Date:Thursday, March 5th, 2020
Commit:a3b4d238 on findroot
Hostname:warfa with Racket 7.5
Seed:2020065
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

series10.8m (84.5%)

Calls

341 calls:

2.9s
(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
2.9s
(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
713.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))
604.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
587.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))) (cos a)))

sample52.2s (6.8%)

Algorithm
59×intervals
Results
12.9s263454×body80valid
9.3s210189×body80nan
7.4s21378×body1280valid
2.8s5300×body2560valid
2.8s10916×body640valid
886.0ms5104×body320valid
420.0ms16512×pre80true
320.0ms2571×body160valid
71.0ms244×body5120valid

prune43.5s (5.7%)

simplify9.2s (1.2%)

Algorithm
158×egg-herbie

regimes7.5s (1.0%)

Accuracy

Total 29.8b remaining (23.1%)

Threshold costs 3.0b (2.3%)

6.6b12.3%Linear.Matrix:det33 from linear-1.19.1.3
4.4b84.7%NMSE problem 3.2.1
3.5b87.4%The quadratic formula (r1)
2.7b0%cos(2*x)/(cos^2(x)*sin^2(x))
1.9b46.3%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite3.2s (0.4%)

Algorithm
100×rewrite-expression-head
Calls

343 calls:

62.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))
50.0ms
(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
45.0ms
(+ (log (+ (/ (sqrt 1.0) (sqrt x)) (sqrt 1.0))) (log (- (/ (sqrt 1.0) (sqrt x)) (sqrt 1.0))))
37.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
34.0ms
(/ (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t) (* (* (cbrt (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) (cbrt (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))) 1))
Rules
4744×*-un-lft-identity
4623×add-sqr-sqrt
4516×times-frac
3585×add-cube-cbrt
1971×add-exp-log
1486×prod-diff
1080×add-cbrt-cube
895×prod-exp
875×associate-*l/
850×associate-*r/
729×pow1
676×flip-- flip3--
605×distribute-rgt-neg-in
591×sqrt-prod
579×frac-sub
559×associate-*r*
536×distribute-lft-neg-in
526×cbrt-prod
505×add-log-exp
420×associate-*l*
418×div-exp
397×frac-times
368×associate-/r*
359×difference-of-squares
351×distribute-lft-out--
347×expm1-log1p-u
343×log1p-expm1-u
320×cbrt-unprod
300×sqrt-div
294×unpow-prod-down div-inv
259×associate-/l*
255×distribute-lft-out
223×associate-/l/
204×flip-+ flip3-+
188×fma-neg
183×pow-exp
181×cbrt-undiv
163×distribute-rgt-in distribute-lft-in
158×associate-/r/
156×pow-prod-down
154×neg-mul-1
149×pow-to-exp
138×cube-prod
123×unswap-sqr
96×fma-def
91×*-commutative
88×sub-neg
81×log-prod
80×associate--r+
77×cbrt-div
71×pow1/3
70×associate-+r+
64×fma-udef 1-exp
61×clear-num frac-2neg
58×exp-sum diff-log
56×rec-exp
53×log-pow
44×swap-sqr
36×tan-quot
34×associate-+l+
30×pow-unpow sqr-pow exp-prod sum-log
29×pow1/2 sqrt-pow1
27×rem-sqrt-square
24×neg-sub0
22×sin-mult
20×neg-log
18×distribute-neg-frac
16×+-commutative cos-mult
14×div-sub associate-+l-
13×associate--l+
12×frac-add pow-flip associate--l- log-div
10×rem-exp-log inv-pow distribute-neg-in sub-div
8×pow-pow
7×log1p-udef
6×pow-sqr pow-prod-up
5×exp-diff distribute-frac-neg
4×unpow3 log1p-expm1 pow2 expm1-log1p cube-mult pow-plus expm1-udef
3×rem-cube-cbrt un-div-inv associate-+r- exp-neg distribute-rgt-out--
2×cube-div sqrt-undiv distribute-lft-neg-out unpow1/3 cos-sum tan-sum rem-cbrt-cube rem-log-exp
1×quot-tan sqrt-unprod cube-neg exp-to-pow

localize2.6s (0.3%)

bsearch971.0ms (0.1%)

end0.0ms (0.0%)