Details

sample5.4m (50.7%)

Algorithm
56×intervals
16×halfpoints
Results
1.2m66565×body1280valid
43.8s17413×body2560valid
27.1s42084×body640valid
14.5s12606×body10240exit
11.9s93962×body80valid
9.3s21075×body320valid
7.3s63688×body80nan
3.6s10555×body160valid
2.1s47460×pre80true
797.0ms639×body1280nan
589.0ms668×body640nan
560.0ms446×body5120valid
163.0ms330×body320nan
58.0ms196×body160nan

simplify2.8m (26.2%)

prune1.4m (13.1%)

series45.3s (7.0%)

Calls

329 calls:

1.1s
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
1000.0ms
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
984.0ms
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))
946.0ms
(cbrt (* (cbrt (fma 1/3 x (* (pow x 5) 2/945))) (cbrt (fma 1/3 x (* (pow x 5) 2/945)))))
941.0ms
(cbrt (fma 1/3 x (* (pow x 5) 2/945)))

rewrite7.7s (1.2%)

Algorithm
112×rewrite-expression-head
Calls

329 calls:

285.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
212.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
160.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
151.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (sin x) (sin eps)) (/ 1 (cos eps))) (cos x)))) (/ (sin x) (cos x)))
127.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
Rules
9789×times-frac
9756×*-un-lft-identity
9314×add-sqr-sqrt
7037×add-cube-cbrt
5047×prod-diff
1903×sqrt-prod
1246×pow1
1049×difference-of-squares
983×add-exp-log
842×add-cbrt-cube
714×div-inv
599×associate-*r*
595×distribute-lft-out--
591×distribute-lft-out
504×fma-neg
493×add-log-exp
383×associate-*l*
325×log1p-expm1-u
323×expm1-log1p-u
321×insert-posit16
320×associate-/r/
282×pow-prod-up
266×cbrt-prod
247×associate-+l+
242×prod-exp
241×pow-prod-down
232×associate-/l*
223×unpow-prod-down
208×associate-/r*
196×cbrt-unprod
184×sqrt-pow1
183×distribute-rgt-neg-in
176×sqrt-div
174×flip-+ flip3-+
173×div-exp
168×distribute-lft-neg-in
154×flip3-- flip--
152×distribute-rgt-out
142×unswap-sqr
127×cbrt-undiv
124×swap-sqr
121×pow1/2
118×pow-sqr
104×pow-unpow
90×associate-*r/
81×pow1/3 sqr-pow
78×pow-plus
70×diff-log
65×sub-neg
62×*-commutative fma-def
59×pow2
56×frac-2neg clear-num neg-mul-1
53×pow-flip
51×frac-times
43×log-prod
41×rem-sqrt-square
40×distribute-rgt-in distribute-lft-in associate-*l/
38×cbrt-div
36×associate-/l/
34×tan-quot
33×1-exp rec-exp
27×pow-pow
26×inv-pow
24×difference-of-sqr-1
22×frac-add
21×fma-udef
18×sum-log pow-exp div-sub
16×cube-unmult pow-to-exp
14×hypot-def log-pow
12×neg-sub0 distribute-rgt1-in associate-+r+ +-commutative distribute-lft1-in
11×exp-prod
10×associate--l- frac-sub
expm1-udef sin-mult
neg-log pow-div
expm1-log1p un-div-inv log1p-udef
sqrt-unprod log-div
quot-tan exp-diff log1p-expm1 associate--r+ exp-neg rem-exp-log rem-log-exp count-2
associate--l+ sqr-sin rem-square-sqrt expm1-def
sin-sum frac-2neg.c sin-cos-mult +.c-commutative tan-sum hypot-1-def exp-to-pow associate-+l- log1p-def cos-sum
diff-atan associate-+r- exp-sum pow3 diff-sin diff-cos associate--r-

regimes5.1s (0.8%)

Accuracy

Total 24.3b remaining (17%)

Threshold costs 3.9b (2.8%)

5.2b81.6%quadm (p42, negative)
5.1b81.6%quad2m (problem 3.2.1, negative)
4.3b84.6%quad2p (problem 3.2.1, positive)
3.5b0%expq3 (problem 3.4.2)
2.3b80.7%2nthrt (problem 3.4.6)

localize4.6s (0.7%)

bsearch2.2s (0.3%)

end1.0ms (0.0%)