Date:Thursday, March 19th, 2020
Commit:2b8af9a1 on simpler-alts
Hostname:warfa with Racket 7.5
Seed:2020079
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

sample1.8m (37.8%)

Algorithm
100×intervals
Results
47.9s15719×body10240exit
17.9s444369×body80valid
13.6s29590×body1280valid
6.7s23571×body640valid
2.9s3096×body1280nan
2.5s70021×body80nan
2.1s11894×body320valid
1.7s2524×body640nan
1.2s9985×body160valid
652.0ms49536×pre80true
607.0ms1276×body320nan
368.0ms1477×body2560valid
209.0ms638×body160nan
142.0ms571×body5120valid

series1.2m (25.4%)

Calls

508 calls:

2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
2.2s
(/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.3s
(exp (log (- 1.0 (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (cbrt (pow (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) 3)))) (exp (- (* (fabs x) (fabs x))))))))
1.3s
(- 1.0 (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (cbrt (pow (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) 3)))) (exp (- (* (fabs x) (fabs x))))))

prune1.1m (23.5%)

Filtered
23687 candidates to 14354 candidates (60.6%)

simplify17.9s (6.1%)

Algorithm
266×egg-herbie

rewrite8.7s (3.0%)

Algorithm
166×rewrite-expression-head
Calls

508 calls:

222.0ms
(/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
219.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
185.0ms
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
182.0ms
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
148.0ms
(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
Rules
25870×times-frac
16121×*-un-lft-identity
14944×add-sqr-sqrt
9762×add-cube-cbrt
5007×add-exp-log
3926×add-cbrt-cube
2445×associate-/r/
2295×prod-exp
2242×pow1
2213×distribute-lft-out
2198×difference-of-squares
1970×sqrt-prod
1761×flip-+ flip3-+
1744×cbrt-unprod
1715×associate-*r*
1362×associate-/l*
1331×div-inv
1297×div-exp
1295×associate-*l*
1198×distribute-lft-out--
891×cbrt-undiv
771×add-log-exp
737×pow-prod-down
670×frac-times
664×frac-add
641×cbrt-div
579×cbrt-prod
568×associate-/r*
566×associate-*r/
427×associate-*l/
347×unswap-sqr
275×swap-sqr
257×log-pow
238×unpow-prod-down
217×sqrt-div
183×associate-/l/
177×pow-prod-up
169×*-commutative
160×log-prod
153×sqrt-pow1
151×pow-plus
140×distribute-rgt-in distribute-lft-in
130×flip3-- flip--
114×pow1/3 cube-prod
113×pow-exp
109×pow1/2
100×sqr-pow
97×pow-to-exp
82×clear-num frac-2neg
79×sub-neg
75×diff-log
73×sum-log
65×pow-sqr
64×pow-unpow
62×rem-sqrt-square associate-+l-
61×1-exp
59×rec-exp
55×pow-sub
49×associate--l+
47×pow2 +-commutative
43×exp-prod
32×unpow3 cube-mult
30×cube-div
25×pow-pow
22×distribute-neg-frac
21×div-sub
17×exp-sum
16×rem-log-exp log-div
13×rem-cube-cbrt rem-cbrt-cube
11×associate-+l+ associate--l- associate-+r+
10×exp-diff
9×un-div-inv pow3
8×associate--r+
7×distribute-rgt-neg-in inv-pow pow-flip
6×distribute-lft-neg-in sin-sum
5×cos-sum rem-exp-log
4×distribute-neg-in unpow-prod-up frac-sub unpow2
3×sqrt-unprod
2×rem-square-sqrt neg-mul-1 sum-cubes distribute-rgt-neg-out
1×sqrt-pow2 associate-+r- distribute-rgt-out-- neg-log associate--r-

regimes7.5s (2.6%)

Accuracy

Total 88.3b remaining (31.5%)

Threshold costs 3.6b (1.3%)

10.7b56.3%math.log10 on complex, real part
10.5b57%math.log/1 on complex, real part
10.1b57%math.abs on complex
10.0b58.8%math.log/2 on complex, real part
9.7b55.6%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.6s (0.9%)

bsearch1.8s (0.6%)

end1.0ms (0.0%)