Details

series11.0m (54.5%)

Calls

320 calls:

1.9m
(fma (- (* y0 c) (* y1 a)) (- (* y2 x) (* z y3)) (* (- (* a b) (* c i)) (- (* x y) (* z t))))
4.3s
(fma (- (* t c) (* i y)) j (fma (- (* i a) (* z c)) b (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t))))))
4.2s
(fma (- (* i a) (* z c)) b (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))))
1.1s
(/ (fma (fma y (fma (+ y a) y b) c) y i) (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t))
1.1s
(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1))))

simplify4.6m (22.7%)

sample2.6m (12.8%)

Algorithm
59×intervals
Results
50.4s262422×body80valid
33.3s206340×body80nan
26.8s21134×body1280valid
11.2s10865×body640valid
7.3s5351×body2560valid
3.1s5159×body320valid
1.0s2555×body160valid
983.0ms16512×pre80true
551.0ms205×body5120valid

prune1.4m (7.1%)

regimes17.5s (1.4%)

Accuracy

Total 35.5b remaining (26.5%)

Threshold costs 5.2b (3.8%)

5.9b2.8%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
5.2b80.9%The quadratic formula (r1)
5.1b23.6%Linear.Matrix:det33 from linear-1.19.1.3
4.7b82.9%NMSE problem 3.2.1
2.8b-1.5%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite9.2s (0.8%)

Algorithm
98×rewrite-expression-head
Calls

321 calls:

409.0ms
(/ (sqrt (+ a t)) (/ t z))
388.0ms
(* (* (* (cbrt (- (* z y) (* t a))) (cbrt (- (* z y) (* t a)))) (cbrt (- (* z y) (* t a)))) x)
356.0ms
(/ (- (/ (cos a) (/ (- 1 (* (tan y) (tan z))) (+ (tan z) (tan y)))) (sin a)) (cos a))
350.0ms
(+ (log (sqrt z)) (+ (log (sqrt (sqrt z))) (+ (- (log (sqrt (sqrt z))) (fma (- 0.5 a) (log t) t)) (log (+ y x)))))
191.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
Rules
7019×*-un-lft-identity
6669×times-frac
6273×add-sqr-sqrt
4505×add-cube-cbrt
1738×prod-diff
1362×add-exp-log
1161×pow1
1047×add-cbrt-cube
1032×associate-*l*
863×distribute-lft-out--
695×difference-of-squares
684×sqrt-prod
566×distribute-lft-out
541×distribute-rgt-neg-in
515×distribute-lft-neg-in
493×add-log-exp
461×prod-exp
433×associate-/r*
383×pow-prod-down
358×associate-*r*
344×associate-/r/
333×cbrt-prod
322×log1p-expm1-u div-inv
321×expm1-log1p-u cbrt-unprod insert-posit16
316×associate-/l*
309×exp-sum
272×div-exp
267×flip3-- flip--
225×fma-neg
220×distribute-rgt-in distribute-lft-in
199×associate--r+
183×log-pow
177×exp-prod
154×neg-mul-1
153×cbrt-undiv
127×unswap-sqr
121×log-prod
112×associate-*l/
93×cbrt-div
90×sub-neg
87×associate-+r+
79×*-commutative
77×frac-times
76×fma-def
73×pow1/3
69×fma-udef
68×tan-quot
67×diff-log
66×1-exp rec-exp
61×frac-2neg clear-num
59×flip-+ flip3-+
57×associate-*r/
56×associate-+l+
54×associate-/l/
47×frac-sub
45×sqrt-pow1
44×pow-flip pow-prod-up
43×associate--l+
40×sqrt-div swap-sqr pow1/2 pow-sqr
34×sum-log
27×rem-sqrt-square
23×frac-add
21×pow-exp pow-plus rem-exp-log
20×sin-mult
19×neg-sub0 div-sub
18×associate-+r-
16×distribute-neg-frac unpow-prod-down
15×exp-diff
13×+-commutative pow-to-exp
12×sqr-pow inv-pow e-exp-1
11×pow2 pow-pow
10×cos-mult pow-unpow neg-log log-div
9×distribute-frac-neg
8×associate--l-
7×sub-div
6×associate-+l- un-div-inv
4×difference-of-sqr-1 expm1-def
3×log1p-udef pow3 distribute-rgt-out
2×cos-sum tan-sum rem-cbrt-cube
1×expm1-log1p expm1-udef distribute-lft-neg-out log1p-expm1 sqrt-unprod exp-to-pow remove-posit16 rem-log-exp associate--r- cos-2

localize5.1s (0.4%)

bsearch3.3s (0.3%)

end1.0ms (0.0%)