Details

sample4.5m (67.0%)

Algorithm
78×intervals
Results
2.7m18077×body10240exit
39.4s44499×body1280valid
13.5s30180×body640valid
12.1s205088×body80valid
8.3s151185×body80nan
6.6s27311×body320valid
5.0s35984×body160valid
5.0s195175×pre80true
3.7s33937×body80overflowed
1.2s3136×body2560valid
614.0ms7632×body160nan
199.0ms227×body5120valid
151.0ms8052×pre80false

prune48.8s (12.1%)

series44.9s (11.2%)

Calls

515 calls:

924.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
910.0ms
(pow (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)) 3)
765.0ms
(* (cbrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))) (cbrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
738.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
712.0ms
(cbrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify13.3s (3.3%)

Algorithm
222×egg-herbie

rewrite12.8s (3.2%)

Algorithm
144×rewrite-expression-head
Calls

515 calls:

1.3s
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))) 3))
567.0ms
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
310.0ms
(- (/ x (+ x 1.0)) (/ (/ 1 (- x 1.0)) (/ 1 (+ x 1.0))))
275.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))
239.0ms
(/ (- (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)))
Rules
9668×times-frac
8288×*-un-lft-identity
7873×add-sqr-sqrt
4844×add-cube-cbrt
3455×add-exp-log
2027×add-cbrt-cube
1250×flip--
1249×flip3--
1212×difference-of-squares
1200×div-exp
1159×associate-*l/
1130×prod-exp
1119×pow1
1099×unpow-prod-down
1066×associate-*r*
1007×sqrt-prod
962×distribute-lft-out--
887×cube-prod
877×associate-/l*
805×add-log-exp
749×frac-times
681×distribute-lft-out
588×associate-/r*
573×associate-/r/
569×frac-add
528×div-inv
513×cbrt-unprod
496×sqrt-div
494×cbrt-undiv
493×associate-*l*
469×associate-*r/
382×cbrt-prod
365×cbrt-div
361×pow-exp
272×distribute-rgt-neg-in
247×log-pow
245×flip-+ pow-prod-down
244×flip3-+
243×pow-to-exp
226×sqr-pow
220×exp-prod
185×1-exp
180×unswap-sqr
125×clear-num frac-2neg
124×log-prod
115×associate-/l/
114×*-commutative
110×rec-exp
106×sub-neg
96×diff-log
76×pow1/3 swap-sqr
75×pow-unpow
66×unpow3 cube-mult
60×sum-log
59×div-sub
57×unpow2
47×sqrt-pow1
41×pow1/2
40×distribute-rgt-out
39×rem-sqrt-square
38×+-commutative
37×cube-div
34×log-div
32×pow-pow
31×distribute-rgt-in distribute-lft-in
28×associate-+l-
27×distribute-lft-neg-in
26×neg-sub0
25×frac-sub
24×rem-cube-cbrt
23×pow-prod-up pow-sqr
22×tan-quot sin-mult
19×associate--l- sin-diff
18×associate--l+ rem-log-exp
17×distribute-lft1-in neg-log cos-mult
15×pow-plus
14×associate-+r+
13×cos-diff pow-flip cos-sum pow2
11×sin-cos-mult inv-pow
9×neg-mul-1
8×associate-+r- acos-asin exp-sum
7×difference-cubes sin-sum associate-+l+ associate--r+
5×un-div-inv
4×distribute-frac-neg associate--r-
3×acos-neg rem-exp-log exp-to-pow rem-cbrt-cube
2×sub0-neg unpow1/3 asin-acos
1×exp-diff unsub-neg tanh-undef distribute-rgt-neg-out

regimes9.8s (2.4%)

Accuracy

Total 21.0b remaining (17.8%)

Threshold costs 7.5b (6.4%)

3.8b73.9%Equirectangular approximation to distance on a great circle
3.8b67.2%Quotient of products
3.7b86.3%Quadratic roots, full range
1.2b0%2-ancestry mixing, zero discriminant
1.1b94.7%Cubic critical

localize2.3s (0.6%)

bsearch810.0ms (0.2%)

end1.0ms (0.0%)