35×log-div
30×distribute-rgt-in distribute-lft-in
29×pow1/3
27×tan-quot fma-udef
23×sum-log associate--l+
20×1-exp pow-flip rec-exp
17×neg-sub0
16×+-commutative
15×rem-log-exp
14×associate--l- associate--r+
13×complex-mul-def cbrt-div
12×exp-diff
9×pow-pow exp-neg pow-to-exp pow-exp
8×pow-div
7×inv-pow sin-mult cube-unmult
6×sqrt-unprod pow3 neg-log cos-mult distribute-rgt-out--
5×difference-cubes hypot-def expm1-udef associate-+l-
4×un-div-inv sub-div expm1-log1p distribute-frac-neg *.c-commutative
3×rem-exp-log log1p-udef log1p-expm1 +.c-commutative complex-add-def cos-sum sin-sum
2×associate-+r- associate--r- +-inverses tan-sum exp-to-pow
1×associate-+l+.c sin-cos-mult distribute-lft-in.c diff-atan diff-cos rem-square-sqrt sqr-cos distribute-rgt-in.c frac-2neg.c associate-*l*.c diff-sin

regimes9.6s (0.7%)

Accuracy

Total 25.1b remaining (19.8%)

Threshold costs 5.7b (4.5%)

5.2b82.2%quadp (p42, positive)
5.1b82.3%quad2p (problem 3.2.1, positive)
3.3b0%expq3 (problem 3.4.2)
3.2b89.8%quad2m (problem 3.2.1, negative)
1.5b83.4%2nthrt (problem 3.4.6)

localize8.0s (0.6%)

bsearch2.8s (0.2%)

end17.0ms (0.0%)