Details

sample13.6m (48.5%)

Algorithm
78×intervals
Results
9.3m53612×body10240exit
1.7m44204×body1280valid
40.7s30163×body640valid
29.1s204916×body80valid
20.9s152695×body80nan
19.1s27443×body320valid
12.7s36311×body160valid
10.6s192757×pre80true
3.0s3085×body2560valid
1.6s8166×body160nan
852.0ms4087×pre10240exit
393.0ms232×body5120valid
2.0ms1×body320nan

simplify9.9m (35.1%)

prune3.0m (10.6%)

series59.5s (3.5%)

Calls

473 calls:

1.5s
(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
1.1s
(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))
725.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
709.0ms
(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
641.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)

regimes20.2s (1.2%)

Accuracy

Total 49.8b remaining (18.9%)

Threshold costs 5.8b (2.2%)

7.4b46.6%Quadratic roots, narrow range
6.2b9%Quadratic roots, medium range
5.4b51.9%Quotient of products
4.9b82.4%Quadratic roots, full range
4.8b83%Cubic critical

rewrite11.1s (0.7%)

Algorithm
143×rewrite-expression-head
Calls

473 calls:

535.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
494.0ms
(+ (+ (/ 3/32 (* (* x x) (* x x))) (log 1/2)) (+ (log (/ -1 x)) (/ -1/4 (* x x))))
454.0ms
(cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1))))
425.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
408.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
Rules
10152×times-frac
9692×*-un-lft-identity
8927×add-sqr-sqrt
6529×add-cube-cbrt
3808×prod-diff
2657×add-exp-log
2117×pow1
1349×add-cbrt-cube
1084×difference-of-squares
984×prod-exp
900×div-exp
796×log-pow
790×distribute-lft-out
693×pow-exp
667×cbrt-prod
646×add-log-exp
623×div-inv
557×distribute-lft-out--
551×sqrt-prod
538×associate-*l*
504×associate-/r*
481×expm1-log1p-u
476×associate-/r/
475×log1p-expm1-u
473×insert-posit16
435×associate-/l*
418×fma-neg
414×associate-*r*
345×pow-to-exp
293×cbrt-unprod
283×difference-of-sqr-1
264×cbrt-div
257×log-prod cbrt-undiv
249×pow-prod-down
233×flip--
232×flip3--
214×pow-prod-up
210×frac-times
197×swap-sqr
166×associate-*l/
160×flip-+
159×flip3-+
151×associate--l+
142×1-exp rec-exp
136×associate-*r/
129×pow-plus
124×fma-def
118×unswap-sqr
106×pow-sqr
103×frac-2neg clear-num
97×*-commutative
95×unpow-prod-down
94×exp-prod
93×tan-quot
78×fma-udef
71×sub-neg
65×sqrt-pow1 pow1/2
63×pow2
62×diff-log
59×cos-sum
57×pow1/3 frac-sub
50×associate-/l/
47×distribute-rgt-in distribute-lft-in
35×associate-+r+
34×exp-sum
33×sum-log
32×pow-flip
31×div-sub
29×distribute-rgt-out--
28×sqrt-div pow3
27×rem-sqrt-square log-div
25×associate-+l+
23×sqr-pow distribute-rgt-neg-in
22×sin-sum inv-pow
21×rem-log-exp
19×+-commutative
18×sin-diff sin-mult
15×distribute-lft-neg-in
13×cos-diff
12×associate--r+
11×cos-mult difference-cubes distribute-rgt-out
10×frac-add
9×acos-asin log1p-udef
8×cube-unmult log1p-expm1 pow-div associate-+l- expm1-def
6×neg-sub0 pow-unpow sin-cos-mult pow-pow rem-exp-log
5×expm1-log1p expm1-udef sub-div neg-mul-1
4×remove-posit16 exp-diff associate--l- associate-+r- neg-log associate--r-
3×distribute-rgt1-in distribute-frac-neg acos-neg distribute-lft-neg-out
2×hypot-udef asin-acos
1×sqrt-undiv unsub-neg tanh-def un-div-inv exp-to-pow tanh-undef rem-cbrt-cube

localize6.4s (0.4%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)