Details

simplify5.5m (44.2%)

sample3.8m (30.6%)

Algorithm

77×

intervals

Results

1.2m	43893×	body	1280	valid
45.9s	16582×	body	10240	exit
28.4s	30581×	body	640	valid
19.2s	202585×	body	80	valid
14.4s	151622×	body	80	nan
11.3s	27577×	body	320	valid
9.0s	35869×	body	160	valid
6.1s	152511×	pre	80	true
2.3s	2963×	body	2560	valid
731.0ms	4146×	pre	10240	exit
719.0ms	7748×	body	160	nan
118.0ms	210×	body	5120	valid

prune1.6m (13.1%)

series49.7s (6.6%)

Calls

423 calls:

1.8s	(* (hypot (* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
1.2s	(- (pow (cos delta) 3) (pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3))
876.0ms	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
702.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
650.0ms	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)

regimes21.8s (2.9%)

Accuracy

Total 51.4b remaining (30.6%)

Threshold costs 4.5b (2.7%)

7.5b	46.7%	Quadratic roots, narrow range
6.7b	51.1%	Cubic critical, narrow range
6.6b	11.3%	Quadratic roots, medium range
5.5b	52.9%	Quotient of products
5.0b	32.3%	Cubic critical, medium range

rewrite13.4s (1.8%)

Algorithm

138×	rewrite-expression-head

Calls

423 calls:

469.0ms	(* (- (- (/ (* m 1.0) v) (/ (* m m) v)) 1.0) m)
452.0ms	(* (- (- (/ (* m 1.0) v) (/ (* m m) v)) 1.0) (- 1.0 m))
438.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
435.0ms	(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
327.0ms	(* (- (/ m (/ v (- 1.0 m))) 1.0) (fma 1 1.0 (- (* (sqrt m) (sqrt m)))))

Rules

6702×	`*-un-lft-identity`
5915×	`add-sqr-sqrt`
5708×	`times-frac`
4504×	`add-cube-cbrt`
2418×	`prod-diff`
1980×	`add-exp-log`
1723×	`add-cbrt-cube`
1512×	`sqrt-prod`
1422×	`pow1`
672×	`distribute-lft-out`
616×	`prod-exp`
567×	`add-log-exp`
534×	`associate-r`
521×	`difference-of-squares`
511×	`cbrt-unprod`
491×	`associate-l`
444×	`div-exp`
429×	`distribute-lft-out--`
427×	`expm1-log1p-u`
423×	`log1p-expm1-u`
412×	`associate-/l*`
400×	`fma-neg`
398×	`div-inv`
366×	`associate-/r*`
360×	`cbrt-undiv`
357×	`associate-/r/`
309×	`log-prod`
296×	`pow-prod-down`
215×	`flip--`
214×	`flip3--`
196×	`pow-prod-up`
187×	`cbrt-prod`
172×	`distribute-rgt-in` `distribute-lft-in`
164×	`flip-+`
163×	`flip3-+`
156×	`sqrt-div`
147×	`unswap-sqr`
138×	`fma-def`
115×	`pow-sqr`
112×	`*-commutative`
107×	`swap-sqr`
105×	`unpow-prod-down`
96×	`frac-2neg` `clear-num`
94×	`distribute-rgt-neg-in`
93×	`cube-prod`
90×	`pow-plus`
88×	`associate-*r/`
87×	`frac-times`
81×	`associate-*l/`
79×	`sqrt-pow1`
71×	`pow1/2` `sub-neg`
70×	`pow2`
69×	`distribute-lft-neg-in`
61×	`cbrt-div`
54×	`log-pow`
53×	`cos-sum` `associate-/l/`
46×	`div-sub` `diff-log`
39×	`1-exp` `sqr-pow`
38×	`fma-udef`
37×	`rem-sqrt-square`
34×	`rec-exp`
33×	`sin-sum` `pow1/3`
32×	`rem-log-exp`
29×	`log-div`
27×	`unpow3` `cube-mult`
26×	`sin-mult`
25×	`sum-log`
24×	`exp-prod`
23×	`neg-mul-1`
22×	`tan-quot`
20×	`associate--l+` `+-commutative`
17×	`sin-diff`
14×	`frac-sub`
12×	`cos-mult` `associate-+l-`
11×	`acos-asin`
10×	`sin-cos-mult` `frac-add`
9×	`pow-flip` `neg-sub0`
8×	`cos-diff`
7×	`inv-pow`
6×	`exp-sum` `sub-div` `pow-unpow`
5×	`distribute-frac-neg` `neg-log` `sqrt-unprod` `acos-neg` `un-div-inv`
4×	`associate--l-` `cube-unmult` `log1p-expm1` `associate--r+` `exp-to-pow` `rem-square-sqrt` `log1p-udef`
3×	`exp-diff` `pow-exp` `distribute-rgt-out--` `asin-acos` `rem-exp-log` `pow-to-exp`
2×	`rem-cube-cbrt` `pow-pow` `hypot-udef` `hypot-def`
1×	`expm1-udef` `difference-cubes` `pow3` `tanh-def` `tanh-undef` `rem-cbrt-cube` `associate--r-` `distribute-rgt-out`

Details

simplify5.5m (44.2%)

sample3.8m (30.6%)

prune1.6m (13.1%)

series49.7s (6.6%)

regimes21.8s (2.9%)

rewrite13.4s (1.8%)

localize5.9s (0.8%)

bsearch747.0ms (0.1%)

end1.0ms (0.0%)