Details

simplify6.3m (40.2%)

sample6.2m (39.6%)

Algorithm
78×intervals
Results
3.0m26914×body10240exit
1.3m43596×body1280valid
27.5s30450×body640valid
19.8s202965×body80valid
14.7s153461×body80nan
11.1s27959×body320valid
8.1s35956×body160valid
7.9s164300×pre80true
1.8s3110×body2560valid
1.0s8154×body160nan
535.0ms4113×pre10240exit
480.0ms215×body5120valid
180.0ms8261×pre80false

prune1.2m (7.9%)

series1.1m (6.8%)

Calls

487 calls:

1.3s
(log (sqrt (exp (* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))))
1.1s
(- (log (* (sqrt (+ (pow 1.0 3) (pow x 3))) (/ (sqrt (+ 1.0 x)) (- 1.0 x)))) (log (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))))
858.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
802.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
791.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite30.6s (3.2%)

Algorithm
145×rewrite-expression-head
Calls

487 calls:

705.0ms
(* (* (- (/ m (/ v (- 1.0 m))) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
658.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
591.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
521.0ms
(- (log (* (sqrt (+ (pow 1.0 3) (pow x 3))) (/ (sqrt (+ 1.0 x)) (- 1.0 x)))) (log (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))))
520.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (+ (sqrt 1.0) (sqrt m)))
Rules
5952×times-frac
5235×add-sqr-sqrt
5206×*-un-lft-identity
3849×add-exp-log
3358×add-cube-cbrt
2656×associate-*l/
1990×add-cbrt-cube
1854×flip--
1853×flip3--
1772×frac-times
1416×div-exp
1382×prod-exp
1347×cbrt-div
1148×pow1
889×sqrt-div
853×associate-*r/
806×frac-add
778×difference-of-squares
744×add-log-exp
693×sqrt-prod
650×associate-/l*
618×associate-*r*
617×associate-/r*
615×pow-exp
535×distribute-lft-out--
522×unpow-prod-down
518×cbrt-unprod
510×cbrt-undiv
490×associate-*l*
434×pow-to-exp
393×associate-/r/
381×div-inv
373×distribute-lft-out
352×cube-prod
329×cbrt-prod
283×pow-prod-down
211×flip-+
210×flip3-+
187×log-prod
185×sqr-pow
176×log-pow
139×distribute-rgt-neg-in
134×unswap-sqr
129×associate-/l/
123×clear-num frac-2neg
121×exp-prod sub-neg
120×1-exp
110×*-commutative
98×cos-mult
93×sin-mult
82×diff-log
70×sqrt-pow1
62×log-div
58×frac-sub
56×distribute-rgt-in distribute-lft-in rec-exp
54×pow-unpow
52×sum-log
49×pow1/2
44×div-sub
43×sin-cos-mult
39×unpow3 cube-mult +-commutative
34×rem-sqrt-square
33×pow-prod-up
32×swap-sqr associate--l+
30×rem-log-exp
29×tan-quot
28×pow1/3
26×exp-sum
24×pow-sqr
23×distribute-rgt-out
21×sub-div pow-pow
20×pow-plus
19×associate--l- associate-+r+
18×rem-cube-cbrt
17×associate-+l+
16×distribute-lft-neg-in cos-diff neg-sub0 sin-diff
15×cos-sum associate--r+
14×distribute-frac-neg
11×associate-+l-
10×acos-asin neg-log pow2
cube-div
exp-diff
associate--r- sum-cubes rem-cbrt-cube
rem-exp-log inv-pow associate-+r- sin-sum pow-flip
sub0-neg distribute-lft1-in unpow2 asin-acos neg-mul-1 exp-to-pow
acos-neg un-div-inv distribute-rgt-neg-out
sqrt-pow2 sqrt-undiv distribute-neg-frac
difference-cubes sin-neg sqrt-unprod distribute-lft-neg-out distribute-rgt-out-- rem-square-sqrt tanh-undef tanh-def

regimes11.2s (1.2%)

Accuracy

Total 34.4b remaining (23.7%)

Threshold costs 6.0b (4.2%)

7.0b0%Quadratic roots, medium range
7.0b0%Cubic critical, medium range
4.6b84.2%Quadratic roots, full range
4.0b71.9%Equirectangular approximation to distance on a great circle
2.4b89.8%Cubic critical

bsearch5.8s (0.6%)

localize4.0s (0.4%)

end1.0ms (0.0%)