Details

sample9.8m (80.4%)

Algorithm
78×intervals
Results
8.1m53198×body10240exit
36.5s43935×body1280valid
12.9s30504×body640valid
12.5s205708×body80valid
8.9s152819×body80nan
6.0s27636×body320valid
5.5s171899×pre80overflowed
4.5s35726×body160valid
908.0ms2973×body2560valid
659.0ms24768×pre80true
552.0ms8081×body160nan
193.0ms8251×pre80false
152.0ms244×body5120valid

prune55.2s (7.5%)

series45.6s (6.2%)

Calls

516 calls:

1.1s
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
868.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
578.0ms
(/ (* (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)))
497.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
470.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite15.7s (2.1%)

Algorithm
146×rewrite-expression-head
Calls

516 calls:

2.0s
(* (/ (/ a1 (cbrt b2)) (cbrt b2)) (/ (/ (* (cbrt a2) (cbrt a2)) (* (cbrt b1) (cbrt b1))) (/ (cbrt b2) (/ (cbrt a2) (cbrt b1)))))
651.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
381.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
325.0ms
(* (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
313.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
Rules
10607×times-frac
8302×add-sqr-sqrt
7687×*-un-lft-identity
5198×add-cube-cbrt
3241×add-exp-log
2524×cbrt-prod
2347×associate-*r*
2051×add-cbrt-cube
1592×pow1
1565×associate-*l/
1284×frac-times
1090×flip--
1088×flip3--
1070×prod-exp
1033×div-exp
899×sqrt-prod
867×associate-*r/
865×associate-*l*
835×add-log-exp
779×distribute-lft-out--
764×difference-of-squares
741×associate-/l*
674×unpow-prod-down
612×associate-/r*
599×sqrt-div cbrt-undiv
587×cbrt-unprod
575×div-inv
542×frac-add
448×distribute-lft-out
417×unswap-sqr
395×pow-exp
326×frac-sub
319×pow-prod-down
294×distribute-rgt-neg-in
290×pow-to-exp
269×associate-/r/
268×cube-prod
252×tan-quot
243×swap-sqr
229×sqr-pow
216×log-prod
183×log-div
181×pow-prod-up
159×flip-+
158×flip3-+
126×sub-neg
122×clear-num frac-2neg
117×pow-sqr
116×*-commutative
113×cbrt-div
112×diff-log
106×log-pow
103×associate-/l/
102×distribute-lft-neg-in
96×pow-plus
74×exp-diff pow1/3
73×unpow2
71×pow2
69×unpow3 cube-mult sum-log
67×pow-sub
65×div-sub
60×pow-unpow exp-prod
56×associate--l+
55×distribute-rgt-in distribute-lft-in
54×associate-+r+
49×pow1/2 sqrt-pow1
46×pow-pow
42×1-exp
41×+-commutative
37×neg-sub0
35×rem-sqrt-square
34×neg-mul-1
31×associate-+l-
29×sin-mult
27×rec-exp exp-sum
25×rem-log-exp
21×neg-log
20×pow-flip
19×associate--l- sin-diff
17×rem-cube-cbrt
14×associate-+l+ sub-div
13×distribute-rgt-out associate--r+
12×cos-diff
11×cube-div inv-pow
10×cos-sum
9×sin-cos-mult rem-exp-log acos-asin
8×associate-+r-
7×sin-sum distribute-frac-neg
6×unpow-prod-up associate--r-
3×acos-neg log-rec cos-mult
2×sin-neg distribute-lft1-in asin-acos distribute-rgt-neg-out
1×rem-cbrt-cube difference-cubes e-exp-1 un-div-inv sqrt-unprod pow3 exp-neg distribute-rgt-out-- unsub-neg rem-square-sqrt tanh-undef sqr-cos pow-neg exp-to-pow tanh-def

simplify13.9s (1.9%)

Algorithm
224×egg-herbie

regimes10.5s (1.4%)

Accuracy

Total 25.5b remaining (22.1%)

Threshold costs 6.8b (5.9%)

8.4b54.6%Equirectangular approximation to distance on a great circle
4.8b78.6%Cubic critical
1.9b67%Quotient of products
1.3b0%2-ancestry mixing, positive discriminant
1.2b94.7%Quadratic roots, full range

localize2.5s (0.3%)

bsearch694.0ms (0.1%)

end1.0ms (0.0%)