Date:Tuesday, February 25th, 2020
Commit:7c13946c on findroot
Hostname:warfa with Racket 7.5
Seed:2020056
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

series10.7m (83.0%)

Calls

332 calls:

728.0ms
(* (cbrt (fma (log t) (- a 0.5) (fma 1 (+ (log (+ x y)) (log z)) (- t)))) (cbrt (fma (log t) (- a 0.5) (fma 1 (+ (log (+ x y)) (log z)) (- t)))))
573.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))
553.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))
551.0ms
(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))
549.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))

sample51.4s (6.7%)

Algorithm
59×intervals
Results
12.3s263445×body80valid
8.8s21318×body1280valid
8.4s205719×body80nan
3.1s11029×body640valid
2.5s5293×body2560valid
963.0ms4993×body320valid
461.0ms16512×pre80true
322.0ms2525×body160valid
57.0ms214×body5120valid

prune49.4s (6.4%)

rewrite9.8s (1.3%)

Algorithm
102×rewrite-expression-head
Calls

334 calls:

1.4s
(- (+ (- (* (* (* x 18.0) (* y z)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
1.4s
(- (+ (- (* (* (* x 18.0) (* y z)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
885.0ms
(- (+ (- (* (* x 18.0) (* (* y z) t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
335.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
294.0ms
(* (+ (* (+ (* (+ (* (* (cbrt (+ (* x y) z)) (cbrt (+ (* x y) z))) (* (cbrt (+ (* x y) z)) y)) 27464.7644705) y) 230661.510616) y) t) (/ 1 (* (fma (fma (fma (+ y a) y b) y c) y i) 1)))
Rules
10228×times-frac
7285×*-un-lft-identity
6531×add-sqr-sqrt
5569×add-cube-cbrt
3116×add-exp-log
1996×prod-exp
1711×unpow-prod-down
1230×associate-*r*
1111×add-cbrt-cube
947×prod-diff
930×cbrt-prod
796×distribute-rgt-neg-in
757×pow1
742×distribute-lft-neg-in
671×associate-/r*
572×exp-sum
554×fma-udef
501×div-exp
489×add-log-exp
481×associate-*l*
461×distribute-lft-out
458×pow-exp
432×pow-to-exp
368×distribute-lft-out--
364×div-inv
350×cbrt-unprod
334×log1p-expm1-u expm1-log1p-u
311×difference-of-squares
294×associate-/l*
289×sqrt-prod
268×distribute-rgt-in distribute-lft-in
252×associate--r+
205×flip3-- flip--
204×neg-mul-1
185×pow-prod-down
172×cbrt-undiv
170×swap-sqr
160×fma-neg
158×sqr-pow
153×cbrt-div
137×unswap-sqr
119×associate-*r/
112×associate-/r/
106×associate-*l/
104×associate-+r+
97×frac-times
95×pow1/3
94×*-commutative
88×fma-def
84×flip-+ flip3-+
79×frac-sub
76×sqrt-div
74×sub-neg
70×cube-prod
68×1-exp
63×associate-/l/
59×rec-exp
58×frac-2neg clear-num
54×log-pow diff-log
51×log-prod
37×sqrt-pow1
33×sum-log
29×tan-quot exp-prod sin-mult
26×distribute-neg-frac
25×distribute-neg-in neg-sub0
24×sub-div cos-mult
23×pow-unpow
22×pow1/2
21×associate-+l-
20×unpow-prod-up associate-+l+
19×div-sub
18×rem-sqrt-square pow-prod-up
15×+-commutative
14×neg-log
12×pow-sqr log-div
11×associate--l- pow-plus associate--l+
10×unpow3 cube-mult
9×rem-exp-log distribute-frac-neg
8×cube-div frac-add pow-flip pow-pow
7×pow2
6×un-div-inv inv-pow
4×associate-+r-
3×exp-diff rem-cube-cbrt
2×cos-sum unsub-neg tan-sum exp-to-pow
1×pow3 exp-neg pow-sub distribute-lft-neg-out sqrt-unprod rem-cbrt-cube pow-neg rem-log-exp

simplify8.7s (1.1%)

Algorithm
160×egg-herbie

regimes8.7s (1.1%)

Accuracy

Total 26.8b remaining (21%)

Threshold costs 5.6b (4.4%)

4.6b82.9%NMSE problem 3.2.1
4.1b85.4%The quadratic formula (r1)
3.9b-5.4%Linear.Matrix:det33 from linear-1.19.1.3
2.4b2.7%cos(2*x)/(cos^2(x)*sin^2(x))
2.1b0%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

localize2.5s (0.3%)

bsearch999.0ms (0.1%)

end1.0ms (0.0%)