Details

simplify5.6m (44.0%)

sample4.5m (35.7%)

Algorithm
56×intervals
16×halfpoints
Results
51.2s66864×body1280valid
32.4s17297×body2560valid
19.0s42188×body640valid
11.7s12596×body10240exit
9.3s94158×body80valid
5.6s20297×body320valid
4.9s62879×body80nan
2.2s10749×body160valid
1.9s47456×pre80true
669.0ms726×body1280nan
410.0ms678×body640nan
287.0ms442×body5120valid
125.0ms368×body320nan
40.0ms187×body160nan

prune1.4m (10.9%)

series45.2s (5.9%)

Calls

365 calls:

769.0ms
(cbrt (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
752.0ms
(* (cbrt (/ 1 (* (sqrt 2.0) 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
746.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
745.0ms
(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))
601.0ms
(- (* 1 (/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))) (tan x))

rewrite16.8s (2.2%)

Algorithm
122×rewrite-expression-head
Calls

365 calls:

770.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
746.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
495.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
276.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))) (cbrt (cbrt (cbrt (+ x 1.0)))))) (cbrt x))
231.0ms
(- (/ (exp (+ x x)) (+ 1.0 (exp x))) (/ (* 1.0 1.0) (+ 1.0 (exp x))))
Rules
17559×times-frac
14479×*-un-lft-identity
12926×add-sqr-sqrt
11373×add-cube-cbrt
8470×prod-diff
2640×distribute-rgt-in distribute-lft-in
2251×sqrt-prod
2184×distribute-rgt-neg-in
2181×unpow-prod-down
2142×distribute-lft-neg-in
1626×pow1
1116×distribute-lft-out
1056×div-inv
1046×add-exp-log
943×log-pow
895×add-cbrt-cube
746×sqr-pow
713×unpow2
616×difference-of-squares
577×add-log-exp
569×neg-mul-1
552×associate-/l*
510×distribute-lft-out--
492×associate-/r/
455×associate-*l*
413×associate-*r*
401×associate-/r*
384×fma-neg
355×expm1-log1p-u
353×log1p-expm1-u
325×cbrt-prod
252×associate-+l+
236×div-exp
231×flip-+ flip3-+
220×flip-- flip3--
196×prod-exp
178×cbrt-undiv
151×cbrt-unprod
145×sqrt-pow1
140×unswap-sqr
135×sqrt-div swap-sqr
134×log-prod
123×pow-prod-down
116×exp-sum
114×fma-def
104×associate-*l/
94×pow1/2
91×sub-neg
88×diff-log
78×frac-2neg clear-num
74×pow-unpow associate-*r/
73×associate-/l/
72×tan-quot
61×pow-prod-up cbrt-div
60×frac-times
54×*-commutative
49×exp-prod
40×div-sub
35×fma-udef
34×pow1/3
33×rem-sqrt-square
31×pow-exp
29×log-div
28×pow-to-exp sum-log
27×pow-sqr
23×frac-add
20×+-commutative
18×neg-sub0
16×associate-+r+ rec-exp frac-sub 1-exp
15×associate--l+
14×pow-flip
13×complex-mul-def
12×hypot-def rem-log-exp
11×pow-pow
10×pow-plus
8×exp-diff associate--l- sqrt-unprod neg-log
7×associate--r+ distribute-rgt-out-- pow2
6×inv-pow associate-+l-
5×log1p-udef log1p-expm1 cos-sum
4×rem-cube-cbrt associate--r- distribute-neg-in distribute-frac-neg *.c-commutative
3×associate-+r- +.c-commutative expm1-log1p rem-square-sqrt sub-div sin-mult expm1-udef sin-sum
2×rem-exp-log exp-neg unpow3 cube-mult complex-add-def cube-prod tan-sum frac-2neg.c
1×associate-+l+.c diff-atan sin-cos-mult diff-cos cube-unmult associate-*l*.c exp-to-pow diff-sin

regimes4.3s (0.6%)

Accuracy

Total 19.1b remaining (14.6%)

Threshold costs 5.3b (4.1%)

4.3b87.3%quadp (p42, positive)
3.2b88.1%quad2p (problem 3.2.1, positive)
1.6b81.1%2nthrt (problem 3.4.6)
1.3b94.7%quadm (p42, negative)
1.3b94.7%quad2m (problem 3.2.1, negative)

localize3.2s (0.4%)

bsearch1.9s (0.3%)

end0.0ms (0.0%)