Details

sample7.5m (71.6%)

Algorithm

78×

intervals

Results

6.1m	28766×	body	10240	exit
35.7s	44187×	body	1280	valid
11.9s	30743×	body	640	valid
7.0s	202521×	body	80	valid
4.7s	152123×	body	80	nan
4.6s	27389×	body	320	valid
3.0s	35764×	body	160	valid
2.6s	157333×	pre	80	true
842.0ms	3132×	body	2560	valid
379.0ms	7965×	body	160	nan
369.0ms	4048×	pre	10240	exit
91.0ms	8225×	pre	80	false
56.0ms	196×	body	5120	valid

prune1.2m (11.5%)

series42.4s (6.7%)

Calls

500 calls:

759.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))
694.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
621.0ms	(cbrt (+ (* 1.5 (* (pow (log 2.0) 2) x)) (+ (pow (log 2.0) 3) (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))))))
576.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
513.0ms	(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

bsearch23.1s (3.7%)

simplify15.7s (2.5%)

Algorithm

223×	egg-herbie

rewrite13.8s (2.2%)

Algorithm

145×	rewrite-expression-head

Calls

500 calls:

300.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
241.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
241.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
241.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
240.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

Rules

43055×	`times-frac`
22205×	`*-un-lft-identity`
21726×	`add-sqr-sqrt`
15557×	`add-cube-cbrt`
3213×	`add-exp-log`
2845×	`distribute-lft-out--`
2839×	`difference-of-squares`
2212×	`div-inv`
2066×	`sqrt-prod`
1943×	`add-cbrt-cube`
1378×	`distribute-rgt-neg-in`
1346×	`associate-r`
1184×	`pow1`
1088×	`div-exp`
1048×	`flip--`
1047×	`flip3--`
1044×	`prod-exp`
1017×	`associate-*l/`
978×	`associate-/l*`
804×	`add-log-exp`
717×	`associate-/r*`
629×	`unpow-prod-down`
561×	`associate-/r/`
560×	`associate-l`
555×	`frac-times`
526×	`sqrt-div`
481×	`cbrt-undiv`
468×	`frac-add`
458×	`cbrt-unprod`
451×	`distribute-lft-out`
427×	`pow-exp`
364×	`associate-*r/`
320×	`pow-to-exp`
296×	`cube-prod`
264×	`pow-prod-down`
226×	`unswap-sqr`
185×	`sqr-pow`
178×	`log-prod`
170×	`cbrt-prod`
152×	`flip-+`
151×	`flip3-+`
143×	`swap-sqr`
141×	`distribute-lft-neg-in`
125×	`*-commutative`
117×	`clear-num` `frac-2neg`
112×	`sub-neg`
109×	`associate-/l/`
99×	`diff-log`
79×	`div-sub`
73×	`unpow2`
69×	`exp-prod`
68×	`sum-log`
67×	`unpow3`
64×	`log-pow`
62×	`tan-quot`
61×	`cube-mult`
56×	`1-exp`
52×	`pow-prod-up`
50×	`cbrt-div` `distribute-rgt-in` `pow-pow` `distribute-lft-in`
48×	`frac-sub`
47×	`neg-mul-1`
42×	`+-commutative`
38×	`pow-unpow` `log-div`
37×	`pow-sqr`
36×	`pow1/2` `rem-sqrt-square` `sqrt-pow1`
35×	`associate--l+`
33×	`neg-sub0`
32×	`associate-+l+`
31×	`associate-+r+` `pow-plus` `rec-exp`
28×	`associate-+l-`
25×	`pow2`
24×	`sin-mult`
23×	`pow1/3` `cos-mult` `rem-log-exp`
22×	`distribute-rgt-out`
20×	`neg-log`
19×	`cos-diff` `sin-diff`
17×	`associate--l-`
14×	`sum-cubes` `acos-asin`
13×	`associate-+r-` `exp-sum`
12×	`cos-sum` `associate--r+`
11×	`distribute-frac-neg`
10×	`sin-cos-mult`
7×	`cube-div` `asin-acos`
6×	`acos-neg` `associate--r-`
5×	`rem-cube-cbrt` `rem-exp-log` `sin-sum` `distribute-rgt-out--` `sub-div`
4×	`exp-diff` `inv-pow` `distribute-lft-neg-out` `pow-flip`
3×	`distribute-rgt-neg-out`
2×	`sin-neg` `distribute-lft1-in` `pow-sub` `unsub-neg` `unpow-prod-up` `sqr-cos`
1×	`un-div-inv` `div0` `distribute-rgt1-in` `sin-asin` `log-rec` `tanh-undef` `rem-cbrt-cube` `tanh-def`

regimes9.1s (1.4%)

Accuracy

Total 21.8b remaining (19.3%)

Threshold costs 8.0b (7.1%)

4.4b	69.1%	Equirectangular approximation to distance on a great circle
3.0b	89.5%	Cubic critical
2.9b	74.2%	Quotient of products
2.4b	91.7%	Quadratic roots, full range
1.2b	0%	(- (/ x0 (- 1 x1)) x0)

Details

sample7.5m (71.6%)

prune1.2m (11.5%)

series42.4s (6.7%)

bsearch23.1s (3.7%)

simplify15.7s (2.5%)

rewrite13.8s (2.2%)

regimes9.1s (1.4%)

localize2.4s (0.4%)

end1.0ms (0.0%)