Details

sample3.4m (29.5%)

Algorithm
60×intervals
Results
1.5m336180×body80valid
30.5s208137×body80nan
28.3s21465×body1280valid
11.1s10819×body640valid
7.1s5448×body2560valid
3.8s5120×body320valid
1.3s2524×body160valid
1.1s16512×pre80true
209.0ms234×body5120valid

prune3.2m (28.1%)

simplify2.9m (25.1%)

series51.7s (7.5%)

Calls

345 calls:

Slowest
1.1s
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- (+ t 1.0) z) (cbrt (- y z)))) (- a x))
716.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
710.0ms
(* (* (- y z) (/ 1 (- (+ t 1.0) z))) (- a x))
701.0ms
(* (* (- y z) (* (* (cbrt (/ 1 (- (+ t 1.0) z))) (cbrt (/ 1 (- (+ t 1.0) z)))) (cbrt (/ 1 (- (+ t 1.0) z))))) (- a x))
637.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))

regimes30.3s (4.4%)

Accuracy

Total 39.8b remaining (26%)

Threshold costs 4.8b (3.1%)

12.7b-21.7%Linear.Matrix:det44 from linear-1.19.1.3
4.6b5.8%Linear.Matrix:det33 from linear-1.19.1.3
4.4b84.2%The quadratic formula (r1)
3.2b37.3%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.3b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2

rewrite18.5s (2.7%)

Algorithm
100×rewrite-expression-head
Calls

345 calls:

Slowest
3.0s
(- (+ (- (* (* (* z x) (* y 18.0)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
2.0s
(* (* (- y z) (* (* (cbrt (/ 1 (- (+ t 1.0) z))) (cbrt (/ 1 (- (+ t 1.0) z)))) (cbrt (/ 1 (- (+ t 1.0) z))))) (- a x))
1.0s
(/ (+ (* (+ (* (* (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))
354.0ms
(* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))
333.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
Rules
3610×*-un-lft-identity
3219×add-sqr-sqrt
3005×times-frac
2198×add-cube-cbrt
1659×add-exp-log
1299×add-cbrt-cube
1045×pow1
656×associate-*l*
647×associate-*r*
575×prod-exp
563×add-log-exp
515×cbrt-prod
478×distribute-rgt-neg-in
443×cbrt-unprod
422×exp-prod
418×distribute-lft-neg-in
385×flip3-- flip--
364×distribute-lft-out--
352×pow-prod-down
345×insert-posit16
324×sqrt-prod
319×div-exp
316×frac-times
311×associate-/r*
303×associate-*l/
297×distribute-lft-out
295×difference-of-squares
238×log-pow
209×associate-*r/
206×associate-/l*
204×cbrt-undiv
200×swap-sqr
172×cbrt-div
171×sqrt-pow1
166×unswap-sqr
147×div-inv
132×sub-neg
128×associate-/r/
126×flip-+ flip3-+
120×sqrt-div
119×*-commutative
108×neg-mul-1
106×distribute-rgt-in distribute-lft-in
101×frac-sub
98×log-prod
84×frac-add
73×tan-quot
65×diff-log
62×sum-log frac-2neg clear-num
60×1-exp rec-exp
52×associate-+r+
50×pow1/3
48×associate-/l/
41×unpow-prod-down
39×pow1/2
36×associate--l+
35×associate--r+
34×pow-unpow
33×rem-sqrt-square
26×sin-mult
23×pow-exp
22×+-commutative pow-prod-up
21×unpow-prod-up
20×cos-mult div-sub
19×pow-flip associate-+l+ pow-sqr
18×associate-+l-
17×neg-sub0
14×distribute-frac-neg
13×exp-sum sqr-pow pow-to-exp
12×sub-div inv-pow log-div
10×pow-plus pow-pow cube-prod rem-exp-log e-exp-1 pow-sub
9×exp-diff
8×un-div-inv
7×neg-log exp-neg rem-log-exp
6×associate--l- pow2 cube-div
4×associate-+r- distribute-neg-frac
3×distribute-rgt-out-- exp-to-pow
2×distribute-lft-neg-out cos-2 cos-sum tan-sum distribute-rgt-out distribute-rgt1-in
1×cube-unmult distribute-rgt-neg-out pow3 unpow3 log-rec difference-of-sqr-1 sqrt-unprod sqrt-pow2 cube-mult +-inverses sqr-neg remove-posit16 rem-cbrt-cube

bsearch11.8s (1.7%)

localize6.6s (1.0%)

end1.0ms (0.0%)