Date:Monday, March 2nd, 2020
Commit:76ce2b17 on master
Hostname:warfa with Racket 7.5
Seed:2020062
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

sample10.4m (83.8%)

Algorithm
78×intervals
Results
9.0m57345×body10240exit
34.3s43816×body1280valid
11.4s30693×body640valid
7.3s204982×body80valid
4.9s152731×body80nan
4.6s27138×body320valid
3.7s197664×pre80true
3.2s36217×body160valid
849.0ms3140×body2560valid
402.0ms7982×body160nan
401.0ms4078×pre10240exit
148.0ms251×body5120valid
95.0ms8126×pre80false

prune52.1s (7.0%)

series39.4s (5.3%)

Calls

463 calls:

737.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
626.0ms
(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))
586.0ms
(/ (* (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)))
447.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
371.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))

simplify12.5s (1.7%)

Algorithm
222×egg-herbie

regimes9.5s (1.3%)

Accuracy

Total 35.7b remaining (25.9%)

Threshold costs 6.6b (4.8%)

5.9b57.4%Cubic critical, narrow range
5.2b54.4%Quotient of products
5.0b30.2%Cubic critical, medium range
3.8b83%Cubic critical
3.6b0%Cubic critical, wide range

rewrite4.5s (0.6%)

Algorithm
144×rewrite-expression-head
Calls

463 calls:

56.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))
49.0ms
(+ (/ 1.0 (- x 1.0)) (cbrt (pow (/ x (+ x 1.0)) 3)))
49.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
47.0ms
(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))
45.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
Rules
10867×times-frac
9750×*-un-lft-identity
9031×add-sqr-sqrt
7345×add-cube-cbrt
3343×prod-diff
2516×sqrt-prod
2396×add-exp-log
1552×add-cbrt-cube
959×pow1
870×associate-*r*
756×div-exp
736×unpow-prod-down
731×prod-exp
707×add-log-exp
680×difference-of-squares
639×associate-/r*
625×div-inv distribute-rgt-neg-in
614×distribute-lft-out--
611×associate-/l*
592×distribute-lft-out
534×associate-/r/
487×distribute-lft-neg-in
469×log1p-expm1-u
467×expm1-log1p-u
400×fma-neg
367×cbrt-undiv
353×cube-prod
326×cbrt-unprod
315×pow-exp
302×cbrt-prod
297×associate-*l*
296×log-prod
264×flip--
263×flip3--
255×distribute-rgt-in distribute-lft-in
254×fma-def
232×pow-to-exp
229×sqr-pow
202×flip-+
201×flip3-+
197×pow-prod-down
160×neg-mul-1
153×unswap-sqr
143×associate-*r/
121×clear-num frac-2neg
105×sqrt-div
101×log-pow
97×associate-/l/
96×associate-*l/ frac-times
89×sub-neg
86×unpow3 cube-mult
85×cos-mult exp-sum
80×unpow2
79×diff-log
78×*-commutative
75×sin-mult
73×frac-add exp-prod
69×pow-unpow
61×tan-quot
52×cbrt-div
51×sum-log
50×log-div
48×1-exp
46×associate-+l+ div-sub cos-sum
42×pow1/3
41×sqrt-pow1
38×pow-pow
37×rem-log-exp
34×sin-sum +-commutative
33×frac-sub
32×pow1/2
31×rem-sqrt-square neg-sub0
30×rec-exp
21×neg-log
20×associate--l+
19×cube-div pow-prod-up pow-sqr associate-+r+ associate-+l-
17×sin-diff
16×sin-cos-mult pow-flip
14×fma-udef cos-diff swap-sqr
13×associate--l- distribute-rgt-out
12×acos-asin distribute-rgt-neg-out
11×inv-pow
10×rem-cube-cbrt pow-plus distribute-frac-neg expm1-udef
9×un-div-inv expm1-log1p associate--r+
8×associate-+r- distribute-neg-frac
7×rem-exp-log pow2
6×acos-neg log1p-udef log1p-expm1 sub-div
5×exp-diff associate--r- rem-cbrt-cube
4×asin-acos
3×unsub-neg hypot-def
2×sin-neg distribute-lft1-in log-rec
1×distribute-neg-out difference-cubes sqrt-unprod exp-neg distribute-neg-in hypot-udef cube-neg

localize2.2s (0.3%)

bsearch722.0ms (0.1%)

end1.0ms (0.0%)