Details

sample20.1m (68.4%)

Algorithm
72×intervals
Results
7.7m80056×body10240exit
51.1s32843×body1280valid
26.7s198227×body80valid
20.9s152416×body80nan
20.6s24326×body640valid
15.6s24770×body320valid
11.3s35302×body160valid
9.7s153658×pre80true
3.4s3044×body2560valid
1.5s7939×body160nan
1.3s4047×pre10240exit
274.0ms256×body5120valid

prune3.8m (12.8%)

simplify3.6m (12.2%)

bsearch44.6s (2.5%)

series37.5s (2.1%)

Calls

376 calls:

Slowest
931.0ms
(cbrt (fma 3/40 (pow x 5) x))
905.0ms
(cbrt (fma 3/40 (pow x 5) x))
892.0ms
(cbrt (fma 3/40 (pow x 5) x))
842.0ms
(cbrt (fma 3/40 (pow x 5) x))
638.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

regimes17.4s (1.0%)

Accuracy

Total 51.3b remaining (35.2%)

Threshold costs 3.3b (2.3%)

7.4b46.2%Quadratic roots, narrow range
6.9b0%Quadratic roots, medium range
5.5b58.8%Cubic critical, narrow range
5.0b24.8%Cubic critical, medium range
4.5b83.3%Quadratic roots, full range

rewrite10.7s (0.6%)

Algorithm
126×rewrite-expression-head
Calls

376 calls:

Slowest
480.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
457.0ms
(* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
271.0ms
(* (- (/ m (/ v (- 1 m))) 1) (- 1 m))
239.0ms
(+ (* (- (/ m (/ v (- 1 m))) 1) 1) (* (- (/ m (/ v (- 1 m))) 1) (- m)))
169.0ms
(* (- (/ m (/ v (- 1 m))) 1) (- m))
Rules
8464×*-un-lft-identity
8187×times-frac
7916×add-sqr-sqrt
5432×add-cube-cbrt
3394×add-exp-log
2539×prod-diff
1566×add-cbrt-cube
1363×prod-exp
1237×div-exp
1078×difference-of-squares
1028×pow1
746×distribute-lft-out
734×sqrt-prod
692×pow-exp
617×associate-*l*
605×associate-*r*
592×associate-/r* add-log-exp
584×distribute-lft-out--
534×div-inv
430×associate-/r/
410×associate-/l*
398×cbrt-undiv
394×cbrt-unprod
379×expm1-log1p-u
376×log1p-expm1-u insert-posit16
347×pow-to-exp
341×associate-+r+
313×cbrt-prod
272×difference-of-sqr-1
268×swap-sqr
265×fma-neg
258×1-exp rec-exp
223×flip-+
222×flip3-+ flip--
221×flip3--
216×fma-def
192×pow-prod-down
175×frac-times unswap-sqr
164×log-prod
140×associate--l+
123×pow-prod-up
122×distribute-lft-neg-in
119×associate-*l/
116×distribute-rgt-neg-in
115×distribute-rgt-in distribute-lft-in
113×associate-*r/
108×distribute-rgt-out
98×frac-2neg clear-num
93×pow-flip
82×*-commutative
80×sub-neg
77×inv-pow
74×sqrt-div
72×diff-log
66×unpow-prod-down
65×frac-add
61×pow-sqr
58×neg-mul-1
57×associate-/l/
56×tan-quot
55×log-pow
53×pow-plus
52×distribute-lft1-in
45×sum-log
37×fma-udef
36×pow2
35×sqrt-pow1 pow1/2
34×exp-prod
33×sin-sum exp-sum
29×cos-sum
28×cbrt-div rem-log-exp
24×div-sub
23×+-commutative log-div
22×frac-sub rem-sqrt-square
20×pow1/3
18×un-div-inv
17×sqr-pow
13×associate--r+
9×neg-sub0 associate-+l-
8×acos-asin
6×neg-log rem-exp-log associate--r- expm1-def log1p-udef
5×pow3
4×expm1-log1p expm1-udef exp-diff log1p-expm1 acos-neg
3×associate-+l+ pow-unpow distribute-rgt-neg-out log-rec sqrt-unprod pow-pow
2×distribute-frac-neg cube-unmult hypot-udef distribute-rgt-out-- log1p-def cos-diff rem-cbrt-cube sin-mult
1×associate-+r- distribute-rgt1-in unsub-neg tanh-undef associate--l- tanh-def exp-to-pow asin-acos rem-square-sqrt sin-diff

localize5.2s (0.3%)

end1.0ms (0.0%)