Details

simplify8.5m (38.4%)

sample6.8m (30.4%)

Algorithm
78×intervals
Results
2.5m23027×body10240exit
1.7m43977×body1280valid
39.8s30309×body640valid
28.5s202307×body80valid
20.8s27867×body320valid
19.8s153582×body80nan
14.1s35906×body160valid
9.6s160815×pre80true
3.2s3077×body2560valid
1.5s8283×body160nan
1.1s4130×pre10240exit
638.0ms222×body5120valid

prune5.3m (23.8%)

series54.6s (4.1%)

Calls

468 calls:

978.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))) (+ (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))))
976.0ms
(/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
873.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
695.0ms
(* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x))))
649.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

regimes22.2s (1.7%)

Accuracy

Total 52.9b remaining (24.9%)

Threshold costs 4.7b (2.2%)

7.4b47.4%Quadratic roots, narrow range
7.3b47.1%Cubic critical, narrow range
7.0b0%Quadratic roots, medium range
5.0b80.9%Quadratic roots, full range
4.9b56%Quotient of products

rewrite13.6s (1.0%)

Algorithm
146×rewrite-expression-head
Calls

468 calls:

548.0ms
(+ (- (- (/ m v) (/ m (/ v m))) 1) (* (- m) (- (- (/ m v) (/ m (/ v m))) 1)))
353.0ms
(* (- m) (- (- (/ m v) (/ m (/ v m))) 1))
340.0ms
(* (- (- (/ m v) (/ m (/ v m))) 1) (- 1 m))
299.0ms
(/ (* (fma (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)) (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))) (* (cos phi2) (cos phi1))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
248.0ms
(exp (log (* (cbrt (- (/ 2 (+ 1 (exp (* -2 x)))) 1)) (cbrt (- (/ 2 (+ 1 (exp (* -2 x)))) 1)))))
Rules
19145×times-frac
16373×*-un-lft-identity
15142×add-sqr-sqrt
11938×add-cube-cbrt
7580×prod-diff
3457×associate--l+
3005×add-exp-log
1593×add-cbrt-cube
1440×sqrt-prod
1382×pow1
1368×div-inv
1326×distribute-rgt-in distribute-lft-in
1292×difference-of-squares
1289×distribute-lft-out
1253×associate-+r+
1108×prod-exp
1048×div-exp
803×associate-/r/
747×associate-*l*
701×distribute-lft-out--
696×pow-exp
667×associate-+l+
664×add-log-exp
583×associate-/r*
572×cbrt-prod
557×associate-*r*
474×expm1-log1p-u
472×log1p-expm1-u
468×insert-posit16
414×associate-/l*
391×cbrt-unprod
387×difference-of-sqr-1
365×fma-neg
349×cbrt-undiv
346×pow-to-exp
282×pow-prod-down
279×flip-+
278×flip3-+
244×flip--
243×flip3--
215×log-prod
206×fma-def
197×swap-sqr
193×exp-prod
174×unswap-sqr
173×pow-prod-up
153×1-exp rec-exp
147×associate-*r/
141×log-pow
138×associate-*l/
133×frac-times
116×cos-mult
105×frac-2neg clear-num
104×sin-mult
102×pow-sqr
101×*-commutative
88×sub-neg
86×sqrt-div
82×pow-plus
75×frac-add
71×diff-log
65×associate-/l/
60×tan-quot
59×cos-sum
57×pow2 fma-udef
54×sqrt-pow1 pow1/2
52×log-div
48×distribute-rgt-neg-in
45×sum-log
42×cbrt-div
41×unpow-prod-down
39×frac-sub
38×pow1/3
37×div-sub
36×distribute-rgt-out
35×rem-sqrt-square
34×sin-sum
32×distribute-lft-neg-in
27×rem-log-exp
26×+-commutative
22×exp-diff
19×pow-flip log1p-udef
18×associate--r+ pow-pow hypot-def
17×sub-div neg-mul-1
16×sin-diff
15×expm1-def
13×inv-pow
12×neg-sub0
11×sin-cos-mult
10×distribute-rgt1-in log1p-expm1 pow3 asin-acos
9×pow-unpow cos-diff
8×associate-+l- acos-asin
7×exp-neg
6×associate--r-
5×expm1-log1p expm1-udef sqrt-undiv sqr-pow
4×distribute-frac-neg cube-unmult neg-log acos-neg rem-cbrt-cube
3×distribute-lft-neg-out sqrt-unprod rem-square-sqrt
2×associate--l- associate-+r- log1p-def rem-exp-log unsub-neg
1×exp-sum tanh-def tanh-undef hypot-udef unpow1/3 un-div-inv

localize6.4s (0.5%)

bsearch919.0ms (0.1%)

end1.0ms (0.0%)