Details

sample4.5m (35.9%)

Algorithm
77×intervals
Results
1.6m42973×body1280valid
42.1s31301×body640valid
26.5s201437×body80valid
24.4s14854×body10240exit
20.0s152623×body80nan
18.5s27952×body320valid
13.2s36233×body160valid
8.6s150526×pre80true
2.4s2949×body2560valid
1.3s8027×body160nan
1.1s4101×pre10240exit
319.0ms192×body5120valid
3.0msbody640nan
1.0msbody320nan

prune3.2m (25.4%)

simplify2.8m (22.5%)

series1.4m (11.2%)

Calls

432 calls:

22.1s
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
1.5s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.2s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
1.0s
(/ (- (* (cos delta) (cos delta)) (cbrt (* (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
989.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

regimes18.0s (2.4%)

Accuracy

Total 54.2b remaining (21%)

Threshold costs 4.4b (1.7%)

7.8b43.1%Cubic critical, narrow range
7.6b44.2%Quadratic roots, narrow range
6.3b6.2%Quadratic roots, medium range
4.8b52.2%Quotient of products
4.3b84.2%Quadratic roots, full range

rewrite12.9s (1.7%)

Algorithm
138×rewrite-expression-head
Calls

432 calls:

997.0ms
(cbrt (* (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
736.0ms
(/ (- (* (cos delta) (cos delta)) (cbrt (* (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
699.0ms
(- (* (cos delta) (cos delta)) (cbrt (* (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))
418.0ms
(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))
301.0ms
(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))
Rules
5891×*-un-lft-identity
5377×add-sqr-sqrt
4490×times-frac
3615×add-cube-cbrt
1951×prod-diff
1490×add-exp-log
1326×add-cbrt-cube
1324×pow1
778×difference-of-squares
654×sqrt-prod
648×frac-times
644×sin-mult
610×distribute-lft-out
584×add-log-exp
516×associate-*r*
451×cbrt-prod
435×expm1-log1p-u
433×log1p-expm1-u
432×insert-posit16
421×associate-*l*
416×associate-*l/
403×distribute-lft-out--
395×prod-exp
388×associate-/r/
355×cbrt-unprod
351×div-inv
346×associate-/l*
333×associate-/r*
298×pow-prod-down
296×associate-*r/
295×cbrt-div
275×div-exp
231×fma-neg
228×cbrt-undiv
199×fma-def
188×flip-+
187×flip3-+
185×flip--
184×flip3-- difference-of-sqr-1
180×cos-mult
143×frac-sub
140×unswap-sqr
134×log-prod
130×associate-/l/
126×pow-prod-up
103×*-commutative
100×distribute-rgt-in distribute-lft-in
99×tanh-def
88×frac-2neg clear-num
87×swap-sqr
81×pow-plus
74×pow-sqr
71×fma-udef
64×tan-quot
61×sub-neg
52×cos-sum
50×frac-add
49×sqrt-pow1 pow2
46×diff-log
43×pow1/2
42×pow1/3
41×div-sub
38×rem-sqrt-square
34×sum-log
33×sin-sum
32×associate-+r+
27×cube-unmult
26×1-exp unpow-prod-down
25×associate-+l+
24×pow-flip sqrt-div
23×+-commutative
22×distribute-rgt-neg-in
19×distribute-lft-neg-in
18×distribute-neg-frac cos-diff log-div
16×rec-exp
15×associate--l+ log-pow
13×expm1-def
12×pow-pow inv-pow distribute-rgt-out
11×difference-cubes pow3 sin-diff
10×sqr-pow
sin-cos-mult sub-div exp-prod
rem-log-exp
neg-mul-1 acos-asin
pow-exp associate-+r- distribute-rgt-out-- associate-+l- rem-cbrt-cube log1p-udef
neg-sub0 distribute-rgt-neg-out log1p-expm1 neg-log
expm1-log1p expm1-udef distribute-frac-neg pow-unpow asin-acos pow-to-exp acos-neg sqr-cos
distribute-rgt1-in un-div-inv hypot-udef rem-exp-log log1p-def
associate--l- sqrt-undiv exp-sum associate--r+ unpow1/3 tanh-undef unsub-neg associate--r-

localize6.0s (0.8%)

bsearch750.0ms (0.1%)

end1.0ms (0.0%)