Details

sample14.0m (60.1%)

Algorithm
78×intervals
Results
9.8m56091×body10240exit
1.7m43350×body1280valid
39.5s30048×body640valid
28.5s204897×body80valid
20.1s151476×body80nan
17.9s27978×body320valid
13.3s36420×body160valid
12.4s196280×pre80true
2.3s3031×body2560valid
1.6s7980×body160nan
905.0ms4130×pre10240exit
331.0ms213×body5120valid
3.0ms1×body640nan

simplify6.1m (26.4%)

prune1.7m (7.2%)

series48.6s (3.5%)

Calls

471 calls:

893.0ms
(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))
749.0ms
(/ (* (* (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))))
651.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
630.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
602.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

regimes19.7s (1.4%)

Accuracy

Total 53.0b remaining (24.2%)

Threshold costs 4.8b (2.2%)

7.6b45.4%Quadratic roots, narrow range
5.8b57.1%Cubic critical, narrow range
5.4b50%Quotient of products
5.2b80.9%Quadratic roots, full range
5.0b24.8%Cubic critical, medium range

rewrite10.6s (0.8%)

Algorithm
145×rewrite-expression-head
Calls

471 calls:

469.0ms
(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
329.0ms
(/ (* (* (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))))
243.0ms
(* (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1) m)
206.0ms
(* (- (/ m (/ v (- 1 m))) 1) (- 1 m))
190.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
Rules
11302×*-un-lft-identity
10554×times-frac
9654×add-sqr-sqrt
7331×add-cube-cbrt
5294×prod-diff
3078×add-exp-log
1624×add-cbrt-cube
1444×pow1
1180×distribute-lft-out
1147×prod-exp
1089×difference-of-squares
1062×div-exp
858×distribute-rgt-in distribute-lft-in
797×div-inv
711×associate-/r/
698×pow-exp
645×add-log-exp
602×sqrt-prod
596×log-prod
570×distribute-lft-out--
508×associate-*l*
486×associate-*r*
477×expm1-log1p-u
473×log1p-expm1-u
472×associate-+r+
471×insert-posit16
470×associate-+l+
425×associate-/r*
420×exp-sum
410×cbrt-unprod
400×cbrt-prod
385×associate-/l*
350×pow-to-exp
345×cbrt-undiv
308×pow-prod-down
302×fma-neg
295×unpow-prod-down
277×flip-+
276×flip3-+
261×flip--
260×flip3--
202×associate-*r/
172×pow-prod-up
171×1-exp rec-exp
168×difference-of-sqr-1
147×unswap-sqr
130×fma-def
125×frac-times
123×swap-sqr
107×frac-2neg clear-num
101×*-commutative
97×associate-*l/
96×pow-sqr
94×associate-/l/
91×sqr-pow
89×sin-mult
84×sub-neg
83×cbrt-div
82×cos-mult
81×log-pow
77×pow-plus
72×sqrt-pow1
64×cos-sum
62×fma-udef
54×pow2 pow1/2 diff-log
52×frac-sub
50×pow1/3
45×exp-prod
40×sin-cos-mult
36×sum-log
33×div-sub
32×distribute-rgt-out
31×rem-log-exp log-div
30×pow-flip rem-sqrt-square
28×frac-add
27×distribute-rgt-neg-in
24×+-commutative tan-quot
22×sin-sum sqrt-div sub-div
19×inv-pow
17×sin-diff
15×distribute-lft-neg-in
13×associate--r+ cos-diff
10×log1p-udef
9×distribute-rgt1-in pow-unpow log1p-expm1
8×neg-sub0 asin-acos associate-+l- acos-asin
7×pow-pow associate--r-
6×cube-unmult distribute-rgt-out-- rem-exp-log log1p-def
5×exp-diff pow3 neg-mul-1 exp-to-pow rem-cbrt-cube
4×expm1-log1p expm1-udef associate--l+ neg-log expm1-def
3×distribute-lft-neg-out distribute-frac-neg log-rec hypot-udef acos-neg
2×sqrt-unprod un-div-inv rem-square-sqrt
1×unsub-neg tanh-def tanh-undef

localize5.7s (0.4%)

bsearch4.1s (0.3%)

end1.0ms (0.0%)