Date:Wednesday, April 22nd, 2020
Commit:1c116713 on better-rr
Hostname:warfa with Racket 7.5
Seed:2020113
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

sample2.2m (36.0%)

Algorithm
77×intervals
Results
50.4s17381×body10240exit
33.2s42968×body1280valid
11.4s30564×body640valid
6.9s202565×body80valid
4.8s151340×body80nan
4.6s27627×body320valid
3.1s36404×body160valid
2.7s157641×pre80true
739.0ms2909×body2560valid
374.0ms7896×body160nan
232.0ms16845×pre80false
49.0ms179×body5120valid

prune2.1m (35.1%)

Filtered
64244 candidates to 32212 candidates (50.1%)

series47.0s (13.0%)

Calls

491 calls:

3.1s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
956.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
774.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
747.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
522.0ms
(- (* (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))))))))

simplify23.4s (6.5%)

Algorithm
219×egg-herbie

rewrite22.7s (6.3%)

Algorithm
143×rewrite-expression-head
Calls

491 calls:

1.3s
(* (/ a1 (* b1 (cbrt (* (cbrt b2) (cbrt b2))))) (/ (* (cbrt a2) (cbrt a2)) (* (cbrt (cbrt b2)) (cbrt b2))))
1.1s
(* (/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))
370.0ms
(/ (* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
340.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
329.0ms
(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
Rules
70303×*-un-lft-identity
62997×add-sqr-sqrt
52509×times-frac
27701×add-cube-cbrt
21579×associate-*l*
19363×associate-/r*
18390×cbrt-prod
18191×associate-*r*
17616×associate-/l*
13993×distribute-lft-out
12149×frac-sub
12012×unswap-sqr
10768×frac-times
9143×distribute-lft-out--
7624×difference-of-squares
4862×sqrt-prod
4707×distribute-rgt-neg-in
4446×swap-sqr
4018×associate-/l/
3647×unpow-prod-down
3579×*-commutative
2822×log-div
2749×frac-2neg
2746×clear-num
2476×add-cbrt-cube
2125×add-exp-log
1408×sqr-pow
1286×distribute-lft-neg-in
1219×frac-add
1170×associate-/r/
1037×pow1
916×cbrt-unprod
869×flip--
868×flip3--
831×add-log-exp
819×associate-*r/
813×div-inv
751×flip-+
750×flip3-+
747×cbrt-undiv
667×associate-*l/
575×prod-exp
522×div-exp
484×sqrt-div
431×pow-unpow
427×unpow3
409×cbrt-div
375×neg-mul-1
336×difference-cubes
224×pow-prod-down
181×log-prod
156×distribute-rgt-out
123×sub-div
106×log-pow
101×sub-neg
95×diff-log
91×div-sub
88×un-div-inv
87×sum-log
80×+-commutative
74×unpow2
64×exp-prod
56×pow1/3
55×distribute-rgt-out--
48×sum-cubes
47×associate-+l-
45×distribute-rgt-in distribute-lft-in
43×pow1/2 pow-exp 1-exp sqrt-pow1
40×pow-to-exp
38×neg-sub0
36×cos-sum
35×associate-+r+
31×cos-mult
30×rem-sqrt-square
26×rec-exp
25×neg-log
22×rem-log-exp
21×associate-+r- sin-mult
20×pow-prod-up tan-quot
18×pow-pow pow-sqr associate--l+
17×cos-diff sin-diff
16×associate--l-
15×rem-cube-cbrt associate--r+
12×log-rec exp-sum
11×pow-plus
10×unsub-neg pow2 associate-+l+ rem-cbrt-cube
9×sin-cos-mult
8×rem-exp-log distribute-frac-neg acos-asin asin-acos
6×associate--r- sin-sum
5×inv-pow pow-flip
4×distribute-lft1-in
3×acos-neg remove-double-div distribute-rgt-neg-out
2×exp-diff sqrt-unprod distribute-lft-neg-out sqr-cos
1×+-inverses sqrt-pow2 rem-square-sqrt tanh-undef exp-to-pow tanh-def

regimes8.5s (2.3%)

Accuracy

Total 26.5b remaining (23.7%)

Threshold costs 6.8b (6.1%)

9.2b51.5%Equirectangular approximation to distance on a great circle
4.7b82.8%Cubic critical
2.3b69.8%Quotient of products
1.3b0%2-ancestry mixing, positive discriminant
1.2b94.9%Quadratic roots, full range

localize2.4s (0.7%)

bsearch510.0ms (0.1%)

end1.0ms (0.0%)