Details

simplify17.1m (42.4%)

sample15.9m (39.3%)

Algorithm
56×intervals
16×halfpoints
Results
2.4m66703×body1280valid
1.6m17280×body2560valid
55.8s41844×body640valid
41.6s12698×body10240exit
34.0s93548×body80valid
17.5s20935×body320valid
16.5s62434×body80nan
5.9s11237×body160valid
5.2s47470×pre80true
2.2s653×body1280nan
1.7s324×body320nan
1.5s659×body640nan
1.0s414×body5120valid
87.0ms210×body160nan

prune4.1m (10.0%)

series2.1m (5.1%)

Calls

372 calls:

10.3s
(expm1 (expm1 (log1p (log1p (fma 1/12 x 1/2)))))
4.3s
(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)))))
2.9s
(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))
2.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (* eps b) (* eps b)) (* eps b))))
2.1s
(cbrt (cbrt x))

rewrite43.0s (1.8%)

Algorithm
120×rewrite-expression-head
Calls

372 calls:

987.0ms
(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))
975.0ms
(/ (- x (sin x)) (- x (tan x)))
891.0ms
(/ (* 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)))))
856.0ms
(* (/ (/ 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))))
766.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
Rules
10842×times-frac
10696×*-un-lft-identity
10388×add-sqr-sqrt
7699×add-cube-cbrt
5198×prod-diff
2385×sqrt-prod
2136×pow1
1241×add-exp-log
1120×add-cbrt-cube
990×difference-of-squares
885×distribute-lft-out--
632×div-inv
600×add-log-exp
556×associate-*l*
529×pow-prod-up
522×distribute-lft-out
514×associate-/r/
478×cbrt-prod
464×pow-prod-down
448×fma-neg
431×associate-*r*
405×associate-/l*
376×unpow-prod-down
362×log1p-expm1-u expm1-log1p-u
350×prod-exp
349×flip-- flip3--
339×associate--r+
324×cbrt-unprod
271×associate-/r*
250×pow-sqr
247×associate-+l+
233×distribute-rgt-in distribute-lft-in
226×div-exp
221×distribute-rgt-neg-in
213×log-pow
203×unswap-sqr
201×pow-plus
197×distribute-lft-neg-in
185×log-prod
184×exp-prod
182×associate-*r/
178×cbrt-undiv
176×flip-+ flip3-+
141×pow2
132×associate--l+
131×sqrt-pow1
128×sub-neg
123×sqrt-div
115×swap-sqr
113×sqr-pow
106×diff-log
105×pow-unpow
89×pow1/2 fma-def
77×associate-/l/ frac-times
73×associate-*l/
70×exp-sum
67×neg-mul-1
66×frac-2neg clear-num
63×*-commutative
49×rem-sqrt-square frac-sub
38×div-sub
35×log-div pow1/3
28×fma-udef
27×tan-quot
20×pow-flip rec-exp 1-exp
18×sum-log
17×neg-sub0
15×rem-log-exp
14×associate--l-
13×complex-mul-def +-commutative cbrt-div
12×exp-diff
10×frac-add
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 associate--r- cos-sum sin-sum
2×sin-cos-mult +-inverses exp-to-pow tan-sum
1×associate-+l+.c associate-+r- associate-+r+ 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

regimes16.4s (0.7%)

Accuracy

Total 25.1b remaining (19.9%)

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)

localize13.2s (0.5%)

bsearch4.9s (0.2%)

end48.0ms (0.0%)