Details

simplify3.7m

sample3.4m

Algorithm
60×intervals
Results
1.6m336382×body80valid
32.6s206198×body80nan
27.3s21600×body1280valid
11.7s10888×body640valid
7.2s5405×body2560valid
3.2s5152×body320valid
1.5s16512×pre80true
1.1s2453×body160valid
261.0ms250×body5120valid

prune3.3m

series55.7s

Calls

348 calls:

Slowest
3.4s
(- (- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
3.0s
(- (- (+ (- (* (* x 18.0) (* y (* z t))) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
1.4s
(/ (- (* (* 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))))
890.0ms
(- (* (* 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)))))
686.0ms
(/ (+ (* (+ (* (* (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y)) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

rewrite44.3s

Algorithm
104×rewrite-expression-head
Calls

348 calls:

Slowest
13.7s
(* (* (/ 1 (* (cbrt (- (+ t 1.0) z)) (* (* (cbrt (cbrt (- (+ t 1.0) z))) (cbrt (cbrt (- (+ t 1.0) z)))) (cbrt (cbrt (- (+ t 1.0) z)))))) (/ (- y z) (cbrt (- (+ t 1.0) z)))) (- a x))
7.7s
(- (- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
4.2s
(- (- (+ (- (* (* x 18.0) (* y (* z t))) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
940.0ms
(/ (* x (* (exp (* 1.0 (log (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))))) (exp (- (* 1.0 (log (pow a -1/3))) (+ (* (log (/ 1 z)) y) (+ b (* t (log (/ 1 a))))))))) y)
903.0ms
(/ (* x (* (exp (* 1.0 (log (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))))) (exp (- (* 1.0 (log (cbrt (/ 1 a)))) (+ (* (log (/ 1 z)) y) (+ b (* t (log (/ 1 a))))))))) y)
Rules
3326×*-un-lft-identity
3184×add-sqr-sqrt
3007×times-frac
2255×add-cube-cbrt
1636×add-exp-log
1329×add-cbrt-cube
1194×pow1
935×associate-*r/
883×associate-*l/
797×flip3-- flip--
610×frac-sub
597×add-log-exp
584×associate-*l*
577×prod-exp
545×associate-*r*
507×frac-times
450×cbrt-unprod
400×cbrt-prod
376×pow-prod-down
373×associate-/r*
348×insert-posit16
322×sqrt-div
290×sqrt-prod
289×div-exp
271×difference-of-squares
269×flip-+ flip3-+
263×distribute-lft-out
256×associate-/l*
252×distribute-lft-out--
249×log-prod
217×div-inv
206×associate-/l/
202×cbrt-undiv
189×distribute-rgt-in distribute-lft-in
175×associate-/r/
156×swap-sqr
152×unswap-sqr
147×sub-neg
123×*-commutative
96×associate--l+
94×cbrt-div
92×exp-sum
91×distribute-rgt-neg-in
84×distribute-lft-neg-in diff-log
73×frac-2neg clear-num
64×sum-log
63×pow-prod-up
54×pow1/3
51×1-exp rec-exp
49×pow-sqr
43×unpow-prod-down
41×associate-+l+ associate-+r+
38×log-pow
34×sqrt-pow1 pow1/2
33×pow-plus
32×pow-unpow
30×frac-add
29×rem-sqrt-square
26×associate--r+ neg-mul-1
25×pow2 +-commutative difference-of-sqr-1
20×pow-flip
19×cos-mult sin-mult rem-exp-log exp-prod
18×tan-quot distribute-rgt-out-- log-div
15×inv-pow div-sub
14×sub-div
13×sqr-pow
11×neg-sub0 associate--l- associate-+l-
10×pow-exp associate-+r-
9×neg-log pow-pow
8×exp-diff log-rec pow-to-exp
7×distribute-rgt-neg-out
6×associate--r-
5×rem-log-exp
3×un-div-inv unsub-neg cos-2
2×quot-tan cos-sum tan-sum exp-to-pow distribute-neg-frac distribute-frac-neg distribute-rgt-out
1×unpow-prod-up pow-div distribute-lft-neg-out sqrt-unprod sqr-sin unpow2 unpow1/3 remove-posit16 acos-asin e-exp-1

regimes30.1s

Accuracy

Total 39.9b remaining (26.8%)

Threshold costs 3.1b (2%)

11.8b-14.7%Linear.Matrix:det44 from linear-1.19.1.3
6.6b0.5%Linear.Matrix:det33 from linear-1.19.1.3
4.3b84.7%The quadratic formula (r1)
2.3b1.3%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
2.1b14.9%cos(2*x)/(cos^2(x)*sin^2(x))

localize6.3s

bsearch5.0s

end1.0ms