Details

sample4.8m (53.1%)

Algorithm
56×intervals
16×halfpoints
Results
1.0m67061×body1280valid
38.9s17739×body2560valid
26.6s41808×body640valid
14.2s13040×body10240exit
10.4s93626×body80valid
8.5s20876×body320valid
7.2s63694×body80nan
3.3s10564×body160valid
1.8s47511×pre80true
791.0ms686×body1280nan
577.0ms479×body5120valid
549.0ms674×body640nan
451.0ms196×body160nan
192.0ms415×body320nan

simplify1.8m (19.4%)

prune1.5m (16.6%)

series40.1s (7.3%)

Calls

347 calls:

1.1s
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
932.0ms
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
922.0ms
(* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945))))
849.0ms
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
848.0ms
(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))

rewrite8.6s (1.6%)

Algorithm
112×rewrite-expression-head
Calls

347 calls:

362.0ms
(/ (- 1 eps) (+ 1 eps))
235.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
168.0ms
(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))
160.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
149.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
Rules
13768×times-frac
13058×*-un-lft-identity
11730×add-sqr-sqrt
9004×add-cube-cbrt
5481×prod-diff
2703×sqrt-prod
1320×difference-of-squares
1265×pow1
1155×distribute-lft-out
1075×add-exp-log
932×div-inv
923×add-cbrt-cube
851×unpow-prod-down
805×distribute-lft-out--
713×associate-*r*
596×cbrt-prod
582×fma-neg
536×add-log-exp
404×associate-/l*
386×associate-/r/
364×associate-/r*
343×log1p-expm1-u
340×expm1-log1p-u
339×insert-posit16
301×associate-*l*
289×pow-prod-up
284×sqr-pow
269×div-exp
250×associate-+l+
248×pow-prod-down
239×distribute-rgt-neg-in
209×prod-exp
197×cbrt-unprod
183×flip-+ flip3-+
172×cbrt-undiv
168×distribute-lft-neg-in
167×flip3-- flip--
161×sqrt-pow1
152×distribute-rgt-out
127×unswap-sqr
124×sqrt-div
121×pow-sqr
114×pow1/2
107×swap-sqr
103×log-prod
97×exp-prod
96×fma-def
81×pow-plus
79×cbrt-div diff-log
72×associate-*r/
70×pow1/3 log-pow sub-neg
68×frac-2neg clear-num
58×exp-sum pow2
56×neg-mul-1 *-commutative
43×associate-/l/ rem-sqrt-square
39×pow-unpow
38×1-exp rec-exp
35×frac-times
32×tan-quot
29×associate-*l/ frac-add
26×fma-udef
24×sum-log
19×cube-unmult distribute-rgt-in +-commutative distribute-lft-in
18×pow-flip div-sub
14×inv-pow hypot-def
12×distribute-rgt1-in distribute-lft1-in
10×neg-sub0 frac-sub difference-of-sqr-1
9×associate--l-
8×pow-exp neg-log pow-to-exp
7×sqrt-unprod associate--r+
6×log-div
5×expm1-log1p expm1-udef rem-log-exp
4×log1p-udef sin-mult pow-div count-2
3×exp-diff associate--l+ sqr-sin pow-pow rem-square-sqrt
2×sin-sum frac-2neg.c log1p-expm1 +.c-commutative un-div-inv tan-sum exp-neg associate-+l- log1p-def cos-sum
1×quot-tan diff-atan associate-+r+ sin-cos-mult pow3 hypot-udef hypot-1-def diff-sin rem-cbrt-cube diff-cos expm1-def

regimes4.1s (0.7%)

Accuracy

Total 22.6b remaining (17.8%)

Threshold costs 4.2b (3.3%)

4.9b83%quadm (p42, negative)
4.5b83.9%quad2m (problem 3.2.1, negative)
4.4b84.5%quad2p (problem 3.2.1, positive)
3.3b0%expq3 (problem 3.4.2)
1.3b89.2%2nthrt (problem 3.4.6)

localize3.9s (0.7%)

bsearch3.1s (0.6%)

end2.0ms (0.0%)