Details

sample19.6m (62.7%)

Algorithm
75×intervals
Results
16.2m129513×body10240exit
1.1m36714×body1280valid
28.1s26279×body640valid
27.5s198155×body80valid
20.2s152129×body80nan
15.6s25938×body320valid
13.2s35125×body160valid
10.4s150652×pre80true
3.4s3070×body2560valid
1.5s7926×body160nan
870.0ms4145×pre10240exit
324.0ms258×body5120valid

simplify6.3m (20.0%)

prune4.3m (13.7%)

series38.8s (2.1%)

Calls

404 calls:

1.1s
(fma (cbrt (pow x 13)) 71/3240 (fma (cbrt (pow x 7)) -1/18 (cbrt x)))
687.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
556.0ms
(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)
489.0ms
(cos (- lambda1 lambda2))
469.0ms
(fma (/ 1 (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x)))))) (/ 2 (cbrt (+ 1 (exp (* -2 x))))) -1)

regimes13.7s (0.7%)

Accuracy

Total 51.9b remaining (35.2%)

Threshold costs 3.9b (2.6%)

7.6b44.1%Quadratic roots, narrow range
6.4b11.2%Quadratic roots, medium range
5.4b59.5%Cubic critical, narrow range
5.0b50%Quotient of products
4.9b29%Cubic critical, medium range

rewrite10.7s (0.6%)

Algorithm
130×rewrite-expression-head
Calls

404 calls:

562.0ms
(* (- (/ (/ (+ m (* (* m m) (- (* m m)))) (+ (* 1 1) (+ (* m m) (* 1 m)))) v) 1) (- 1 m))
504.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
482.0ms
(/ (* (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x)))) (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))))
354.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
195.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
Rules
19237×times-frac
14941×*-un-lft-identity
14095×add-sqr-sqrt
11294×add-cube-cbrt
6294×prod-diff
2137×sqrt-prod
1775×add-exp-log
1571×add-cbrt-cube
1239×difference-of-squares
1087×pow1
1015×div-inv
894×distribute-lft-out
887×associate-*l*
696×associate-/r/
647×distribute-lft-out--
573×associate-*r*
556×add-log-exp
489×fma-neg
481×associate-/r*
464×div-exp
450×associate-/l*
444×prod-exp
411×expm1-log1p-u
406×log1p-expm1-u
404×insert-posit16
399×cbrt-unprod
390×cbrt-undiv
352×difference-of-sqr-1
314×cbrt-prod
269×frac-times
266×swap-sqr
258×flip--
257×flip3--
245×flip-+
244×flip3-+
181×pow-prod-down
177×unswap-sqr
148×associate-*l/
139×distribute-rgt-in distribute-lft-in
137×associate-*r/
132×fma-def
122×cbrt-div
116×pow-prod-up
102×frac-2neg clear-num
99×tanh-def
92×tan-quot
87×*-commutative
75×pow-plus
74×pow-sqr
72×associate-/l/
65×log-pow sub-neg
59×fma-udef
58×log-prod
57×exp-prod
53×pow2
52×diff-log
46×sqrt-div
44×pow1/3
40×1-exp
39×pow-flip
35×sqrt-pow1 rec-exp distribute-rgt-neg-in pow1/2
33×sin-sum
32×pow3 rem-sqrt-square
28×sum-log
25×div-sub
24×inv-pow cos-sum
20×+-commutative
19×distribute-lft-neg-in
17×exp-sum associate--l+
15×unpow-prod-down
14×expm1-def
13×difference-cubes
12×log1p-udef
11×neg-sub0 frac-sub associate-+l- log-div
9×log1p-expm1
7×distribute-rgt-out-- sqr-pow neg-mul-1 rem-log-exp acos-asin associate--r-
6×neg-log associate--r+
5×expm1-log1p expm1-udef distribute-rgt-neg-out asin-acos
4×associate-+l+ exp-diff rem-cbrt-cube distribute-rgt-out
3×pow-exp rem-exp-log pow-to-exp
2×associate--l- unsub-neg distribute-frac-neg acos-neg cos-diff frac-add pow-div
1×cos-mult distribute-rgt1-in distribute-lft1-in associate-+r+ cube-unmult sub-div tanh-undef un-div-inv hypot-udef sin-mult sin-diff

localize4.3s (0.2%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)