Details

sample13.0m (65.6%)

Algorithm
78×intervals
Results
9.9m58508×body10240exit
1.2m43594×body1280valid
25.3s30501×body640valid
20.3s204834×body80valid
14.2s152369×body80nan
11.9s27609×body320valid
9.6s36214×body160valid
7.6s197153×pre80true
1.9s3141×body2560valid
1.0s7851×body160nan
766.0ms4168×pre10240exit
162.0ms8421×pre80false
159.0ms231×body5120valid
2.0ms1×body640nan

simplify4.0m (19.9%)

prune1.1m (5.7%)

series1.0m (5.2%)

Calls

458 calls:

2.0s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
1.3s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.2s
(cbrt (pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3)))
1.2s
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))
966.0ms
(- (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite22.9s (1.9%)

Algorithm
143×rewrite-expression-head
Calls

458 calls:

517.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))
462.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
456.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
451.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
441.0ms
(* (* (sqrt (sqrt m)) (* (sqrt (sqrt m)) (- (/ (* m (- 1.0 m)) v) 1.0))) (sqrt m))
Rules
4368×*-un-lft-identity
4351×add-sqr-sqrt
4191×times-frac
2888×add-cube-cbrt
2614×add-exp-log
1745×add-cbrt-cube
1184×associate-*r*
1088×pow1
900×frac-times
894×associate-*l/
869×sqrt-prod prod-exp
833×associate-*r/
780×flip--
779×flip3--
778×div-exp
676×add-log-exp
631×unpow-prod-down
537×associate-*l*
466×associate-/r*
457×difference-of-squares
434×flip-+
433×cbrt-unprod flip3-+
416×sqrt-div
409×cbrt-undiv cube-prod
405×associate-/l*
388×frac-sub
383×distribute-lft-out--
361×cbrt-prod
328×pow-exp
325×distribute-lft-out
279×frac-add
277×div-inv
262×associate-/r/
256×associate-/l/
236×pow-to-exp
233×unswap-sqr
224×pow-prod-down
207×swap-sqr
177×sqr-pow
118×log-prod
113×sub-neg
106×clear-num frac-2neg
100×*-commutative sqrt-pow1
85×unpow3 cube-mult
80×diff-log
73×pow1/2
69×cbrt-div
67×pow1/3
66×log-pow
55×distribute-rgt-neg-in pow-unpow
51×sin-mult
49×rem-sqrt-square
48×pow-prod-up
47×distribute-rgt-in distribute-lft-in
42×pow-sqr div-sub
36×sum-log tan-quot
34×log-div
33×exp-prod
31×1-exp
30×unpow2
28×pow-plus rec-exp
26×pow2
24×associate--l+
22×+-commutative distribute-rgt-out
21×pow-pow associate-+r+
19×rem-cube-cbrt rem-log-exp
18×sin-diff
17×cos-sum
15×exp-sum
14×cos-diff
12×cube-div sin-cos-mult
11×acos-asin
8×associate-+l+
7×associate--l- sqrt-unprod associate-+r- neg-sub0 sub-div cos-mult sin-sum
6×distribute-lft-neg-in neg-log rem-cbrt-cube
5×un-div-inv distribute-neg-in distribute-rgt-out-- pow-flip distribute-rgt-neg-out associate-+l-
4×distribute-lft1-in inv-pow
3×exp-diff acos-neg distribute-lft-neg-out distribute-frac-neg
2×sin-neg rem-exp-log sqr-sin unsub-neg rem-square-sqrt neg-mul-1 associate--r- exp-to-pow
1×unpow1/3 tanh-undef asin-acos sqr-cos sum-cubes tanh-def associate--r+

regimes15.3s (1.3%)

Accuracy

Total 50.0b remaining (26.7%)

Threshold costs 6.0b (3.2%)

7.9b43.6%Cubic critical, narrow range
6.9b0%Cubic critical, medium range
6.8b0%Quadratic roots, medium range
6.3b45.6%Quotient of products
3.5b74.2%Equirectangular approximation to distance on a great circle

localize4.3s (0.4%)

bsearch686.0ms (0.1%)

end0.0ms (0.0%)