Details

sample22.2m (61.6%)

Algorithm
76×intervals
Results
18.8m138972×body10240exit
1.1m36386×body1280valid
28.3s199110×body80valid
27.2s26345×body640valid
21.0s153200×body80nan
14.4s26206×body320valid
12.8s35064×body160valid
9.9s163492×pre80true
2.6s3127×body2560valid
1.4s7902×body160nan
944.0ms4144×pre10240exit
591.0ms228×body5120valid

simplify8.9m (24.8%)

prune3.2m (9.0%)

series1.2m (3.2%)

Calls

407 calls:

21.5s
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
1.5s
(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
1.3s
(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))
721.0ms
(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (sqrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))))
719.0ms
(cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1))

regimes13.9s (0.6%)

Accuracy

Total 51.7b remaining (29%)

Threshold costs 3.4b (1.9%)

7.5b31%Quotient of products
7.3b47.6%Quadratic roots, narrow range
6.0b13%Quadratic roots, medium range
6.0b25.4%Cubic critical, narrow range
4.4b84.2%Quadratic roots, full range

rewrite10.8s (0.5%)

Algorithm
130×rewrite-expression-head
Calls

407 calls:

333.0ms
(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi2)) (cos (* 1/2 phi1))) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))))
327.0ms
(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))
318.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (fma y x (log1p (exp x))) (* y x) (* (log1p (exp x)) (log1p (exp x)))))
267.0ms
(* (- (/ m (/ v (- 1 m))) 1) (- 1 m))
260.0ms
(* (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)) (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)))
Rules
8074×*-un-lft-identity
7410×add-sqr-sqrt
7329×times-frac
5160×add-cube-cbrt
2820×add-exp-log
2527×prod-diff
1358×add-cbrt-cube
1182×sqrt-prod
1160×pow1
1072×prod-exp
991×div-exp
950×difference-of-squares
780×associate-*l*
738×distribute-lft-out
701×pow-exp
581×add-log-exp
568×associate-*r*
556×associate-/l*
512×distribute-lft-out--
443×div-inv
427×associate-/r*
412×fma-neg
409×expm1-log1p-u log1p-expm1-u
407×insert-posit16
405×associate-/r/
381×cbrt-prod
353×pow-to-exp
314×cbrt-unprod
288×tan-quot
285×cbrt-undiv
245×frac-times difference-of-sqr-1
228×flip--
227×flip3--
201×log-prod
194×pow-prod-down
192×unpow-prod-down
175×associate-*r/
170×unswap-sqr associate-*l/
169×flip-+
168×flip3-+
167×1-exp rec-exp
139×pow-prod-up
133×swap-sqr
121×distribute-rgt-in distribute-lft-in
105×cbrt-div
104×*-commutative
97×frac-2neg clear-num
95×fma-def
79×pow-plus
78×sub-neg
72×log-pow pow-sqr
65×diff-log
58×sqr-pow
56×fma-udef
55×associate-/l/
52×pow2
49×sqrt-div
46×sqrt-pow1 pow1/2
40×pow3
38×frac-sub
37×pow1/3
36×exp-prod
34×rem-sqrt-square log-div
33×sin-sum
32×pow-flip sum-log
26×cos-sum
25×rem-log-exp
24×inv-pow
22×exp-sum div-sub sin-mult
21×frac-add
18×associate-+l+ associate--l+
15×difference-cubes
14×+-commutative
13×cos-mult expm1-def
10×associate--r+ distribute-rgt-neg-in
7×log1p-udef
6×pow-unpow sub-div pow-pow acos-asin distribute-lft-neg-in distribute-rgt-out
4×log1p-expm1 log-rec associate-+l-
3×expm1-log1p neg-sub0 expm1-udef exp-diff
2×distribute-rgt1-in distribute-frac-neg cube-unmult neg-log neg-mul-1 un-div-inv rem-exp-log acos-neg cos-diff associate--r-
1×distribute-lft-neg-out associate--l- associate-+r+ tanh-def exp-to-pow tanh-undef asin-acos hypot-udef remove-posit16 sin-diff rem-cbrt-cube

localize4.5s (0.2%)

bsearch833.0ms (0.0%)

end1.0ms (0.0%)