Details

sample13.2m (58.2%)

Algorithm
78×intervals
Results
9.8m58006×body10240exit
1.3m43306×body1280valid
31.0s30587×body640valid
20.8s205039×body80valid
13.7s152559×body80nan
13.7s27969×body320valid
9.7s197297×pre80true
8.4s36128×body160valid
1.9s3124×body2560valid
1.2s7892×body160nan
703.0ms4142×pre10240exit
232.0ms250×body5120valid
154.0ms8365×pre80false
1.0ms1×body640nan

simplify6.7m (29.3%)

prune1.3m (5.6%)

series54.2s (4.0%)

Calls

443 calls:

1.1s
(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))
1.1s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
758.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
714.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
703.0ms
(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))

rewrite21.9s (1.6%)

Algorithm
143×rewrite-expression-head
Calls

443 calls:

490.0ms
(* (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))))
460.0ms
(cos (- lambda1 lambda2))
439.0ms
(* (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))))
434.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a))
382.0ms
(* (* 2.0 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) a)
Rules
15733×*-un-lft-identity
14978×times-frac
12487×add-sqr-sqrt
9304×add-cube-cbrt
6686×prod-diff
2219×add-exp-log
1888×distribute-lft-out
1551×add-cbrt-cube
1445×difference-of-squares
1278×distribute-lft-out--
1170×associate-/r/
998×unpow-prod-down
988×distribute-rgt-in distribute-lft-in
894×sqrt-prod
862×cube-prod
859×div-inv
820×pow1
742×associate-*r*
704×prod-exp
641×add-log-exp
638×div-exp
545×associate-*l*
525×associate-/l*
488×associate-/r*
447×expm1-log1p-u
443×log1p-expm1-u
433×flip-+
432×flip3-+
405×flip--
404×flip3--
374×fma-neg
368×cbrt-unprod
344×cbrt-undiv
341×distribute-rgt-neg-in
305×pow-exp
284×cbrt-prod
275×distribute-lft-neg-in
236×sqr-pow
217×pow-to-exp
161×pow-prod-down
139×unswap-sqr
132×unpow3 cube-mult
124×log-prod
120×associate-*r/
116×sub-neg
115×fma-def
102×clear-num frac-2neg
97×frac-times
96×*-commutative
89×neg-mul-1
87×associate-/l/
86×sum-cubes
85×associate-*l/
77×diff-log
62×sqrt-div
60×cos-sum
56×log-pow
54×associate--l+
50×exp-sum
47×exp-prod
44×sin-sum
43×div-sub
42×pow-unpow
39×fma-udef
36×cbrt-div
30×log-div
29×pow1/2 sqrt-pow1
28×rem-sqrt-square
27×pow1/3 frac-sub
26×sum-log
21×frac-add sin-mult pow-pow
20×cos-mult
18×+-commutative rem-log-exp sin-diff
17×rem-cube-cbrt
14×sin-cos-mult unpow2
13×cos-diff rec-exp 1-exp
10×acos-asin associate--r+
9×rem-exp-log swap-sqr associate-+r+
8×distribute-frac-neg neg-sub0 tan-quot
7×cube-div
6×exp-diff pow-flip associate-+l-
5×log1p-udef associate--l- distribute-neg-in sub-div associate-+l+ expm1-log1p distribute-rgt-out expm1-udef
4×acos-neg inv-pow log1p-expm1 neg-log asin-acos associate--r- distribute-rgt-neg-out rem-cbrt-cube
3×un-div-inv pow-prod-up pow2 pow-sqr pow-plus
2×difference-cubes sin-neg
1×expm1-def distribute-lft1-in distribute-lft-neg-out sqr-sin difference-of-sqr-1 hypot-udef unsub-neg tanh-undef sqr-cos distribute-neg-frac tanh-def associate-+r-

regimes13.7s (1.0%)

Accuracy

Total 43.0b remaining (30.6%)

Threshold costs 5.7b (4.1%)

7.9b43.8%Quadratic roots, narrow range
7.7b44.1%Cubic critical, narrow range
4.6b84.1%Quadratic roots, full range
3.9b64.6%Quotient of products
3.5b0%Quadratic roots, wide range

localize4.1s (0.3%)

bsearch996.0ms (0.1%)

end1.0ms (0.0%)