Details

series10.8m (82.9%)

Calls

320 calls:

3.0s
(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)))))
2.8s
(fma t (- (* x (* 18.0 (* y 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))))
2.7s
(/ (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)) (fma (tan a) (+ (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))))

prune55.8s (7.1%)

sample51.9s (6.6%)

Algorithm
59×intervals
Results
12.0s263232×body80valid
8.9s21508×body1280valid
8.3s208197×body80nan
3.2s11260×body640valid
2.4s5254×body2560valid
976.0ms5119×body320valid
474.0ms16512×pre80true
328.0ms2463×body160valid
54.0ms210×body5120valid

simplify8.4s (1.1%)

Algorithm
155×egg-herbie

regimes7.3s (0.9%)

Accuracy

Total 29.1b remaining (22.3%)

Threshold costs 2.9b (2.2%)

5.6b80.3%NMSE problem 3.2.1
4.8b83.7%The quadratic formula (r1)
3.7b3.9%Linear.Matrix:det33 from linear-1.19.1.3
2.4b7.1%cos(2*x)/(cos^2(x)*sin^2(x))
2.3b44.1%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite7.0s (0.9%)

Algorithm
97×rewrite-expression-head
Calls

322 calls:

673.0ms
(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
576.0ms
(/ (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)) (fma (tan a) (+ (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))))
465.0ms
(* (pow (sqrt (/ 1 a)) 1.0) (/ x (/ y (/ (pow (sqrt (/ 1 a)) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
165.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
142.0ms
(* (cbrt (/ (- (+ f n)) (- f n))) (cbrt (/ (- (+ f n)) (- f n))))
Rules
13336×times-frac
8634×*-un-lft-identity
8081×add-sqr-sqrt
6655×add-cube-cbrt
2591×unpow-prod-down
1787×add-exp-log
1468×sqrt-prod
1321×associate-*r*
971×add-cbrt-cube
944×cbrt-prod
902×prod-diff
798×prod-exp
786×associate-/r*
757×fma-udef
741×pow1
729×exp-sum
688×distribute-rgt-neg-in
625×distribute-lft-neg-in
528×distribute-lft-out
493×associate-*l*
488×difference-of-squares
462×add-log-exp
437×distribute-lft-out--
387×div-inv
366×div-exp
322×log1p-expm1-u expm1-log1p-u
277×cbrt-unprod
250×associate-/l*
243×associate-+r+
237×cube-prod
231×sqr-pow
215×swap-sqr
181×distribute-rgt-in distribute-lft-in
175×flip-- flip3-- neg-mul-1
168×pow-exp
167×unswap-sqr
156×cbrt-undiv
153×fma-neg
146×pow-prod-down
145×pow-to-exp
140×associate-/r/
110×associate-*l/
109×fma-def
104×log-pow
90×*-commutative cbrt-div
86×associate-*r/
80×flip-+ flip3-+ associate-+l+
79×sub-neg log-prod
68×sqrt-div
63×frac-times
62×associate--r+
60×pow1/3
54×1-exp
53×frac-2neg clear-num
47×diff-log
42×frac-sub
39×associate-/l/
36×rec-exp sum-log
35×sqrt-pow1
33×rem-sqrt-square
31×pow1/2
26×sin-mult
20×exp-prod cos-mult
19×pow-unpow neg-sub0
18×associate-+l-
17×tan-quot +-commutative
12×neg-log
11×sub-div
10×pow-flip div-sub
9×frac-add
8×inv-pow log-div
7×associate--l+ pow-pow
6×cube-div rem-exp-log exp-diff pow-prod-up pow-sqr associate--l- unpow2
5×rem-cube-cbrt un-div-inv distribute-neg-in
4×difference-cubes exp-neg pow2 unpow3 cube-mult pow-plus distribute-frac-neg distribute-neg-frac
3×associate-+r-
2×tan-sum cos-sum
1×rem-cbrt-cube sqrt-unprod distribute-lft-neg-out cube-neg rem-log-exp

localize2.4s (0.3%)

bsearch1.3s (0.2%)

end1.0ms (0.0%)