Details

simplify27.2m

Calls

16242 calls:

Slowest

2.7s	(- (+ (* 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)))))))))))))))))))
1.9s	(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	(/ (* (* (* (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)))))
1.7s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
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)))

sample5.1m

Algorithm

56×	intervals
16×	halfpoints

Results

1.1m	67565×	body	1280	valid
39.8s	17315×	body	2560	valid
27.2s	41847×	body	640	valid
14.4s	12696×	body	10240	exit
12.0s	93651×	body	80	valid
8.1s	20628×	body	320	valid
7.4s	62797×	body	80	nan
2.8s	10586×	body	160	valid
1.9s	47454×	pre	80	true
760.0ms	675×	body	1280	nan
608.0ms	657×	body	640	nan
565.0ms	469×	body	5120	valid
406.0ms	179×	body	160	nan
250.0ms	381×	body	320	nan

prune2.8m

series37.7s

Calls

365 calls:

Slowest

1.6s	(- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))) (/ (sin x) (cos x)))
1.2s	(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)))
752.0ms	(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
596.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
510.0ms	(* (cbrt (/ (log1p (- x)) (log1p x))) (cbrt (/ (log1p (- x)) (log1p x))))

rewrite9.5s

Algorithm

115×	rewrite-expression-head

Calls

365 calls:

Slowest

448.0ms	(cbrt (* (* (* (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x)))) (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))) (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))) (expm1 (* a x))))
439.0ms	(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
319.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))) (cbrt (* (* (cbrt x) (cbrt x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))
213.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
167.0ms	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))

Rules

8179×	`*-un-lft-identity`
7503×	`add-sqr-sqrt`
7460×	`times-frac`
5871×	`add-cube-cbrt`
3403×	`prod-diff`
2948×	`sqrt-prod`
1469×	`pow1`
1148×	`add-exp-log`
984×	`add-cbrt-cube`
770×	`associate-l`
716×	`distribute-lft-out`
567×	`difference-of-squares`
557×	`add-log-exp`
532×	`div-inv`
472×	`associate-+l+`
467×	`distribute-lft-out--`
460×	`cbrt-prod`
426×	`associate-r`
360×	`log1p-expm1-u`
358×	`expm1-log1p-u`
357×	`insert-posit16`
340×	`fma-neg`
337×	`log-prod` `associate-/r/`
307×	`associate-/l*`
294×	`associate-/r*`
292×	`pow-prod-down`
279×	`prod-exp`
274×	`unpow-prod-down`
263×	`swap-sqr`
243×	`pow-prod-up`
241×	`cbrt-unprod`
234×	`distribute-rgt-neg-in`
208×	`div-exp`
184×	`flip-+` `flip3-+`
166×	`distribute-lft-neg-in`
159×	`pow-sqr`
156×	`sqrt-div` `unswap-sqr`
149×	`cbrt-undiv`
146×	`flip3--` `flip--`
130×	`exp-sum`
122×	`pow-plus`
111×	`sqrt-pow1`
107×	`fma-def`
101×	`pow1/2`
99×	`tan-quot`
98×	`pow-unpow`
95×	`associate-*r/`
91×	`pow2`
87×	`sqr-pow`
85×	`frac-times`
78×	`*-commutative`
71×	`diff-log`
69×	`associate-*l/`
64×	`sub-neg`
62×	`pow-flip`
61×	`pow1/3`
60×	`frac-2neg` `clear-num`
55×	`neg-mul-1`
47×	`cbrt-div`
41×	`associate-/l/`
39×	`rem-sqrt-square`
36×	`sum-log`
35×	`rem-log-exp`
33×	`1-exp` `rec-exp`
32×	`fma-udef`
31×	`log-pow`
23×	`frac-add`
21×	`+-commutative` `exp-prod`
20×	`div-sub` `hypot-def`
19×	`cube-prod`
16×	`inv-pow`
15×	`log-div`
14×	`associate--l+`
13×	`frac-sub` `pow-exp` `pow-to-exp`
10×	`pow-div`
9×	`associate--l-` `distribute-rgt-in` `difference-of-sqr-1` `pow-pow` `distribute-lft-in`
8×	`neg-sub0` `associate-+r+`
7×	`neg-log` `sqrt-unprod`
5×	`cos-mult` `associate--r+` `cube-mult`
4×	`expm1-log1p` `expm1-udef` `pow3` `sum-cubes` `distribute-neg-frac` `distribute-rgt-out--` `rem-square-sqrt` `sin-mult`
3×	`sin-sum` `sqr-cos` `rem-cbrt-cube`
2×	`log1p-def` `distribute-frac-neg` `+.c-commutative` `sqr-sin` `un-div-inv` `frac-2neg-c` `associate-+l-` `cos-sum` `tan-sum` `log1p-udef`
1×	`distribute-lft-neg-out` `diff-atan` `associate-+r-` `rem-cube-cbrt` `log1p-expm1` `unpow3` `sub0-neg` `sub-div` `diff-sin` `diff-cos` `expm1-def`

localize4.8s

regimes4.4s

Accuracy

Total 21.5b remaining (19.9%)

4.6b	83.6%	quadm (p42, negative)
4.1b	85.5%	quadp (p42, positive)
3.3b	0%	expq3 (problem 3.4.2)
3.2b	87.5%	quad2m (problem 3.2.1, negative)
1.3b	89.2%	2nthrt (problem 3.4.6)

Details

simplify27.2m

sample5.1m

prune2.8m

series37.7s

rewrite9.5s

localize4.8s

regimes4.4s

bsearch2.9s

end1.0ms