Details

sample2.1m (55.3%)

Algorithm
56×intervals
16×halfpoints
Results
30.6s66748×body1280valid
19.7s17539×body2560valid
11.6s42086×body640valid
5.3s94022×body80valid
3.8s20773×body320valid
3.0s62834×body80nan
1.3s10734×body160valid
756.0ms12911×body80overflowed
748.0ms47547×pre80true
372.0ms630×body1280nan
282.0ms659×body640nan
204.0ms429×body5120valid
90.0ms338×body320nan
28.0ms175×body160nan

series40.2s (17.8%)

Calls

383 calls:

1.3s
(log (exp (+ (- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2))) (fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2))))))
968.0ms
(- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2)))
907.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
893.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
711.0ms
(/ (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))

prune37.8s (16.8%)

simplify11.2s (5.0%)

Algorithm
195×egg-herbie

rewrite5.9s (2.6%)

Algorithm
123×rewrite-expression-head
Calls

383 calls:

227.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
203.0ms
(log (exp (+ (- (* (sqrt (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n)))) (pow x (/ (/ 1.0 n) 2))) (fma (sqrt (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow x (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2))))))
145.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
139.0ms
(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))))
116.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
Rules
9508×*-un-lft-identity
7666×times-frac
7452×add-sqr-sqrt
5683×add-cube-cbrt
3251×sqrt-prod
3089×prod-diff
1480×distribute-lft-out
1289×add-exp-log
1235×unpow-prod-down
929×add-cbrt-cube
904×cbrt-prod
746×difference-of-squares
721×pow1
635×associate-*r*
633×add-log-exp
525×distribute-lft-out--
513×associate-/l*
492×cube-prod
456×sqr-pow
448×associate-*l*
431×div-inv
400×log-prod
369×log1p-expm1-u expm1-log1p-u
357×fma-neg
346×associate-/r*
337×associate-/r/
319×prod-exp
305×div-exp
248×associate-+l+
233×distribute-rgt-neg-in
223×unswap-sqr
190×flip-+ flip3-+
184×flip-- flip3--
179×cbrt-undiv
167×cbrt-unprod
149×unpow2
146×exp-sum
142×fma-def
141×swap-sqr
135×distribute-lft-neg-in
127×pow-unpow
123×sqrt-div
117×exp-prod
111×log-pow
107×sqrt-pow1
104×pow-prod-down
102×unpow3 cube-mult
87×diff-log associate-*l/
86×sub-neg
77×distribute-rgt-in associate-*r/ distribute-lft-in
76×pow1/2
75×pow-exp
73×tan-quot
72×pow-to-exp
67×fma-udef
66×associate-/l/ pow1/3 frac-times
65×frac-2neg clear-num
57×pow-prod-up
55×*-commutative
45×1-exp neg-mul-1
41×sum-log
40×cbrt-div
30×+-commutative rec-exp
29×pow-sqr
28×rem-log-exp
27×pow-pow rem-sqrt-square log-div
26×div-sub
24×frac-add complex-mul-def
21×difference-of-sqr-1
17×cube-div
15×neg-sub0
14×exp-to-pow
12×associate-+r+
11×rem-cube-cbrt associate--l+
10×associate--l-
pow-flip pow-plus neg-log frac-sub
exp-diff pow2 hypot-def associate-+l-
difference-cubes sqrt-unprod
inv-pow *.c-commutative
un-div-inv associate--r+
rem-exp-log expm1-def +.c-commutative complex-add-def sin-mult
cos-mult expm1-udef
associate-+l+.c associate-+r- exp-neg pow-sub rem-square-sqrt associate-*l*.c cos-sum tan-sum pow-neg rem-cbrt-cube sin-sum
sin-cos-mult unpow1/3 diff-atan sub-div diff-cos expm1-log1p sqr-cos diff-sin

regimes2.9s (1.3%)

Accuracy

Total 33.5b remaining (16.2%)

Threshold costs 6.1b (3%)

5.0b81.7%quadp (p42, positive)
5.0b82.9%quad2m (problem 3.2.1, negative)
4.8b83.2%quadm (p42, negative)
3.0b0%expq3 (problem 3.4.2)
2.9b72.1%2cos (problem 3.3.5)

localize1.9s (0.8%)

bsearch913.0ms (0.4%)

end1.0ms (0.0%)