Details

sample6.0m (39.4%)

Algorithm

78×

intervals

Results

2.8m	26306×	body	10240	exit
1.2m	44062×	body	1280	valid
27.7s	30590×	body	640	valid
18.9s	202821×	body	80	valid
15.2s	151501×	body	80	nan
11.8s	27500×	body	320	valid
9.1s	36204×	body	160	valid
8.3s	163295×	pre	80	true
1.8s	3073×	body	2560	valid
685.0ms	7916×	body	160	nan
623.0ms	4177×	pre	10240	exit
161.0ms	231×	body	5120	valid
3.0ms	2×	body	640	nan

simplify5.6m (36.4%)

prune1.9m (12.7%)

series55.4s (6.0%)

Calls

445 calls:

1.4s	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0s	(/ (- (* (cos delta) (cos delta)) (fma (* (* (sin delta) (cos phi1)) (* (sin delta) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (fma (* (cos theta) (* (* (* (cos delta) (cos phi1)) (sin delta)) (* (* (sin phi1) (sin phi1)) (sin phi1)))) 2 (* (* (cos delta) (* (sin phi1) (sin phi1))) (* (cos delta) (* (sin phi1) (sin phi1))))))) (fma (cos delta) (* (sin phi1) (sin phi1)) (fma (sin delta) (* (* (cos theta) (cos phi1)) (sin phi1)) (cos delta))))
882.0ms	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
852.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
795.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

regimes24.4s (2.7%)

Accuracy

Total 53.9b remaining (33.4%)

Threshold costs 4.6b (2.8%)

7.9b	42.3%	Quadratic roots, narrow range
6.8b	0%	Quadratic roots, medium range
6.7b	0%	Cubic critical, medium range
5.7b	57.2%	Cubic critical, narrow range
4.2b	87.6%	Cubic critical

rewrite19.5s (2.1%)

Algorithm

145×	rewrite-expression-head

Calls

445 calls:

1.8s	(* (- (/ (/ m (sqrt v)) (/ (sqrt v) (- 1.0 m))) 1.0) m)
818.0ms	(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
503.0ms	(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
434.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
377.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

Rules

12309×	`times-frac`
11016×	`*-un-lft-identity`
10160×	`add-sqr-sqrt`
7745×	`add-cube-cbrt`
3420×	`prod-diff`
2521×	`add-exp-log`
2497×	`sqrt-prod`
1743×	`add-cbrt-cube`
1294×	`pow1`
926×	`difference-of-squares`
855×	`distribute-lft-out`
835×	`prod-exp`
783×	`distribute-lft-out--`
724×	`div-exp`
705×	`fma-neg`
680×	`associate-r`
635×	`associate-/r/`
603×	`add-log-exp`
600×	`associate-/r*`
580×	`associate-l`
575×	`div-inv`
487×	`cbrt-prod`
485×	`associate-/l*`
463×	`cbrt-unprod`
448×	`log1p-expm1-u`
446×	`expm1-log1p-u`
389×	`cbrt-undiv`
333×	`flip--`
332×	`flip3--`
314×	`pow-prod-down`
265×	`pow-exp`
233×	`associate-*r/`
232×	`flip-+`
231×	`flip3-+`
228×	`log-prod`
204×	`unswap-sqr`
200×	`frac-times`
190×	`sqrt-div`
185×	`pow-to-exp`
177×	`distribute-rgt-in` `distribute-lft-in`
168×	`associate--l+` `swap-sqr`
141×	`associate-*l/`
127×	`sin-mult`
120×	`frac-2neg` `clear-num`
119×	`distribute-rgt-neg-in`
117×	`associate-/l/`
112×	`log-pow`
111×	`*-commutative`
108×	`cos-mult`
105×	`distribute-lft-neg-in`
104×	`unpow-prod-down`
92×	`sub-neg`
87×	`fma-def`
74×	`pow-prod-up`
67×	`cbrt-div`
65×	`frac-sub`
60×	`cos-sum`
59×	`diff-log`
56×	`pow-sqr`
52×	`pow-plus`
49×	`sqrt-pow1` `pow1/2`
47×	`pow1/3`
44×	`exp-sum`
43×	`sin-cos-mult`
41×	`log-div`
39×	`1-exp` `rec-exp`
38×	`div-sub`
35×	`neg-mul-1`
33×	`sub-div`
32×	`exp-prod` `tan-quot`
31×	`associate--r+` `fma-udef`
30×	`pow2` `rem-log-exp`
26×	`sqr-pow`
25×	`sum-log`
23×	`rem-sqrt-square`
22×	`sin-sum`
21×	`pow-flip`
18×	`+-commutative` `sin-diff`
14×	`hypot-def`
13×	`pow3`
11×	`neg-sub0` `inv-pow`
10×	`cube-unmult`
9×	`difference-cubes` `associate-+l-` `cos-diff`
7×	`acos-asin`
6×	`pow-unpow`
5×	`exp-diff` `neg-log` `rem-exp-log` `frac-add` `associate--r-`
4×	`expm1-log1p` `expm1-udef` `associate--l-` `distribute-frac-neg` `un-div-inv`
3×	`associate-+r+` `log1p-expm1` `distribute-rgt-out` `log1p-udef`
2×	`sqrt-unprod` `pow-pow` `hypot-udef` `asin-acos` `sqr-cos`
1×	`associate-+l+` `distribute-rgt-neg-out` `tanh-def` `exp-to-pow` `tanh-undef` `acos-neg` `rem-square-sqrt` `rem-cbrt-cube`

Details

sample6.0m (39.4%)

simplify5.6m (36.4%)

prune1.9m (12.7%)

series55.4s (6.0%)

regimes24.4s (2.7%)

rewrite19.5s (2.1%)

localize6.1s (0.7%)

bsearch464.0ms (0.1%)

end1.0ms (0.0%)