Details

sample5.7m (71.0%)

Algorithm
78×intervals
Results
4.3m34949×body10240exit
34.1s43795×body1280valid
11.0s30257×body640valid
7.2s203920×body80valid
4.8s152700×body80nan
4.6s27477×body320valid
3.4s36183×body160valid
3.0s173178×pre80true
730.0ms2945×body2560valid
391.0ms4117×pre10240exit
368.0ms7810×body160nan
104.0ms8409×pre80false
78.0ms221×body5120valid

prune50.4s (10.5%)

series50.1s (10.4%)

Calls

509 calls:

2.5s
(/ (- (* (* (cos delta) (cos delta)) (* (cos delta) (cos delta))) (* (* (* (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))))))) (* (* (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))))))))) (* (+ (* (pow (sin phi1) 2) (* (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 (cos delta) 2)) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
1.0s
(pow (/ (- (* (cos delta) (cos delta)) (* (* (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)))))))) 3)
816.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (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))))))))
811.0ms
(cbrt (pow (/ (- (* (cos delta) (cos delta)) (* (* (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)))))))) 3))
803.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (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))))))))

rewrite14.3s (3.0%)

Algorithm
145×rewrite-expression-head
Calls

509 calls:

848.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
628.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
564.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
551.0ms
(* (- (/ 1 (/ (/ v m) (- 1.0 m))) 1.0) m)
454.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
6576×times-frac
6285×*-un-lft-identity
6145×add-sqr-sqrt
3832×add-cube-cbrt
3234×pow1
2946×add-exp-log
1992×add-cbrt-cube
1251×pow-prod-down
1136×sqrt-prod
1101×associate-*r*
1068×prod-exp
1035×difference-of-squares
861×associate-/l*
826×flip--
825×flip3--
789×add-log-exp
786×associate-*l/
769×div-exp
709×frac-times
708×unpow-prod-down
702×distribute-lft-out--
606×cbrt-unprod
567×associate-/r*
564×associate-*l*
483×distribute-lft-out associate-*r/
418×frac-add
406×pow-prod-up
380×cbrt-undiv
378×pow-exp
368×sqrt-div
356×div-inv
351×cbrt-prod
329×cube-prod
306×associate-/r/
305×pow-sqr
278×pow-to-exp
275×sin-mult
273×log-prod
268×sqr-pow
261×distribute-rgt-neg-in
253×cos-mult
245×associate-/l/
240×unswap-sqr
204×flip-+
203×flip3-+
188×cbrt-div
161×swap-sqr
156×frac-sub
135×pow-plus
126×clear-num frac-2neg
120×*-commutative
111×exp-prod
96×sub-neg
91×log-pow
90×diff-log
70×unpow2
68×div-sub
65×pow-pow
63×unpow3 cube-mult
60×pow-unpow
57×sum-log
54×distribute-lft-neg-in
51×pow2 log-div
45×rem-sqrt-square sub-div
43×sin-cos-mult
42×pow1/3 sqrt-pow1
41×pow1/2
37×+-commutative
33×distribute-rgt-in distribute-lft-in
31×rem-log-exp
30×neg-sub0 associate-+l-
28×tan-quot
24×1-exp rec-exp
20×neg-log
18×neg-mul-1
17×sin-diff
15×cos-diff distribute-rgt-out
13×rem-cube-cbrt associate--l+
12×pow-flip
11×cube-div cos-sum associate--l-
10×distribute-frac-neg
8×acos-asin
7×inv-pow associate-+r+ associate-+r-
6×rem-cbrt-cube distribute-rgt-neg-out
5×sin-sum associate-+l+ unpow-prod-up associate--r+
4×exp-diff acos-neg un-div-inv distribute-rgt-out-- sum-cubes
3×difference-cubes rem-exp-log sqr-cos exp-sum
2×distribute-lft1-in pow-sub asin-acos associate--r-
1×sqrt-undiv sqrt-pow2 sqrt-unprod sqr-sin unsub-neg tanh-undef tanh-def

simplify13.4s (2.8%)

Algorithm
223×egg-herbie

regimes8.0s (1.7%)

Accuracy

Total 27.4b remaining (20.2%)

Threshold costs 7.7b (5.7%)

8.8b35.5%Equirectangular approximation to distance on a great circle
5.2b81.4%Quadratic roots, full range
3.2b71.3%Quotient of products
1.4b0%2-ancestry mixing, positive discriminant
1.0b0%2-ancestry mixing, zero discriminant

localize2.4s (0.5%)

bsearch677.0ms (0.1%)

end1.0ms (0.0%)