Details

sample1.8m (51.7%)

Algorithm
56×intervals
16×halfpoints
Results
23.9s66812×body1280valid
16.7s17297×body2560valid
8.3s42549×body640valid
3.7s12689×body10240exit
2.9s93761×body80valid
2.5s20638×body320valid
1.7s63332×body80nan
839.0ms10586×body160valid
562.0ms47332×pre80true
314.0ms664×body1280nan
225.0ms690×body640nan
133.0ms465×body5120valid
75.0ms382×body320nan
24.0ms212×body160nan

prune38.0s (18.4%)

series37.4s (18.1%)

Calls

421 calls:

890.0ms
(- (pow (pow (exp (cbrt x)) (* 2 (cbrt x))) (cbrt x)) (* 1.0 1.0))
590.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
497.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
491.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
437.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify10.1s (4.9%)

Algorithm
197×egg-herbie

rewrite7.7s (3.8%)

Algorithm
125×rewrite-expression-head
Calls

421 calls:

435.0ms
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
301.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
296.0ms
(/ (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))) (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)))
199.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
177.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
8648×times-frac
7711×*-un-lft-identity
7108×add-sqr-sqrt
4730×add-cube-cbrt
2976×sqrt-prod
1584×add-exp-log
1175×add-cbrt-cube
955×difference-of-squares
872×associate-*l*
797×distribute-lft-out--
772×distribute-lft-out
761×add-log-exp
737×pow1
659×associate-/l*
625×associate-*r*
520×unpow-prod-down
502×associate-/r*
412×div-exp
383×prod-exp
382×div-inv
378×associate-*l/
320×associate-/r/
308×log-prod
292×flip3-- flip--
251×cbrt-undiv
240×flip-+ flip3-+
237×cbrt-prod
235×frac-add
225×cbrt-unprod
221×unswap-sqr
220×sqr-pow
203×associate-*r/
148×distribute-rgt-neg-in
140×associate-/l/
136×frac-times
135×sqrt-div
129×swap-sqr
127×unpow2
124×diff-log exp-prod
122×sub-neg
119×cube-prod
114×pow-unpow
111×log-pow
93×pow-prod-down
92×sqrt-pow1
83×clear-num frac-2neg
78×pow-to-exp pow-exp
77×*-commutative
66×pow1/2
64×1-exp
55×rec-exp sum-log
49×pow1/3
44×cbrt-div
38×pow-pow frac-sub
37×tan-quot
36×rem-sqrt-square +-commutative
34×distribute-rgt-in distribute-lft-in
27×associate-+l+
26×pow-flip rem-log-exp
25×log-div
24×complex-mul-def
21×pow-prod-up div-sub associate--l+
20×cube-div
18×neg-sub0
17×pow-sqr
14×associate--r+
13×unpow3 associate--l- cube-mult exp-to-pow
12×inv-pow
11×neg-log associate-+l-
10×pow-div rem-cube-cbrt
9×exp-diff
8×pow2 pow-plus sin-mult cos-mult
6×un-div-inv rem-exp-log *.c-commutative difference-of-sqr-1 exp-sum
5×difference-cubes sqrt-unprod exp-neg
4×sub-div +.c-commutative complex-add-def
3×distribute-lft-neg-in distribute-rgt-out-- sqr-cos associate-+r+ distribute-rgt-out
2×sqrt-undiv associate-+l+.c associate-+r- rem-square-sqrt associate-*l*.c cos-sum tan-sum sin-sum
1×sin-cos-mult sum-cubes associate--r- diff-atan diff-cos neg-mul-1 rem-cbrt-cube frac-2neg.c diff-sin

regimes3.1s (1.5%)

Accuracy

Total 22.4b remaining (10.7%)

Threshold costs 6.9b (3.3%)

3.5b87.8%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)
2.4b87.6%2nthrt (problem 3.4.6)
1.6b84.8%2cos (problem 3.3.5)
1.3b94.4%quad2p (problem 3.2.1, positive)

localize2.0s (1.0%)

bsearch1.3s (0.6%)

end1.0ms (0.0%)