Details

simplify8.8m

Calls

6235 calls:

Slowest
2.1s
(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)))
1.7s
(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)))
1.3s
(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
1.2s
(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
957.0ms
(- (+ (/ (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)))))))))))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66345×body1280valid
42.0s18017×body2560valid
26.8s42393×body640valid
12.0s12720×body10240exit
10.6s93427×body80valid
8.9s63700×body80nan
8.7s20654×body320valid
3.2s10654×body160valid
1.9s47219×pre80true
758.0ms699×body1280nan
549.0ms445×body5120valid
495.0ms625×body640nan
164.0ms347×body320nan
49.0ms176×body160nan

prune1.6m

series39.5s

Calls

357 calls:

Slowest
676.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))
671.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (- (tan x)))
605.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
554.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
537.0ms
(/ (- x (sin x)) (- x (tan x)))

regimes4.3s

Accuracy

Total 24.6b remaining (19.7%)

5.0b82.6%quad2m (problem 3.2.1, negative)
5.0b82.4%quadm (p42, negative)
4.4b83.4%quadp (p42, positive)
2.9b16.3%expq3 (problem 3.4.2)
1.3b88.7%2nthrt (problem 3.4.6)

localize3.3s

rewrite3.3s

Algorithm
115×rewrite-expression-head
Calls

357 calls:

Slowest
128.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
124.0ms
(- (pow (cbrt (+ x 1)) 3) (pow (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))) 3))
98.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))
88.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
61.0ms
(cbrt (* (* (* (cbrt (* (expm1 (* a x)) (expm1 (* a x)))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (cbrt (* (expm1 (* a x)) (expm1 (* a x))))) (expm1 (* a x))))
Rules
1821×*-un-lft-identity
1782×add-sqr-sqrt
1608×add-cube-cbrt
840×prod-diff
742×times-frac
609×pow1
597×add-exp-log
556×add-cbrt-cube
547×sqrt-prod
451×add-log-exp
355×log1p-expm1-u
351×expm1-log1p-u
349×insert-posit16
319×div-inv
313×cbrt-prod
290×associate-*l*
278×unpow-prod-down
215×associate-/r*
209×associate-*r*
205×fma-neg
171×cube-prod
160×associate-/l*
149×associate-/r/
132×sqrt-div
128×flip-+ flip3-+
98×log-prod
97×distribute-lft-out
96×flip3-- flip--
87×pow-prod-down frac-times
81×difference-of-squares
80×associate-*r/
78×prod-exp
75×pow1/2
74×cbrt-unprod
73×associate-*l/
72×frac-2neg clear-num
68×*-commutative
64×tan-quot
62×log-pow
60×sub-neg
59×frac-sub associate-/l/
57×pow1/3
55×distribute-lft-out--
52×cbrt-div
49×exp-prod
48×pow-prod-up
46×div-exp diff-log
43×fma-def
42×cbrt-undiv
37×rem-sqrt-square
33×pow-flip
32×unpow3 cube-mult neg-mul-1
31×pow-unpow
29×pow-plus fma-udef
26×associate-+l+ frac-add
25×pow2
23×rec-exp
22×exp-sum inv-pow un-div-inv
19×div-sub
13×+-commutative
11×rem-log-exp
10×pow-to-exp sin-mult
associate--l- sqrt-unprod log-div
neg-sub0 expm1-udef
expm1-log1p sum-log rem-square-sqrt
associate--l+ difference-of-sqr-1 sub-div associate--r+
pow-pow distribute-rgt-out--
pow-exp log1p-udef pow3 rem-exp-log
quot-tan sin-sum associate-+r+ log1p-def log1p-expm1 distribute-frac-neg distribute-rgt-in +.c-commutative sqr-sin tan-sum frac-2neg-c cos-sum distribute-lft-in rem-cbrt-cube
exp-diff diff-atan rem-cube-cbrt sqrt-undiv difference-cubes sub0-neg associate-+l- diff-sin diff-cos expm1-def

bsearch2.0s

end1.0ms