Details

sample2.2m (52.2%)

Algorithm
56×intervals
16×halfpoints
Results
31.8s67128×body1280valid
20.4s17497×body2560valid
12.1s41467×body640valid
6.9s94238×body80valid
4.4s20924×body320valid
4.0s63747×body80nan
1.5s10500×body160valid
1.0s13027×body80overflowed
848.0ms47507×pre80true
389.0ms626×body1280nan
305.0ms649×body640nan
263.0ms459×body5120valid
104.0ms352×body320nan
33.0ms164×body160nan

series43.9s (17.4%)

Calls

429 calls:

1.2s
(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.2s
(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.2s
(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.1s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
997.0ms
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

prune43.8s (17.4%)

rewrite12.6s (5.0%)

Algorithm
125×rewrite-expression-head
Calls

429 calls:

1.6s
(/ (/ (- (pow (pow eps 2) 3) (pow (+ (/ (pow eps 2) (pow 1.0 2)) eps) 3)) (sqrt (+ (* (+ (/ (pow eps 2) (pow 1.0 2)) eps) (+ (+ (/ (pow eps 2) (pow 1.0 2)) eps) (pow eps 2))) (pow eps 4)))) (sqrt (+ (* (+ (/ (pow eps 2) (pow 1.0 2)) eps) (+ (+ (/ (pow eps 2) (pow 1.0 2)) eps) (pow eps 2))) (pow eps 4))))
1.0s
(/ (- (pow (pow eps 2) 3) (pow (+ (/ (pow eps 2) (pow 1.0 2)) eps) 3)) (+ (* (+ (/ (pow eps 2) (pow 1.0 2)) eps) (+ (+ (/ (pow eps 2) (pow 1.0 2)) eps) (pow eps 2))) (pow eps 4)))
994.0ms
(/ (- (pow (pow eps 2) 3) (pow (+ (/ (pow eps 2) (pow 1.0 2)) eps) 3)) (sqrt (+ (* (+ (/ (pow eps 2) (pow 1.0 2)) eps) (+ (+ (/ (pow eps 2) (pow 1.0 2)) eps) (pow eps 2))) (pow eps 4))))
375.0ms
(+ (- (/ 1 (/ (+ x 1.0) 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
334.0ms
(sqrt (+ (* (+ (/ (pow eps 2) (pow 1.0 2)) eps) (+ (+ (/ (pow eps 2) (pow 1.0 2)) eps) (pow eps 2))) (pow eps 4)))
Rules
15312×times-frac
11870×add-sqr-sqrt
11399×*-un-lft-identity
6960×add-cube-cbrt
4240×sqrt-prod
3134×unpow-prod-down
2942×difference-of-squares
1987×cube-prod
1809×add-exp-log
1489×sqr-pow
1275×distribute-lft-out--
1196×associate-/l*
1161×add-cbrt-cube
1157×distribute-lft-out
797×pow1 add-log-exp
786×associate-*r*
617×unpow2
591×cbrt-prod
589×associate-*l*
512×div-exp
491×prod-exp
397×associate-/r*
382×div-inv
318×unswap-sqr
258×flip-- flip3--
250×log-prod
247×associate-/r/
239×cbrt-undiv
226×cbrt-unprod
221×flip-+ flip3-+
206×cbrt-div
182×distribute-rgt-neg-in
150×sqrt-div
143×associate-*l/
135×diff-log
134×log-pow
133×sub-neg
128×pow-exp
125×pow-prod-down
114×pow-to-exp
97×pow-unpow
89×associate-*r/
87×1-exp frac-times
85×associate-/l/ exp-prod
80×*-commutative sqrt-pow1
74×frac-2neg clear-num
71×sum-log
63×rec-exp
60×pow1/3
59×pow1/2
55×difference-cubes
48×associate-+l+
43×associate-+r+
36×distribute-rgt-in +-commutative distribute-lft-in
34×frac-add
33×frac-sub
32×tan-quot
31×rem-sqrt-square
30×pow-pow
29×cube-div
26×log-div div-sub
25×swap-sqr
24×complex-mul-def
23×pow-prod-up unpow3 cube-mult
22×associate--r+
21×rem-cube-cbrt
18×cos-mult associate--l+
17×pow-sqr rem-log-exp
15×neg-sub0
12×associate-+l-
11×neg-log
10×associate--l- pow-flip
inv-pow
exp-diff pow-plus exp-sum *.c-commutative
un-div-inv sqrt-unprod distribute-rgt-out-- pow2
pow-div associate-+r- +.c-commutative complex-add-def rem-cbrt-cube
sin-cos-mult difference-of-sqr-1
cos-sum rem-exp-log distribute-lft-neg-in associate-+l+.c associate--r- exp-neg rem-square-sqrt associate-*l*.c neg-mul-1 tan-sum distribute-neg-frac exp-to-pow sin-sum
sqrt-pow2 diff-atan sub-div diff-cos unpow1/2 sin-mult frac-2neg.c diff-sin

simplify12.4s (4.9%)

Algorithm
197×egg-herbie

regimes3.3s (1.3%)

Accuracy

Total 23.8b remaining (9.2%)

Threshold costs 9.5b (3.7%)

4.3b48.1%expq3 (problem 3.4.2)
3.1b88.1%quadm (p42, negative)
3.1b88.6%quad2p (problem 3.2.1, positive)
2.1b77.3%2nthrt (problem 3.4.6)
1.7b83.4%2cos (problem 3.3.5)

bsearch2.3s (0.9%)

localize2.1s (0.8%)

end1.0ms (0.0%)