Details

simplify25.3m

Calls

15807 calls:

Slowest

1.7s	(/ (* (* (* (- 0 (* a (* c -4))) -1/2) (* (- 0 (* a (* c -4))) -1/2)) (* (- 0 (* a (* c -4))) -1/2)) (* (* (* (- b (sqrt (fma a (* c -4) (* b b)))) a) (* (- b (sqrt (fma a (* c -4) (* b b)))) a)) (* (- b (sqrt (fma a (* c -4) (* b b)))) 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)))
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)))
1.5s	(/ (* (* (* a c) (* a c)) (* a c)) (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
1.4s	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))

sample5.1m

Algorithm

56×	intervals
16×	halfpoints

Results

1.1m	66418×	body	1280	valid
39.9s	17056×	body	2560	valid
26.3s	42807×	body	640	valid
14.9s	12984×	body	10240	exit
12.7s	93471×	body	80	valid
10.4s	20760×	body	320	valid
7.3s	63052×	body	80	nan
3.9s	11201×	body	160	valid
2.1s	47573×	pre	80	true
545.0ms	670×	body	1280	nan
539.0ms	455×	body	5120	valid
396.0ms	649×	body	640	nan
153.0ms	372×	body	320	nan
61.0ms	190×	body	160	nan

prune2.8m

series36.8s

Calls

359 calls:

Slowest

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)))
700.0ms	(cbrt (* (/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))) (/ (expm1 (* (+ a b) eps)) (* (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))))))
664.0ms	(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
648.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
597.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))

rewrite10.0s

Algorithm

115×	rewrite-expression-head

Calls

359 calls:

Slowest

420.0ms	(- (/ 1 x) (/ 1 (tan x)))
266.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
253.0ms	(* eps (* (cbrt (- (* (* eps -2/3) eps) 2)) (cbrt (- (* (* eps -2/3) eps) 2))))
181.0ms	(* (sin (* eps 1/2)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
151.0ms	(+ (- (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

Rules

7226×	`*-un-lft-identity`
6809×	`add-sqr-sqrt`
5891×	`times-frac`
5157×	`add-cube-cbrt`
3413×	`prod-diff`
1826×	`sqrt-prod`
1666×	`pow1`
1279×	`add-exp-log`
1077×	`add-cbrt-cube`
618×	`unpow-prod-down`
598×	`distribute-lft-out`
562×	`difference-of-squares`
548×	`add-log-exp`
524×	`cbrt-prod`
485×	`associate-r`
448×	`associate-l`
422×	`div-inv`
418×	`distribute-lft-out--`
390×	`fma-neg`
358×	`log1p-expm1-u`
353×	`expm1-log1p-u` `insert-posit16`
345×	`pow-prod-down`
342×	`prod-exp`
331×	`associate-/r/`
308×	`associate-/l*`
296×	`pow-prod-up`
280×	`cbrt-unprod`
268×	`associate-/r*`
265×	`associate-+l+`
255×	`div-exp`
215×	`swap-sqr`
202×	`sqr-pow`
201×	`log-prod`
186×	`pow-sqr`
178×	`flip3--` `flip--`
177×	`unswap-sqr`
174×	`cbrt-undiv`
149×	`pow-plus`
144×	`flip-+` `flip3-+`
139×	`associate-*r/`
129×	`sqrt-div`
120×	`fma-def`
108×	`pow2`
101×	`tan-quot`
100×	`sqrt-pow1`
86×	`frac-times`
85×	`associate-*l/`
82×	`pow1/2`
81×	`*-commutative`
80×	`sub-neg`
76×	`diff-log`
74×	`pow-unpow`
71×	`distribute-rgt-neg-in`
64×	`frac-2neg` `clear-num`
62×	`pow-flip`
59×	`exp-neg`
52×	`distribute-lft-neg-in`
51×	`associate-+r+`
50×	`1-exp` `rec-exp` `log-pow`
44×	`frac-sub` `cbrt-div`
42×	`neg-sub0` `rem-sqrt-square`
39×	`exp-diff`
35×	`exp-prod`
34×	`distribute-rgt-in` `associate-/l/` `distribute-lft-in`
33×	`fma-udef`
32×	`pow1/3`
27×	`inv-pow`
26×	`sum-log`
24×	`un-div-inv`
19×	`cube-prod` `+-commutative`
18×	`sub-div` `pow-pow` `div-sub` `log-div`
17×	`neg-mul-1`
14×	`frac-add`
13×	`associate--l+` `rem-log-exp`
12×	`pow-exp` `pow-to-exp`
9×	`difference-of-sqr-1` `sin-mult`
8×	`hypot-def`
7×	`expm1-udef`
6×	`cos-mult` `cube-mult`
5×	`expm1-log1p` `sin-sum` `unpow3` `sqrt-unprod` `distribute-rgt-out--` `log1p-def`
4×	`associate--l-` `pow3` `associate--r+` `distribute-neg-frac` `associate-+l-` `rem-cbrt-cube`
3×	`rem-cube-cbrt` `sin-cos-mult` `neg-log` `cos-sum` `pow-div`
2×	`distribute-lft-neg-out` `+.c-commutative` `sqr-sin` `tan-sum` `rem-square-sqrt` `cube-div`
1×	`diff-atan` `associate-+r-` `sub0-neg` `log1p-udef` `distribute-frac-neg` `sum-cubes` `exp-to-pow` `diff-sin` `sqr-cos` `diff-cos` `expm1-def`

localize4.6s

regimes4.2s

Accuracy

Total 24.0b remaining (17.6%)

5.4b	80.8%	quad2p (problem 3.2.1, positive)
5.0b	81.9%	quadp (p42, positive)
3.4b	0%	expq3 (problem 3.4.2)
2.9b	60.2%	2tan (problem 3.3.2)
1.4b	94.2%	quadm (p42, negative)

Details

simplify25.3m

sample5.1m

prune2.8m

series36.8s

rewrite10.0s

localize4.6s

regimes4.2s

bsearch2.9s

end41.0ms