Details

sample10.8m (46.2%)

Algorithm
78×intervals
Results
7.6m47769×body10240exit
1.3m44067×body1280valid
29.2s30234×body640valid
19.6s203869×body80valid
13.8s153435×body80nan
13.3s27760×body320valid
9.6s36376×body160valid
8.5s186776×pre80true
2.7s3206×body2560valid
915.0ms7956×body160nan
777.0ms4074×pre10240exit
147.0ms216×body5120valid
1.0msbody320nan

simplify7.0m (29.8%)

prune3.8m (16.1%)

series53.9s (3.8%)

Calls

458 calls:

1.2s
(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
829.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* 0.5 (* t c_p)) (+ (* c_p (log 0.5)) 1)) (* (pow (sqrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n) (pow (sqrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))
800.0ms
(sqrt (* (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
754.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* 0.5 (* t c_p)) (+ (* c_p (log 0.5)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
745.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite26.8s (1.9%)

Algorithm
142×rewrite-expression-head
Calls

458 calls:

1.9s
(* (* (/ (* (* (* -1.5 -1.5) -1.5) (/ (* a c) b)) (* (* 3.0 (* 3.0 3.0)) a)) (/ (/ (* a c) b) a)) (/ (/ (* a c) b) a))
1.8s
(cbrt (* (* (/ (* (* (* -1.5 -1.5) -1.5) (/ (* a c) b)) (* (* 3.0 (* 3.0 3.0)) a)) (/ (/ (* a c) b) a)) (/ (/ (* a c) b) a)))
744.0ms
(/ (- (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))) (* (* (* y x) (* y x)) (* y x))) (+ (* (* y x) (+ (log (+ 1.0 (exp x))) (* y x))) (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))))
633.0ms
(sqrt (* (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
608.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
18537×associate-*l/
14003×flip--
14002×flip3--
13723×frac-times
13680×add-exp-log
11046×add-cbrt-cube
9261×cbrt-div
9175×frac-add
6744×prod-exp
6355×times-frac
5557×*-un-lft-identity
5539×cbrt-unprod
5093×add-sqr-sqrt
5082×div-exp
4878×sqrt-div
4807×associate-*r/
3862×cbrt-undiv
3697×add-cube-cbrt
1541×pow1
1266×cbrt-prod
1157×associate-*l*
789×sqrt-prod
740×associate-*r*
703×add-log-exp
524×distribute-lft-out--
518×pow-exp
414×associate-/r*
394×associate-/l*
390×pow-to-exp
380×difference-of-squares
360×div-inv
356×distribute-lft-out
310×pow-prod-down
299×flip-+
298×flip3-+
250×swap-sqr
223×unswap-sqr
222×pow-prod-up
220×1-exp
169×associate-/r/
155×log-prod
135×unpow-prod-down
130×pow-sqr
117×*-commutative
107×frac-2neg clear-num
104×pow-plus
100×sub-neg
95×associate-/l/
84×sqrt-pow1 diff-log
80×pow2
70×pow1/2
69×log-pow
58×exp-prod
55×pow1/3
49×distribute-rgt-in distribute-lft-in
44×div-sub
43×sum-log
34×rem-sqrt-square log-div
32×frac-sub
31×rec-exp
30×+-commutative
24×pow-unpow
21×cos-diff tan-quot
19×associate--l+
18×sqr-pow
17×sin-diff rem-log-exp
16×sin-mult
14×pow3
13×distribute-rgt-out
12×cos-sum acos-asin
11×tanh-def
10×distribute-frac-neg associate--r+ pow-pow
associate--l- associate-+r- sin-cos-mult
associate-+r+
exp-diff cos-mult cube-unmult distribute-rgt-neg-in
pow-flip exp-sum acos-neg
sin-sum sqrt-unprod difference-cubes inv-pow rem-exp-log
neg-sub0 un-div-inv rem-square-sqrt associate--r-
associate-+l+ distribute-rgt-neg-out neg-log distribute-neg-in exp-to-pow rem-cbrt-cube
distribute-lft1-in associate-+l-
tanh-undef sqrt-pow2 distribute-neg-frac asin-acos distribute-rgt1-in

regimes23.0s (1.6%)

Accuracy

Total 58.7b remaining (28.9%)

Threshold costs 5.2b (2.6%)

7.5b45.1%Quadratic roots, narrow range
7.4b45%Cubic critical, narrow range
6.7b0%Cubic critical, medium range
6.0b10.7%Quadratic roots, medium range
4.7b16.6%Quotient of products

localize7.1s (0.5%)

bsearch758.0ms (0.1%)

end1.0ms (0.0%)