Details

simplify6.9m (62.4%)

sample1.3m (11.9%)

Algorithm
73×intervals
Results
26.1s286450×body80valid
9.8s25107×body160valid
9.1s13861×body1280valid
4.4s3831×body2560valid
4.1s9354×body640valid
3.3s100605×pre80true
3.1s2227×body10240exit
1.5s6845×body320valid
1.2s19460×body80nan
572.0ms253×body5120valid
3.0ms100×pre80false

prune1.3m (11.8%)

series43.9s (6.7%)

Calls

325 calls:

1.2s
(* (* (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (* r w)) (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (* r w))) (* (- 3.0 (* 2.0 v)) (* (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v)))) (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v)))))))
833.0ms
(+ (+ (* (* x x) (- (- (* 11.0 (* (* x y) (* x y))) (pow y 6.0)) (+ 2.0 (* (pow y 4.0) 121.0)))) (* (pow y 6.0) 333.75)) (+ (* (pow y 8.0) 5.5) (/ x (* 2.0 y))))
703.0ms
(* (* (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (/ (cbrt 0.125) (cbrt (- 1.0 v)))) (* (* w r) (* w r))) (- 3.0 (* 2.0 v)))
656.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
645.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite35.5s (5.4%)

Algorithm
109×rewrite-expression-head
Calls

325 calls:

3.6s
(* (* (* (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (* r w)) (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (* r w))) (* (- 3.0 (* 2.0 v)) (* (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v)))) (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v))))))) (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v)))))
2.9s
(* (* (* (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (/ (cbrt 0.125) (cbrt (- 1.0 v)))) (* (* w r) (* w r))) (- 3.0 (* 2.0 v))) (/ (cbrt 0.125) (cbrt (- 1.0 v))))
2.2s
(+ (+ (* (* x x) (- (- (* 11.0 (* (* x y) (* x y))) (pow y 6.0)) (+ 2.0 (* (pow y 4.0) 121.0)))) (* (pow y 6.0) 333.75)) (+ (* (pow y 8.0) 5.5) (/ x (* 2.0 y))))
1.8s
(* (* (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (* r w)) (* (/ (cbrt 0.125) (cbrt (- 1.0 v))) (* r w))) (* (* (- 3.0 (* 2.0 v)) (* (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v)))) (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v)))))) (cbrt (/ (cbrt 0.125) (cbrt (- 1.0 v))))))
1.2s
(+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))
Rules
4703×times-frac
4085×*-un-lft-identity
3958×add-sqr-sqrt
3861×add-exp-log
2887×add-cbrt-cube
2686×add-cube-cbrt
2316×prod-exp
2268×cbrt-unprod
1647×pow1
1389×associate-*r/
1221×frac-times
1016×cbrt-div
944×associate-*l/
876×pow-prod-down
858×sqrt-prod
799×flip3-- flip--
783×associate-*r*
727×add-log-exp
560×div-exp
525×cbrt-undiv
520×associate-*l*
469×difference-of-squares
400×distribute-lft-out--
349×associate-/l*
342×distribute-lft-out
303×frac-add
285×associate-/r/
282×flip-+ flip3-+
280×div-inv
277×cbrt-prod
274×associate-/r*
189×frac-sub
173×sqrt-div
158×sum-log
133×distribute-rgt-neg-in
130×unswap-sqr
121×unpow-prod-down
103×sub-neg
95×*-commutative
89×exp-neg
81×diff-log
78×neg-sub0 associate-/l/
75×pow-prod-up
74×sqr-pow
69×exp-diff distribute-rgt-in distribute-lft-in
62×exp-prod
58×distribute-lft-neg-in
56×frac-2neg clear-num
48×sqrt-pow1 pow1/2
47×log-prod
41×pow1/3 swap-sqr
40×+-commutative
37×rem-sqrt-square
34×associate-+l+
33×pow-plus
31×pow-sqr
27×log-pow
24×un-div-inv
21×associate-+r+ associate--r+
20×neg-mul-1 div-sub
19×pow2
16×associate--l+
15×pow-exp pow-to-exp
14×log-div
12×exp-sum
11×1-exp rec-exp
associate--l- pow3 neg-log rem-exp-log
distribute-frac-neg
sqrt-unprod
distribute-lft-neg-out cube-unmult rem-log-exp
cube-prod associate-+r- associate-+l-
pow-unpow rem-cbrt-cube associate--r-
distribute-lft1-in sum-cubes distribute-rgt-out
distribute-rgt-out-- pow-flip unpow3 sub-div pow-pow inv-pow exp-to-pow rem-square-sqrt cube-mult unsub-neg

regimes5.9s (0.9%)

Accuracy

Total 32.9b remaining (8.3%)

Threshold costs 2.8b (0.7%)

10.7b53.1%Compound Interest
4.5b76.8%Kahan p9 Example
4.3b84.1%The quadratic formula (r1)
3.7b87.1%The quadratic formula (r2)
3.1b0%Complex division, real part

localize5.2s (0.8%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)