Details

simplify6.5m

Calls

4846 calls:

Slowest
2.1s
(re (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0)))
1.9s
(im (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0)))
1.5s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
1.0s
(fma (* (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps)))) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (+ (/ (/ (sin eps) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (cos eps)) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps)))))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps)))) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (+ (/ (/ (sin eps) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (cos eps)) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps)))) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (+ (/ (/ (sin eps) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (cos eps)) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps)))))))))))) (- (* (/ (cbrt (sin x)) (sqrt (cos x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (cos x))))))
1.0s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))

sample4.9m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67314×body1280valid
37.1s17433×body2560valid
25.7s41943×body640valid
13.1s12693×body10240exit
11.1s93816×body80valid
8.2s20435×body320valid
6.8s63373×body80nan
3.1s10580×body160valid
2.3s47371×pre80true
787.0ms693×body1280nan
509.0ms447×body5120valid
471.0ms629×body640nan
151.0ms327×body320nan
54.0ms189×body160nan

prune1.5m

series37.5s

Calls

347 calls:

Slowest
1.5s
(- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (* (cos eps) (cos eps))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps)))) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (+ (/ (/ (sin eps) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))) (cos eps)) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (sin eps) (/ (* (* (cos eps) (cos eps)) (cos eps)) (* (sin eps) (sin eps))))))))))) (/ (sin x) (cos x)))
1.1s
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
1.1s
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
661.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
614.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))

regimes4.7s

Accuracy

Total 26.8b remaining (16.7%)

4.5b86.8%quadm (p42, negative)
4.3b81.8%quad2m (problem 3.2.1, negative)
4.2b84.9%quadp (p42, positive)
3.3b6.2%expq3 (problem 3.4.2)
1.4b88.3%2nthrt (problem 3.4.6)

bsearch3.6s

localize2.8s

rewrite2.8s

Algorithm
114×rewrite-expression-head
Calls

347 calls:

Slowest
84.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
82.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
74.0ms
(cbrt (* (* (* (fma -2/3 (* eps eps) -2) eps) (* (fma -2/3 (* eps eps) -2) eps)) (* (* (cbrt (fma -2/3 (* eps eps) -2)) (cbrt (fma -2/3 (* eps eps) -2))) (* (cbrt (fma -2/3 (* eps eps) -2)) eps))))
60.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
54.0ms
(* (* (* (fma -2/3 (* eps eps) -2) eps) (* (fma -2/3 (* eps eps) -2) eps)) (* (fma -2/3 (* eps eps) -2) eps))
Rules
1406×*-un-lft-identity
1365×add-sqr-sqrt
1225×add-cube-cbrt
617×pow1
616×add-exp-log
599×prod-diff
567×add-cbrt-cube
442×add-log-exp
431×times-frac
347×log1p-expm1-u
341×expm1-log1p-u
340×insert-posit16
281×sqrt-prod
257×div-inv
244×associate-*l*
203×fma-neg
198×associate-*r*
181×cbrt-prod
151×associate-/r*
129×associate-/l*
128×sqrt-div flip-+ flip3-+
117×associate-/r/
97×pow-prod-down
93×prod-exp
91×associate-*r/
90×flip3-- flip--
88×tan-quot cbrt-unprod
78×frac-times
62×pow1/3 frac-2neg clear-num distribute-lft-out--
60×pow1/2
59×*-commutative sub-neg
58×unpow-prod-down associate-*l/
57×cbrt-div
54×associate-+l+ distribute-lft-out
53×div-exp
51×fma-def
50×difference-of-squares
48×log-prod
45×cbrt-undiv pow-prod-up
40×diff-log
37×fma-udef
33×pow-plus rem-sqrt-square
30×rec-exp neg-mul-1
29×associate-/l/
27×pow-flip
26×pow2
25×frac-sub
23×div-sub
20×distribute-rgt-neg-in distribute-lft-neg-in
19×inv-pow
17×log-pow
16×pow-unpow frac-add
15×+-commutative
14×sum-log
13×exp-sum
10×neg-sub0 expm1-udef log-div
expm1-log1p sqrt-unprod rem-log-exp
associate--l- exp-prod associate--l+
pow3 difference-of-sqr-1 log1p-udef
associate-+r+ log1p-expm1 pow-to-exp associate-+l- sin-mult
quot-tan distribute-rgt-in sub-div rem-square-sqrt cos-sum distribute-lft-in rem-cbrt-cube
exp-diff sin-sum log1p-def exp-neg pow-exp distribute-frac-neg +.c-commutative sqr-sin pow-pow rem-exp-log tan-sum distribute-rgt-out--
diff-atan associate--r+ frac-2neg-c diff-sin diff-cos un-div-inv associate--r- expm1-def

end19.0ms