Details

simplify10.4m (56.1%)

sample5.0m (27.1%)

Algorithm
78×intervals
Results
1.6m20426×body10240exit
1.3m43746×body1280valid
30.5s30691×body640valid
21.0s202771×body80valid
14.1s153013×body80nan
12.5s27749×body320valid
8.2s35759×body160valid
7.8s158253×pre80true
2.8s3100×body2560valid
833.0ms7869×body160nan
447.0ms4116×pre10240exit
214.0ms8292×pre80false
116.0ms220×body5120valid
2.0ms1×body640nan

prune1.4m (7.3%)

series1.1m (5.9%)

Calls

478 calls:

2.8s
(/ (+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3)) (fma (cos phi1) (cos phi1) (* (- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
1.9s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
984.0ms
(+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3))
823.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
731.0ms
(log1p (/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite19.7s (1.8%)

Algorithm
147×rewrite-expression-head
Calls

478 calls:

457.0ms
(* (- (* (/ (* m (- (* 1.0 1.0) (* m m))) (* v (- (* 1.0 1.0) (* m m)))) (- 1.0 m)) 1.0) (- 1.0 m))
290.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
277.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
274.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
270.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
Rules
8202×*-un-lft-identity
7155×add-sqr-sqrt
6661×times-frac
5531×add-cube-cbrt
3476×prod-diff
2715×add-exp-log
1719×add-cbrt-cube
1121×sqrt-prod
1024×associate-*r*
996×pow1
898×prod-exp
824×div-exp
729×distribute-lft-out
722×add-log-exp
621×difference-of-squares
595×unpow-prod-down
554×distribute-lft-out--
504×associate-/l*
483×associate-/r* expm1-log1p-u
480×log1p-expm1-u
454×associate-*l*
449×div-inv
430×associate-/r/
424×cbrt-unprod
407×fma-neg
387×cube-prod
386×cbrt-undiv
319×distribute-rgt-neg-in
307×pow-exp
302×distribute-rgt-in distribute-lft-in
283×flip--
282×flip3--
237×distribute-lft-neg-in cbrt-prod
231×pow-prod-down
222×pow-to-exp
208×sqr-pow
201×unswap-sqr
200×log-prod
182×flip-+
181×flip3-+
165×fma-def
132×exp-prod
129×sub-neg
116×clear-num associate-*r/ frac-2neg
111×unpow3 cube-mult
101×*-commutative
95×diff-log
81×associate-/l/
80×neg-mul-1
73×log-pow
72×unpow2
68×frac-times
65×associate-*l/
64×associate--l+
57×sqrt-div
55×swap-sqr
53×1-exp
52×rec-exp cos-sum
47×div-sub
44×associate-+l+ sqrt-pow1
38×pow1/2 fma-udef
37×pow1/3 exp-sum
36×pow-prod-up log-div
34×pow-sqr sum-log
33×sin-sum
32×cbrt-div sin-mult
29×pow-unpow frac-sub
28×rem-sqrt-square
25×+-commutative rem-log-exp
20×cos-mult
19×neg-sub0 sin-diff
14×exp-diff sin-cos-mult cos-diff
13×associate-+r+ pow-pow
12×acos-asin associate--r+
11×pow-plus
10×cube-div rem-cube-cbrt tan-quot neg-log
9×associate--l- pow2
8×un-div-inv frac-add associate-+l-
7×exp-neg pow-flip
6×acos-neg inv-pow distribute-frac-neg unpow-prod-up
5×rem-exp-log sum-cubes log1p-udef log1p-expm1 associate--r- expm1-udef
4×sub-div
3×sqrt-unprod distribute-neg-in expm1-log1p asin-acos rem-cbrt-cube
2×e-exp-1 associate-+r- hypot-udef distribute-rgt-out distribute-rgt-neg-out
1×rem-square-sqrt tanh-undef tanh-def

regimes15.4s (1.4%)

Accuracy

Total 40.0b remaining (30.9%)

Threshold costs 5.0b (3.9%)

7.6b45.5%Quadratic roots, narrow range
6.4b10.7%Cubic critical, medium range
5.6b83.4%Quadratic roots, full range
4.6b59.7%Quotient of products
3.7b0%Cubic critical, wide range

localize4.3s (0.4%)

bsearch818.0ms (0.1%)

end1.0ms (0.0%)