Details

simplify35.2m

Calls

20126 calls:

Slowest
2.8s
(- (+ (* 4/9 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 14))) 1/3))) (+ (* 8/3 (* (/ (pow (log -1) 5) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 2/3 (* (/ 1 x) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 5/9 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 2)) 1/3) (+ (* 1/3 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 2/3 (* (/ 1 x) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 2 (* (/ (pow (log -1) 2) x) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 80/9 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)) (+ (* 1/3 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 8/3 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 17) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 2/3 (* (/ (pow (log -1) 2) x) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 1/3 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 4/9 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 14) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)) (+ (* 1/3 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ 1 (* (pow (log (/ -1 x)) 4) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 1/3 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 8/9 (* (/ (pow (log -1) 5) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 20))) 1/3))) (* 32/9 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3)))))))))))))))))))))) (+ (* 4/9 (* (/ (pow (log -1) 6) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)) (+ (* 20/3 (* (/ (pow (log -1) 4) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 28/9 (* (/ (pow (log -1) 4) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* 4/9 (* (/ (pow (log -1) 4) (pow x 2)) (pow (/ 1 (* (pow (log (/ -1 x)) 4) (pow (- (log -1) (log (/ -1 x))) 14))) 1/3))) (+ (* 20/3 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 14) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 4/9 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 20) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 1/3 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 2/3 (* (/ (pow (log -1) 3) x) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 4/3 (* (/ (log -1) x) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 8/9 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* 14/9 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 2/3 (* (/ (log -1) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 8/9 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* 2/3 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (* 2 (* (/ (log -1) x) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)))))))))))))))))))
1.6s
(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)))
1.6s
(/ (/ (/ (* (* (* (* a a) a) (* (* 4 4) 4)) (* (* c c) c)) (* (* (- (sqrt (fma a (* c -4) (* b b))) b) (- (sqrt (fma a (* c -4) (* b b))) b)) (- (sqrt (fma a (* c -4) (* b b))) b))) (* (* 2 2) 2)) (* (* a a) a))
1.6s
(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) (* a 4)) (* a 4)) (* (* c c) c)) (* (* (- (sqrt (fma a (* c -4) (* b b))) b) (- (sqrt (fma a (* c -4) (* b b))) b)) (- (sqrt (fma a (* c -4) (* b b))) b))) (* (* 2 2) 2)) (* (* a a) a))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67132×body1280valid
40.4s17267×body2560valid
25.6s42290×body640valid
14.6s12984×body10240exit
12.1s94122×body80valid
8.4s20523×body320valid
6.6s62817×body80nan
3.5s10502×body160valid
2.2s47598×pre80true
979.0ms461×body5120valid
594.0ms680×body1280nan
391.0ms690×body640nan
138.0ms415×body320nan
36.0ms183×body160nan

prune2.5m

series42.0s

Calls

349 calls:

Slowest
1.4s
(log (exp (* (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (expm1 (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))))
1.3s
(fma (* (tan x) (tan eps)) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (/ (+ (tan eps) (tan x)) (- (pow 1 3) (pow (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) 3))) (+ (* 1 1) (+ (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (* 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (tan x))))
1.1s
(fma (* (tan x) (tan eps)) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x)))
984.0ms
(fma (/ (+ (tan eps) (tan x)) (- (pow 1 3) (pow (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) 3))) (+ (* 1 1) (+ (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (* 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (tan x)))
652.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))

rewrite8.3s

Algorithm
115×rewrite-expression-head
Calls

349 calls:

Slowest
343.0ms
(- (exp x) 2)
194.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
146.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
109.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
106.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
Rules
7308×*-un-lft-identity
6763×add-sqr-sqrt
6563×times-frac
5149×add-cube-cbrt
3072×prod-diff
1690×pow1
1611×sqrt-prod
1178×add-exp-log
1066×add-cbrt-cube
628×distribute-lft-out
604×difference-of-squares
518×cbrt-prod
512×add-log-exp
459×div-inv
456×associate-*l*
431×distribute-lft-out--
424×unpow-prod-down
412×associate-*r*
398×associate-/l*
385×associate-/r/
356×pow-prod-down
349×fma-neg
346×log1p-expm1-u
342×expm1-log1p-u
341×insert-posit16
305×pow-prod-up
293×prod-exp
275×cbrt-unprod
272×associate-/r*
248×associate-+l+
233×div-exp
224×swap-sqr
199×pow-sqr
197×log-prod
188×cbrt-undiv
159×flip3-- unswap-sqr flip--
158×tan-quot
155×pow-plus
152×flip-+ flip3-+
141×sqr-pow
137×distribute-rgt-neg-in
112×pow2
105×distribute-lft-neg-in
92×sqrt-div
89×frac-times
88×fma-def
84×pow-unpow
81×log-pow
80×associate-*r/
77×associate-*l/
74×*-commutative
70×sqrt-pow1
65×pow1/3 exp-prod
64×pow1/2
62×diff-log
61×frac-2neg cbrt-div clear-num
59×sub-neg
49×neg-mul-1
38×associate-/l/
29×sum-log rem-sqrt-square fma-udef
25×1-exp rec-exp
23×pow-pow
21×div-sub
20×pow-flip
19×+-commutative distribute-rgt-out
18×rem-log-exp
15×cube-div
14×inv-pow
13×log-div
12×pow-exp
10×frac-sub frac-add
9×difference-of-sqr-1 exp-to-pow
8×expm1-udef neg-sub0 distribute-rgt-in pow-to-exp distribute-lft-in
7×cube-prod associate--r+
6×expm1-log1p rem-cube-cbrt
5×associate--l- log1p-udef
4×pow3 neg-log sqrt-unprod rem-cbrt-cube sin-mult
3×exp-diff associate-+r+ unpow3 distribute-frac-neg sqr-sin distribute-rgt-out-- rem-exp-log cube-mult
2×sin-sum distribute-rgt1-in distribute-lft1-in log1p-expm1 +.c-commutative hypot-udef un-div-inv tan-sum frac-2neg-c exp-neg associate-+l- log1p-def hypot-def rem-square-sqrt cos-sum
1×diff-atan cos-mult exp-sum associate--l+ sub-div diff-sin diff-cos expm1-def

localize4.1s

regimes3.4s

Accuracy

Total 13.0b remaining (13.2%)

Threshold costs 7.9b (8%)

3.5b0%expq3 (problem 3.4.2)
1.6b86.3%2nthrt (problem 3.4.6)
1.0b95.9%quad2p (problem 3.2.1, positive)
1.0b95.9%quad2m (problem 3.2.1, negative)
0.9b96.1%quadm (p42, negative)

bsearch2.1s

end1.0ms