Details

simplify33.4m

Calls

18090 calls:

Slowest
2.0s
(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 2) 2) (* (* (+ (sqrt (fma b b (* (* a c) -4))) b) (+ (sqrt (fma b b (* (* a c) -4))) b)) (+ (sqrt (fma b b (* (* a c) -4))) b))))
2.0s
(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)))
1.8s
(/ (* (* (* (* 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))))
1.8s
(/ (* (* (* (* a a) a) (* (* -4 -4) -4)) (* (* c c) 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))))

sample5.1m

Algorithm
55×intervals
16×halfpoints
Results
1.1m65422×body1280valid
42.1s16928×body2560valid
27.7s41966×body640valid
15.1s12720×body10240exit
11.8s87590×body80valid
9.2s20421×body320valid
5.5s60758×body80nan
3.5s10533×body160valid
1.9s47219×pre80true
1.3s699×body1280nan
484.0ms625×body640nan
330.0ms340×body5120valid
185.0ms347×body320nan
58.0ms176×body160nan

prune2.9m

series40.6s

Calls

370 calls:

Slowest
828.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
725.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (- (tan x)))
687.0ms
(cbrt c)
601.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
597.0ms
(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))

rewrite9.7s

Algorithm
116×rewrite-expression-head
Calls

370 calls:

Slowest
208.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
192.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
156.0ms
(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
152.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (/ 1 (- x 1))))
127.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
Rules
35462×times-frac
23130×*-un-lft-identity
21374×add-sqr-sqrt
20082×add-cube-cbrt
11331×prod-diff
5796×sqrt-prod
2255×distribute-rgt-neg-in
2224×distribute-lft-neg-in
1424×div-inv
1392×distribute-lft-out
1370×pow1
1121×add-exp-log
1006×add-cbrt-cube
741×neg-mul-1
702×unpow-prod-down
645×cbrt-prod
543×add-log-exp
499×associate-*l*
482×fma-neg
472×associate-+l+
406×associate-*r*
375×difference-of-squares
372×associate-/l*
368×log1p-expm1-u
363×expm1-log1p-u
362×insert-posit16
332×associate-/r*
308×log-prod
280×swap-sqr
267×associate-/r/
265×distribute-lft-out--
260×prod-exp
254×pow-prod-down
250×pow-prod-up
231×cbrt-unprod
213×div-exp
208×sqr-pow
207×cube-prod
179×sqrt-pow1 unswap-sqr
174×flip-+ flip3-+
169×cbrt-undiv
146×pow-sqr
138×exp-prod
136×sqrt-div
129×pow1/2
126×log-pow
125×fma-def
110×pow-plus
100×flip3-- flip--
97×pow-unpow
76×*-commutative
75×pow2
73×tan-quot associate-*r/
71×frac-2neg clear-num
70×frac-times
66×diff-log
65×pow1/3
64×associate-*l/
63×sub-neg
59×associate-/l/
58×exp-sum
55×frac-sub
52×pow-flip
50×cbrt-div
40×rem-sqrt-square
36×unpow3 cube-mult
32×fma-udef
30×frac-add
29×sum-log 1-exp rec-exp
22×inv-pow div-sub
21×un-div-inv
19×rem-log-exp
18×+-commutative
14×associate--l+
12×pow-exp
10×pow-pow pow-to-exp sin-mult
distribute-rgt-in difference-of-sqr-1 distribute-lft-in
associate--l- associate--r+ hypot-def log-div
neg-sub0 expm1-udef distribute-rgt-out--
expm1-log1p sqrt-unprod
sub-div
pow3 distribute-neg-frac rem-square-sqrt e-exp-1
associate-+r+ log1p-udef neg-log
pow-div sin-sum log1p-expm1 distribute-frac-neg +.c-commutative sqr-sin tan-sum frac-2neg-c exp-to-pow rem-exp-log associate-+l- log1p-def cos-sum rem-cbrt-cube
distribute-lft-neg-out exp-diff diff-atan rem-cube-cbrt sqrt-undiv sub0-neg diff-sin difference-cubes diff-cos expm1-def

localize5.0s

regimes3.8s

Accuracy

Total 19.0b remaining (16.7%)

5.0b82.6%quad2m (problem 3.2.1, negative)
3.7b-9.6%expq3 (problem 3.4.2)
3.4b85.7%quadp (p42, positive)
1.3b88.7%2nthrt (problem 3.4.6)
0.9b86.3%2tan (problem 3.3.2)

bsearch2.1s

end1.0ms