Details

simplify8.4m (44.6%)

sample6.6m (34.8%)

Algorithm
78×intervals
Results
2.5m23027×body10240exit
1.6m43977×body1280valid
36.8s30309×body640valid
26.7s202307×body80valid
20.1s27867×body320valid
19.8s153582×body80nan
13.0s35906×body160valid
10.0s160815×pre80true
2.7s3077×body2560valid
1.9s8283×body160nan
866.0ms4130×pre10240exit
731.0ms222×body5120valid

prune2.3m (12.1%)

series53.5s (4.7%)

Calls

468 calls:

968.0ms
(/ (- (* (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)))))))))))
925.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
818.0ms
(/ (* (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))))))
711.0ms
(* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x))))
654.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))

regimes22.1s (1.9%)

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

rewrite13.4s (1.2%)

Algorithm
146×rewrite-expression-head
Calls

468 calls:

577.0ms
(+ (- (- (/ m v) (/ m (/ v m))) 1) (* (- m) (- (- (/ m v) (/ m (/ v m))) 1)))
392.0ms
(* (- m) (- (- (/ m v) (/ m (/ v m))) 1))
330.0ms
(* (- (- (/ m v) (/ m (/ v m))) 1) (- 1 m))
319.0ms
(cos (- lambda1 lambda2))
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))))))
Rules
19115×times-frac
16297×*-un-lft-identity
15107×add-sqr-sqrt
11925×add-cube-cbrt
7580×prod-diff
3457×associate--l+
3003×add-exp-log
1591×add-cbrt-cube
1372×pow1
1349×sqrt-prod
1341×div-inv
1326×distribute-rgt-in distribute-lft-in
1292×difference-of-squares
1257×distribute-lft-out
1253×associate-+r+
1107×prod-exp
1048×div-exp
803×associate-/r/
737×associate-*l*
701×distribute-lft-out--
696×pow-exp
667×associate-+l+
666×add-log-exp
580×associate-/r*
572×cbrt-prod
531×associate-*r*
474×expm1-log1p-u
472×log1p-expm1-u
468×insert-posit16
417×associate-/l*
390×cbrt-unprod
387×difference-of-sqr-1
365×fma-neg
349×cbrt-undiv
346×pow-to-exp
279×pow-prod-down
272×flip-+
271×flip3-+
244×flip--
243×flip3--
219×fma-def
215×log-prod
193×exp-prod
172×pow-prod-up
170×unswap-sqr
169×swap-sqr
153×1-exp rec-exp
150×associate-*r/
141×log-pow
129×associate-*l/
124×frac-times
116×cos-mult
105×frac-2neg clear-num
104×sin-mult
100×*-commutative
99×pow-sqr
88×sub-neg
86×pow-plus
71×diff-log
68×frac-add
65×associate-/l/
62×sqrt-div
60×tan-quot
59×cos-sum
57×fma-udef
56×pow2
52×log-div
51×sqrt-pow1 pow1/2
48×distribute-rgt-neg-in
46×sum-log
42×cbrt-div
41×unpow-prod-down
39×frac-sub
38×pow1/3 div-sub
35×rem-sqrt-square
34×sin-sum
32×distribute-lft-neg-in
27×+-commutative rem-log-exp
23×distribute-rgt-out
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×log1p-expm1 asin-acos
9×pow-unpow cos-diff
8×associate-+l- acos-asin
7×distribute-rgt1-in pow3 exp-neg
6×cube-unmult associate--r-
5×expm1-log1p expm1-udef sqrt-undiv sqr-pow
4×distribute-frac-neg neg-log acos-neg rem-cbrt-cube
3×distribute-lft-neg-out
2×associate--l- associate-+r- log1p-def sqrt-unprod rem-exp-log rem-square-sqrt unsub-neg
1×exp-sum tanh-def tanh-undef hypot-udef unpow1/3 un-div-inv

localize6.6s (0.6%)

bsearch770.0ms (0.1%)

end1.0ms (0.0%)