Details

simplify5.6m (46.4%)

sample4.4m (36.4%)

Algorithm
56×intervals
16×halfpoints
Results
48.8s66599×body1280valid
33.9s17327×body2560valid
18.0s41902×body640valid
10.2s12868×body10240exit
8.6s93800×body80valid
7.2s64266×body80nan
5.8s21104×body320valid
1.9s10710×body160valid
1.7s47408×pre80true
599.0ms654×body1280nan
447.0ms674×body640nan
354.0ms510×body5120valid
126.0ms374×body320nan
41.0ms207×body160nan

prune51.3s (7.1%)

series49.4s (6.8%)

Calls

353 calls:

1.9s
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))
1.7s
(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)))
624.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
597.0ms
(+ (fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- 2.0)) (exp (- x)))
589.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite14.8s (2.0%)

Algorithm
123×rewrite-expression-head
Calls

353 calls:

560.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
470.0ms
(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (+ 1.0 (exp x)) (fma 1.0 1.0 (exp (* 2 x)))))
248.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
241.0ms
(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (cos y)))
188.0ms
(+ (/ (- 1.0 (/ 0.5 N)) N) (/ 0.3333333333333333 (pow N 3)))
Rules
8081×*-un-lft-identity
7461×times-frac
7373×add-sqr-sqrt
5817×add-cube-cbrt
3307×prod-diff
2209×sqrt-prod
1115×add-exp-log
906×add-cbrt-cube
708×unpow-prod-down
691×pow1
664×distribute-lft-out
635×difference-of-squares
553×add-log-exp
510×cbrt-prod
506×distribute-lft-out--
481×associate-/l* div-inv
455×associate-*l*
410×fma-neg
368×associate-/r*
362×associate-*r*
342×log1p-expm1-u expm1-log1p-u
321×associate-/r/
293×distribute-rgt-neg-in
285×distribute-lft-neg-in
250×div-exp
248×associate-+l+
244×prod-exp
234×sqr-pow
208×cube-prod
205×flip-- flip3--
180×cbrt-undiv
172×cbrt-unprod
167×pow-unpow
148×flip-+ flip3-+
144×log-prod
127×unswap-sqr
102×fma-def
100×pow-prod-down sub-neg
95×sqrt-div neg-mul-1
92×diff-log associate-*l/
82×swap-sqr
81×log-pow
76×sqrt-pow1
75×distribute-rgt-in distribute-lft-in
70×associate-*r/
67×frac-2neg clear-num
66×tan-quot
59×associate-/l/ frac-times
58×pow1/3 exp-sum
55×pow1/2
52×cbrt-div
50×*-commutative unpow2
48×unpow3 cube-mult
43×pow-exp associate--l+
40×pow-to-exp
31×div-sub
30×log-div
28×fma-udef
27×pow-prod-up
25×frac-add 1-exp rec-exp
24×rem-sqrt-square
23×pow-pow
21×pow-sqr
16×exp-prod sum-log
13×complex-mul-def +-commutative
11×rem-cube-cbrt
10×associate--r+ pow-flip rem-log-exp
9×pow-plus frac-sub
8×pow2
7×associate--l- inv-pow
6×cube-div exp-diff neg-sub0
5×sqrt-unprod
4×*.c-commutative associate-+l-
3×+.c-commutative distribute-frac-neg
2×rem-exp-log sin-cos-mult log1p-udef associate--r- exp-neg log1p-expm1 expm1-log1p complex-add-def rem-square-sqrt neg-log cos-sum sin-mult tan-sum rem-cbrt-cube expm1-udef exp-to-pow sin-sum
1×associate-+l+.c difference-cubes sqrt-pow2 un-div-inv diff-atan diff-cos associate-*l*.c frac-2neg.c diff-sin

regimes3.6s (0.5%)

Accuracy

Total 34.4b remaining (23.9%)

Threshold costs 5.8b (4%)

6.0b82.2%quadp (p42, positive)
5.9b82.7%quad2p (problem 3.2.1, positive)
5.5b77.2%quad2m (problem 3.2.1, negative)
5.5b77.2%quadm (p42, negative)
3.3b0%expq3 (problem 3.4.2)

localize3.2s (0.4%)

bsearch2.1s (0.3%)

end1.0ms (0.0%)