Details

sample11.9m (53.1%)

Algorithm
78×intervals
Results
8.6m52262×body10240exit
1.4m43284×body1280valid
28.4s30355×body640valid
23.3s205151×body80valid
14.6s152746×body80nan
14.4s27731×body320valid
9.6s190763×pre80true
8.1s36097×body160valid
1.8s3059×body2560valid
848.0ms8254×body160nan
652.0ms4142×pre10240exit
217.0ms215×body5120valid
1.0ms1×body320nan
1.0ms1×body640nan

simplify6.4m (28.6%)

prune2.0m (9.1%)

series1.4m (6.1%)

Calls

488 calls:

21.0s
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)
1.6s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
1.4s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.4s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.3s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

regimes18.8s (1.4%)

Accuracy

Total 49.9b remaining (27.8%)

Threshold costs 4.9b (2.8%)

7.3b47.6%Quadratic roots, narrow range
6.4b9.4%Cubic critical, medium range
6.1b10%Quadratic roots, medium range
4.3b32.6%Quotient of products
4.3b84.4%Cubic critical

rewrite15.9s (1.2%)

Algorithm
147×rewrite-expression-head
Calls

488 calls:

464.0ms
(cbrt (* (* (* (/ x (+ x 1)) (/ x (+ x 1))) (/ x (+ x 1))) (* (* (/ x (+ x 1)) (/ x (+ x 1))) (/ x (+ x 1)))))
417.0ms
(* (* (* (/ x (+ x 1)) (/ x (+ x 1))) (/ x (+ x 1))) (* (* (/ x (+ x 1)) (/ x (+ x 1))) (/ x (+ x 1))))
371.0ms
(* (tan x) (tan x))
348.0ms
(cbrt (* (* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
335.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
Rules
13580×times-frac
12007×add-sqr-sqrt
11720×*-un-lft-identity
8402×add-cube-cbrt
6181×add-exp-log
3638×prod-diff
2919×add-cbrt-cube
2565×prod-exp
2436×div-exp
2167×pow1
1680×associate-*l*
1510×cbrt-prod
1336×difference-of-squares
1066×cbrt-unprod
1053×sqrt-prod
852×cbrt-undiv
814×associate-*r*
752×associate-/r*
716×distribute-lft-out
696×add-log-exp
695×pow-exp
668×distribute-lft-out--
665×div-inv
609×associate-/r/
548×pow-prod-up
493×expm1-log1p-u
491×log1p-expm1-u
488×insert-posit16
477×associate-/l*
473×1-exp
449×rec-exp
447×frac-times
436×pow-prod-down
420×associate--l+
378×swap-sqr
363×associate-+l+
361×fma-neg
347×pow-to-exp
335×associate-*l/
289×difference-of-sqr-1
282×pow-plus
274×unswap-sqr
268×flip--
267×flip3--
265×associate-*r/
256×unpow-prod-down
236×log-prod
235×flip-+
234×flip3-+
215×pow-sqr
191×sqrt-pow1
174×pow1/2
131×fma-def
130×*-commutative
126×sqrt-div
113×frac-2neg clear-num
111×log-pow
106×associate-/l/
105×pow2
98×distribute-rgt-in distribute-lft-in
90×cbrt-div
85×cube-prod
81×sub-neg
80×distribute-rgt-out--
79×pow-flip inv-pow
78×sqr-pow
73×diff-log
68×fma-udef
59×exp-prod
50×cube-unmult
49×cos-sum
46×div-sub
44×associate-+r+
41×sin-mult
40×sum-log
39×tan-quot
37×pow3
33×sin-sum pow1/3 frac-add
30×rem-sqrt-square
29×rem-log-exp
28×unpow3 cube-mult
27×frac-sub
26×difference-cubes distribute-rgt-neg-in
23×+-commutative
21×cos-mult log-div
18×sin-diff distribute-lft-neg-in
16×associate--r+
15×sin-cos-mult
14×un-div-inv
10×cos-diff
9×expm1-udef associate-+l- log1p-udef
8×expm1-def
7×expm1-log1p associate-+r- sqrt-unprod acos-asin
6×pow-unpow log1p-expm1 neg-mul-1 pow-pow exp-to-pow
5×neg-sub0 distribute-rgt-neg-out log-rec
4×associate--l- neg-log sub-div associate--r-
3×rem-square-sqrt rem-cbrt-cube
2×distribute-lft-neg-out exp-diff hypot-udef rem-exp-log
1×unsub-neg exp-sum distribute-frac-neg tanh-def tanh-undef asin-acos acos-neg

localize6.3s (0.5%)

bsearch891.0ms (0.1%)

end1.0ms (0.0%)