Details

simplify8.4m

Calls

5708 calls:

Slowest
1.8s
(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)))
1.7s
(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)))
1.1s
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
949.0ms
(- (+ (/ (log (/ -1 x)) (* x (pow (- (log -1) (log (/ -1 x))) 2))) (/ 1 (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (+ (/ (log (/ -1 x)) (- (log -1) (log (/ -1 x)))) (+ (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 3))) (+ (/ 1 (* x (- (log -1) (log (/ -1 x))))) (+ (* 1/2 (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (* 1/2 (/ 1 (* (pow x 2) (- (log -1) (log (/ -1 x)))))))))))
939.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))

sample4.9m

Algorithm
56×intervals
16×halfpoints
Results
1.0m66717×body1280valid
37.7s17445×body2560valid
25.5s42249×body640valid
13.3s12614×body10240exit
11.6s93619×body80valid
8.5s20720×body320valid
6.9s62794×body80nan
3.1s10575×body160valid
2.1s47386×pre80true
924.0ms628×body1280nan
586.0ms672×body640nan
536.0ms439×body5120valid
215.0ms362×body320nan
58.0ms193×body160nan

prune1.5m

series24.2s

Calls

348 calls:

Slowest
1.1s
(- (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)))
997.0ms
(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)))
473.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
452.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))
423.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

regimes4.2s

Accuracy

Total 20.2b remaining (16.1%)

4.3b84.3%quadm (p42, negative)
4.3b84.7%quadp (p42, positive)
3.2b4.5%expq3 (problem 3.4.2)
1.6b86.8%2nthrt (problem 3.4.6)
1.0b93.1%2tan (problem 3.3.2)

rewrite3.0s

Algorithm
112×rewrite-expression-head
Calls

348 calls:

Slowest
72.0ms
(/ (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))
60.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
59.0ms
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) 2) a)
56.0ms
(* (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) 2) (/ 1 a))
55.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
Rules
1619×*-un-lft-identity
1477×add-sqr-sqrt
1320×add-cube-cbrt
788×prod-diff
619×pow1
587×add-exp-log
549×add-cbrt-cube
479×add-log-exp
473×times-frac
360×sqrt-prod
347×log1p-expm1-u
344×div-inv
343×expm1-log1p-u
342×insert-posit16
275×associate-/r/
253×associate-*r/
244×associate-*l*
227×fma-neg
213×frac-times
211×associate-*r*
209×frac-add
207×associate-*l/
169×un-div-inv
156×distribute-lft-out
155×frac-sub
150×associate-/l*
145×unpow-prod-down
137×flip-+
136×flip3-+
135×flip--
134×flip3--
126×associate-/r*
112×cbrt-prod
110×fma-def
100×pow-prod-down
91×prod-exp
90×cube-prod cbrt-div
86×tan-quot
85×sqrt-div
83×cbrt-unprod
68×sub-neg
67×pow1/2
66×difference-of-squares
64×*-commutative
61×frac-2neg clear-num
56×sub-div distribute-lft-out--
50×neg-mul-1
48×diff-log
42×fma-udef
40×pow-prod-up
37×associate-/l/
36×log-prod
35×div-exp pow1/3
32×cbrt-undiv
30×associate-+l+
29×rem-sqrt-square
28×+-commutative pow-plus
25×pow-flip rec-exp
24×pow2
23×sum-log
21×div-sub
18×distribute-rgt-neg-in inv-pow log-pow distribute-lft-neg-in
16×pow-unpow
12×neg-sub0 log-div
10×sqrt-unprod
associate--l-
expm1-udef associate-+r+ rem-square-sqrt rem-log-exp
expm1-log1p distribute-rgt-out-- sin-mult associate--l+ sum-cubes
difference-of-sqr-1 pow-to-exp sqr-sin associate-+l-
pow3 distribute-rgt-in distribute-lft-in cube-div cube-mult
log1p-expm1 unpow3 rem-cbrt-cube log1p-udef
exp-diff sin-sum exp-neg pow-exp distribute-frac-neg +.c-commutative pow-pow tan-sum log1p-def cos-sum
diff-atan associate-+r- rem-cube-cbrt associate--r+ sub0-neg diff-sin diff-cos associate--r- expm1-def

localize2.8s

bsearch2.3s

end1.0ms