Date:Wednesday, March 11th, 2020
Commit:79312c80 on better-rr
Hostname:warfa with Racket 7.5
Seed:2020071
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

prune11.0m (70.7%)

Filtered
46780 candidates to 45016 candidates (96.2%)

sample1.7m (10.9%)

Algorithm
99×intervals
Results
43.4s11602×body10240exit
20.3s475657×body80valid
11.1s26932×body1280valid
5.0s21073×body640valid
2.5s71211×body80nan
1.8s1568×body1280nan
1.6s10454×body320valid
1.1s1367×body640nan
985.0ms9466×body160valid
671.0ms49536×pre80true
343.0ms617×body320nan
341.0ms1466×body2560valid
131.0ms562×body5120valid
116.0ms330×body160nan

simplify1.2m (7.4%)

Algorithm
242×egg-herbie

series48.5s (5.2%)

Calls

405 calls:

1.9s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
813.0ms
(* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5))
801.0ms
(+ (- (* (/ 1 (exp (pow (fabs x) 2))) (- (/ 0.284496736 (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (* (/ 1 (exp (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))))) (fma 1.453152027 (/ (/ 1 (exp (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 4)) 1.0))
796.0ms
(/ (/ 6.0 1.0) (pow (* -2.0 (log u1)) 0.5))
776.0ms
(/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0)))

rewrite47.1s (5.0%)

Algorithm
144×rewrite-expression-head
Calls

409 calls:

3.0s
(* (/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp z)) (/ (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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 (+ (+ (- 1.0) 7.0) 0.5))))
2.2s
(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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)))
1.4s
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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))))
759.0ms
(/ (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (/ (* (- (- z 1.0) 1.0) z) (- (- z 1.0) 1.0)))) (/ -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 (+ (+ (- 1.0) 7.0) 0.5)))
562.0ms
(+ (- (* (/ 1 (exp (pow (fabs x) 2))) (- (/ 0.284496736 (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (* (/ 1 (exp (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))))) (fma 1.453152027 (/ (/ 1 (exp (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 4)) 1.0))
Rules
176192×frac-add
79838×clear-num
78392×frac-2neg
55099×frac-times
36159×associate-*r/
14009×flip-+ flip3-+
13523×associate-/l/
13136×associate-+l-
13124×pow-sub
12781×frac-sub
11327×associate-*l/
8930×associate-/r*
4854×sqr-pow
2468×un-div-inv
2451×unpow2
1447×unpow3
550×associate-/r/
522×*-commutative
405×associate-*l*
387×flip-- flip3--
362×div-inv
251×associate-+l+
239×sub-div
203×associate-/l*
200×associate-*r*
151×times-frac
128×+-commutative
114×sub-neg
105×sqrt-prod
98×exp-sum
86×prod-diff
81×distribute-rgt-in distribute-lft-in
75×sqrt-div
68×associate--l+
65×hypot-def
60×fma-udef
58×fma-neg
50×unpow-prod-down
45×fma-def
40×unpow-prod-up
35×pow1/2
33×neg-mul-1 difference-of-squares
27×inv-pow
22×distribute-rgt-neg-in distribute-lft-neg-in pow2
21×associate--r+
19×pow-to-exp
18×div-sub
17×associate--l-
15×swap-sqr
12×pow3 sin-sum pow-plus
10×remove-double-div
6×pow-flip distribute-neg-frac rec-exp
5×exp-diff associate-+r+ distribute-rgt-neg-out log-pow
4×difference-cubes neg-sub0 distribute-lft-out-- distribute-frac-neg cos-sum pow-exp
3×distribute-lft-out pow-pow sin-diff
2×log-div log-prod distribute-rgt-out distribute-lft-neg-out distribute-rgt-out-- sum-cubes distribute-neg-in
1×exp-prod associate--r- pow-prod-down prod-exp unswap-sqr distribute-rgt1-in diff-log

regimes3.8s (0.4%)

Accuracy

Total 27.3b remaining (23.6%)

Threshold costs 5.1b (4.4%)

5.4b16.8%Octave 3.8, jcobi/2
5.2b57.3%math.sqrt on complex, real part
4.8b31.5%_divideComplex, real part
3.3b80%Octave 3.8, jcobi/1
2.2b43%Octave 3.8, jcobi/4

localize2.3s (0.3%)

bsearch1.3s (0.1%)

end1.0ms (0.0%)