Details

simplify6.1m (41.8%)

sample5.2m (35.6%)

Algorithm
78×intervals
Results
1.9m21677×body10240exit
1.3m44002×body1280valid
29.0s30671×body640valid
20.1s202829×body80valid
15.1s152220×body80nan
12.3s27697×body320valid
8.3s35848×body160valid
7.4s159048×pre80true
1.5s2961×body2560valid
756.0ms7872×body160nan
715.0ms4103×pre10240exit
209.0ms230×body5120valid
195.0ms8220×pre80false

prune1.1m (7.7%)

series58.7s (6.7%)

Calls

484 calls:

789.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
755.0ms
(* (cbrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (cbrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))
740.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
714.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
713.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite29.4s (3.4%)

Algorithm
146×rewrite-expression-head
Calls

484 calls:

2.0s
(- (+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x)) (/ 3.0 (pow x 3)))
615.0ms
(* (pow (- (/ (- 1.0 m) (/ v m)) 1.0) 1) m)
603.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
582.0ms
(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3))
534.0ms
(pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3)
Rules
12633×times-frac
9069×*-un-lft-identity
8211×add-sqr-sqrt
5437×add-cube-cbrt
3123×add-exp-log
1875×add-cbrt-cube
1622×sqrt-prod
1208×difference-of-squares
1100×div-exp
1097×distribute-lft-out--
1012×pow1
982×prod-exp
951×div-inv
911×flip--
910×flip3--
880×unpow-prod-down
818×associate-*l/
778×add-log-exp
743×distribute-lft-out
667×associate-/l*
654×associate-*r*
628×cube-prod
603×associate-/r*
566×log-prod
496×cbrt-undiv
486×sqrt-div frac-times
452×cbrt-prod
446×cbrt-unprod
444×frac-add
418×associate-*r/
413×associate-*l*
385×pow-exp
365×associate-/r/
301×distribute-rgt-neg-in
281×pow-to-exp
218×sqr-pow
206×pow-prod-down
187×flip-+
186×flip3-+
182×log-pow
170×unswap-sqr
132×exp-prod
127×sub-neg
114×clear-num frac-2neg
103×associate-/l/
102×*-commutative
97×diff-log
82×cbrt-div
80×1-exp
68×sum-cubes
60×pow-unpow sum-log
56×log-div
51×cube-mult
50×unpow3
46×distribute-rgt-in distribute-lft-in
44×rec-exp
43×pow1/3 div-sub
42×swap-sqr
40×pow1/2 sqrt-pow1
39×+-commutative
38×rem-sqrt-square
33×distribute-rgt-out
31×unpow2
27×associate--l+ rem-log-exp
26×cos-mult
25×cube-div
24×pow-pow
22×associate-+r+
21×tan-quot
20×sin-mult
19×cos-diff cos-sum
18×rem-cube-cbrt neg-sub0
17×frac-sub
15×associate--l- sin-diff
14×exp-sum
13×pow-prod-up pow-sqr neg-log
11×distribute-frac-neg associate--r+
10×sin-cos-mult acos-asin associate--r-
9×pow-plus associate-+l-
8×associate-+l+ pow2 associate-+r-
7×rem-exp-log rem-cbrt-cube
5×distribute-lft-neg-in sin-sum
4×exp-diff distribute-lft1-in pow-flip asin-acos
3×acos-neg un-div-inv inv-pow distribute-lft-neg-out unsub-neg distribute-rgt-neg-out
2×difference-cubes distribute-neg-frac
1×distribute-neg-out sin-neg exp-lft-sqr tanh-undef neg-mul-1 exp-to-pow tanh-def

bsearch25.7s (3.0%)

regimes12.5s (1.4%)

Accuracy

Total 33.8b remaining (23.1%)

Threshold costs 6.5b (4.5%)

6.2b11%Cubic critical, medium range
4.5b84.2%Quadratic roots, full range
3.9b71.5%Equirectangular approximation to distance on a great circle
3.6b0%Cubic critical, wide range
3.5b0%Quadratic roots, wide range

localize3.7s (0.4%)

end1.0ms (0.0%)