Details

sample8.6m (71.6%)

Algorithm
78×intervals
Results
5.4m38120×body10240exit
1.3m43912×body1280valid
26.4s30679×body640valid
18.8s203725×body80valid
13.2s153010×body80nan
12.2s27600×body320valid
10.3s35915×body160valid
7.5s176424×pre80true
2.2s3078×body2560valid
776.0ms7827×body160nan
669.0ms4091×pre10240exit
194.0ms211×body5120valid
144.0ms8473×pre80false
3.0ms2×body640nan

prune1.3m (10.5%)

series1.1m (8.9%)

Calls

511 calls:

2.3s
(sqrt (+ (* (* (- lambda1 lambda2) (+ (log (sqrt (exp (cos (/ (+ phi1 phi2) 2.0))))) (log (sqrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
1.9s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
1.1s
(sqrt (+ (* (* (- lambda1 lambda2) (+ (* 2 (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))))) (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
650.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
641.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite29.7s (4.1%)

Algorithm
146×rewrite-expression-head
Calls

511 calls:

763.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
759.0ms
(- (pow (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) 3) (pow (pow 1.0 3) 3))
684.0ms
(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
505.0ms
(+ (* (- (* m (/ (- 1.0 m) v)) 1.0) 1.0) (- (+ (* 1.0 m) (/ (pow m 3) v)) (* 1.0 (/ (pow m 2) v))))
461.0ms
(log (exp (- (pow (/ x0 (* (- 1.0 x1) (- 1.0 x1))) 3) (pow x0 3))))
Rules
6165×add-sqr-sqrt
5565×*-un-lft-identity
5434×times-frac
3343×add-cube-cbrt
2864×add-exp-log
1956×add-cbrt-cube
1583×pow1
1268×unpow-prod-down
1265×associate-*r*
1204×difference-of-squares
1091×flip--
1090×flip3--
984×associate-*l/
945×prod-exp
896×frac-times
868×cube-prod
822×add-log-exp
817×div-exp
788×associate-/l*
763×sqrt-prod
712×distribute-lft-out--
636×sqrt-div
633×associate-*l*
571×frac-add
556×associate-*r/
523×cbrt-unprod
489×associate-/r*
473×pow-prod-down
460×sqr-pow
416×cbrt-undiv
407×flip-+
406×flip3-+
397×distribute-lft-out
391×cbrt-prod
362×associate-/r/
336×pow-exp
317×div-inv
265×unswap-sqr
253×distribute-rgt-neg-in
240×pow-to-exp
234×log-prod
126×*-commutative
125×associate-/l/
120×clear-num frac-2neg
119×log-pow
109×sub-neg
95×diff-log
91×pow-prod-up
85×exp-prod swap-sqr
75×pow-sqr
74×sum-log
70×unpow3 cube-mult frac-sub
69×log-div
64×pow-unpow
60×cbrt-div
50×sqrt-pow1
49×distribute-rgt-in distribute-lft-in pow1/3
48×pow1/2
45×+-commutative
43×pow-plus div-sub
38×1-exp
37×associate--r+
33×distribute-lft-neg-in rec-exp
32×rem-sqrt-square rem-log-exp
30×pow2 neg-sub0 unpow2
29×associate--l+
28×tan-quot
26×associate--l-
25×pow-pow
22×rem-cube-cbrt
21×associate-+r+
20×difference-cubes
19×cos-diff neg-log associate-+l-
17×cube-div
16×sin-mult
15×exp-sum
13×cos-sum associate-+r- sin-diff
12×sin-cos-mult distribute-rgt-out
11×associate-+l+ distribute-frac-neg neg-mul-1
10×pow-flip acos-asin rem-cbrt-cube
8×distribute-rgt-neg-out
7×associate--r-
6×rem-exp-log inv-pow
5×acos-neg sin-sum cos-mult exp-to-pow
4×distribute-rgt-out--
3×exp-diff sqrt-unprod
2×sin-neg distribute-lft1-in sum-cubes asin-acos distribute-neg-frac
1×unsub-neg remove-double-div rem-square-sqrt sub-div tanh-undef tanh-def

simplify15.6s (2.2%)

regimes13.5s (1.9%)

Accuracy

Total 28.5b remaining (22.3%)

Threshold costs 6.5b (5.1%)

8.9b36.3%Equirectangular approximation to distance on a great circle
5.1b30.4%Quotient of products
4.2b84.6%Quadratic roots, full range
2.5b89.6%Cubic critical
1.2b0%2-ancestry mixing, positive discriminant

localize4.8s (0.7%)

bsearch772.0ms (0.1%)

end1.0ms (0.0%)