Details

series10.8m (80.3%)

Calls

349 calls:

3.0s
(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt 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)))))
2.9s
(fma t (- (* (* (* y 18.0) x) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
2.8s
(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
768.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))

sample1.2m (9.1%)

Algorithm
59×intervals
Results
22.2s320786×body80valid
8.6s21502×body1280valid
8.0s207407×body80nan
3.3s10978×body640valid
2.5s5336×body2560valid
892.0ms4953×body320valid
441.0ms16512×pre80true
321.0ms2478×body160valid
57.0ms232×body5120valid

prune46.9s (5.8%)

regimes12.1s (1.5%)

Accuracy

Total 35.9b remaining (23.1%)

Threshold costs 3.9b (2.5%)

9.5b-4.3%Linear.Matrix:det44 from linear-1.19.1.3
4.5b84.2%NMSE problem 3.2.1
4.0b-6.3%Linear.Matrix:det33 from linear-1.19.1.3
2.2b19.1%cos(2*x)/(cos^2(x)*sin^2(x))
2.1b34.3%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite12.1s (1.5%)

Algorithm
105×rewrite-expression-head
Calls

352 calls:

503.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
499.0ms
(/ (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
481.0ms
(* (* (* x (/ (sqrt (pow (/ 1 a) 1.0)) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (sqrt (pow (/ 1 a) 1.0)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ 1 y))
467.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
440.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a)))
Rules
4984×*-un-lft-identity
4227×add-sqr-sqrt
3346×times-frac
3234×add-exp-log
3214×add-cube-cbrt
2088×prod-exp
1571×prod-diff
1194×add-cbrt-cube
780×distribute-rgt-neg-in
762×pow1
746×cbrt-prod
694×distribute-lft-neg-in
662×associate-*r*
558×sqrt-prod
517×associate-*l*
490×add-log-exp
473×div-exp
458×pow-exp
449×distribute-lft-out
435×pow-to-exp
395×distribute-lft-out--
380×cbrt-unprod
376×difference-of-squares
363×unpow-prod-down
352×log1p-expm1-u expm1-log1p-u
319×distribute-rgt-in distribute-lft-in
310×associate-/r*
252×associate--r+
237×associate-/l*
219×flip-- flip3-- div-inv
209×fma-neg cube-prod
205×associate-+r+
198×neg-mul-1
194×cbrt-undiv
173×swap-sqr
163×pow-prod-down
158×associate-/r/
140×fma-def
125×unswap-sqr
103×*-commutative
102×associate-*r/
100×flip-+ flip3-+
95×cbrt-div
90×sub-neg
87×frac-times
86×fma-udef
84×log-prod
83×associate-*l/
75×pow1/3
72×log-pow
63×clear-num frac-2neg
58×exp-sum
57×1-exp
56×frac-sub
55×rec-exp
47×sqrt-div
43×diff-log
42×associate-/l/
41×sqr-pow
39×pow-unpow
35×sum-log
32×associate-+l+
28×sin-mult associate-+l-
27×neg-sub0
25×cos-mult
22×sqrt-pow1 log-div
21×pow1/2 neg-log +-commutative exp-prod
20×tan-quot
19×rem-sqrt-square
15×unpow3 cube-mult
12×sub-div associate--l-
10×distribute-frac-neg distribute-neg-in distribute-neg-frac
9×cube-div pow-flip
8×pow-pow inv-pow pow-sqr div-sub pow-prod-up
7×rem-exp-log
6×un-div-inv associate--l+
5×pow2 unpow-prod-up pow-plus
4×rem-cube-cbrt rem-cbrt-cube distribute-rgt-neg-out
3×exp-diff distribute-lft-neg-out associate-+r- frac-add distribute-rgt-out-- rem-log-exp
2×cos-sum tan-sum
1×e-exp-1 pow-neg exp-neg pow-sub sqr-neg sqrt-unprod cube-neg exp-to-pow

simplify8.8s (1.1%)

Algorithm
163×egg-herbie

bsearch3.5s (0.4%)

localize2.6s (0.3%)

end1.0ms (0.0%)