Details

simplify31.1m

Calls

16192 calls:

Slowest

1.8s	(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	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.4s	(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.2s	(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))

sample5.0m

Algorithm

54×	intervals
16×	halfpoints

Results

1.1m	65249×	body	1280	valid
41.0s	17581×	body	2560	valid
27.2s	38685×	body	640	valid
15.3s	12771×	body	10240	exit
10.9s	85755×	body	80	valid
8.9s	18687×	body	320	valid
6.1s	55360×	body	80	nan
2.8s	9694×	body	160	valid
1.9s	47339×	pre	80	true
773.0ms	645×	body	1280	nan
595.0ms	479×	body	5120	valid
505.0ms	695×	body	640	nan
187.0ms	354×	body	320	nan
50.0ms	192×	body	160	nan

prune2.5m

series35.6s

Calls

359 calls:

Slowest

776.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
710.0ms	(cbrt x)
646.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
480.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
460.0ms	(log (pow x (/ (/ 1 n) 2)))

rewrite9.0s

Algorithm

113×	rewrite-expression-head

Calls

359 calls:

Slowest

486.0ms	(+ (- (exp x) 2) (exp (- x)))
276.0ms	(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
254.0ms	(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
227.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
180.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

Rules

18369×	`times-frac`
14337×	`*-un-lft-identity`
13715×	`add-sqr-sqrt`
11908×	`add-cube-cbrt`
8095×	`sqrt-prod`
7997×	`prod-diff`
1438×	`pow1`
1244×	`add-exp-log`
1140×	`div-inv`
1135×	`distribute-rgt-in` `distribute-lft-in`
973×	`add-cbrt-cube`
753×	`distribute-lft-out`
606×	`difference-of-squares`
591×	`fma-neg`
538×	`add-log-exp`
467×	`associate-/r/`
462×	`sqrt-div`
418×	`associate-r`
405×	`distribute-lft-out--`
403×	`associate-/l*`
398×	`associate-l`
358×	`log1p-expm1-u`
353×	`expm1-log1p-u`
352×	`insert-posit16`
316×	`unpow-prod-down`
309×	`associate-/r*`
305×	`div-exp`
286×	`prod-exp`
262×	`pow-prod-up`
255×	`pow-prod-down`
247×	`associate-+l+`
230×	`flip-+` `flip3-+`
219×	`log-prod`
207×	`cbrt-unprod`
203×	`cbrt-prod`
187×	`swap-sqr`
181×	`cbrt-undiv`
168×	`pow-sqr`
147×	`flip3--` `flip--`
146×	`unswap-sqr`
133×	`fma-def`
131×	`pow-plus`
124×	`pow-unpow`
123×	`pow-flip`
117×	`distribute-rgt-neg-in`
107×	`sqr-pow`
96×	`pow2`
91×	`distribute-lft-neg-in`
80×	`exp-prod`
74×	`sqrt-pow1` `frac-2neg` `clear-num` `log-pow`
73×	`tan-quot`
68×	`exp-sum`
63×	`pow1/2`
62×	`sub-neg` `diff-log`
60×	`*-commutative`
56×	`frac-times`
53×	`associate-*l/`
48×	`associate-/l/`
46×	`associate-*r/`
44×	`pow-exp`
42×	`1-exp` `rec-exp` `fma-udef`
39×	`pow1/3`
35×	`sum-log`
31×	`pow-to-exp` `rem-log-exp`
30×	`neg-mul-1` `rem-sqrt-square`
27×	`+-commutative`
24×	`cbrt-div`
22×	`frac-sub`
19×	`inv-pow` `div-sub`
18×	`frac-add`
14×	`associate--r+` `log-div`
13×	`e-exp-1`
9×	`associate--l+` `difference-of-sqr-1`
8×	`pow-div` `pow-pow` `hypot-def`
7×	`expm1-log1p` `neg-sub0` `expm1-udef` `associate--l-`
6×	`distribute-neg-frac`
5×	`neg-log` `log1p-def` `sin-mult` `log1p-udef`
4×	`log1p-expm1`
3×	`sqrt-unprod` `distribute-rgt-out--` `associate-+l-` `rem-square-sqrt`
2×	`exp-diff` `sin-sum` `associate-+r+` `pow3` `distribute-frac-neg` `sub-div` `+.c-commutative` `distribute-lft-neg-out` `sqr-sin` `un-div-inv` `tan-sum` `exp-neg` `rem-exp-log` `cos-sum` `rem-cbrt-cube` `unpow1/3` `associate--r-`
1×	`remove-posit16` `diff-atan` `cube-unmult` `frac-2neg-c` `sub0-neg` `diff-sin` `diff-cos` `expm1-def` `distribute-rgt-out`

localize4.0s

regimes3.9s

Accuracy

Total 21.2b remaining (17.2%)

5.2b	81.3%	quadm (p42, negative)
3.5b	87.2%	quadp (p42, positive)
3.4b	0%	expq3 (problem 3.4.2)
2.3b	79.8%	2nthrt (problem 3.4.6)
1.4b	94.2%	quad2p (problem 3.2.1, positive)

Details

simplify31.1m

sample5.0m

prune2.5m

series35.6s

rewrite9.0s

localize4.0s

regimes3.9s

bsearch3.1s

end1.0ms