Details

sample31.5s (26.8%)

Algorithm
73×intervals
Results
9.5s294019×body80valid
4.8s13872×body1280valid
2.5s3827×body2560valid
1.8s9358×body640valid
1.8s16899×body160valid
1.4s100646×pre80true
1.1s2129×body10240exit
728.0ms6830×body320valid
539.0ms18963×body80nan
81.0ms220×body5120valid
3.0ms100×pre80false

prune28.4s (24.1%)

series28.4s (24.1%)

Calls

323 calls:

550.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
534.0ms
(log (pow (exp 1) (pow (sqrt (/ (* 2.0 t) (+ 1.0 t))) 4)))
523.0ms
(* (sqrt (log (+ 1.0 x))) (sqrt (+ (log (sqrt (+ 1.0 x))) (log (sqrt (+ 1.0 x))))))
435.0ms
(cbrt (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
423.0ms
(cbrt (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))

rewrite13.9s (11.8%)

Algorithm
111×rewrite-expression-head
Calls

323 calls:

1.1s
(+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0)))
592.0ms
(+ (+ (+ (* 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))) (/ 77617.0 (* 2.0 33096.0)))
550.0ms
(+ (+ (* 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)))
285.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* (* x1 x1) (* (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
275.0ms
(* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))
Rules
3503×*-un-lft-identity
3385×add-sqr-sqrt
3327×times-frac
2213×add-cube-cbrt
1900×add-exp-log
1605×add-cbrt-cube
977×associate-*r*
876×pow1
705×add-log-exp
683×prod-exp
634×associate-*r/
559×cbrt-unprod
505×sqrt-prod
458×associate-*l*
440×div-exp
427×distribute-lft-out
421×flip-- flip3--
404×difference-of-squares
367×frac-times
359×cbrt-prod
349×cbrt-undiv
348×cbrt-div
311×unpow-prod-down
288×flip-+ flip3-+
281×associate-/l*
274×associate-/r/
266×associate-/r*
255×distribute-lft-out--
230×pow-prod-down
227×associate-*l/
216×div-inv
210×frac-add
167×unswap-sqr
158×sum-log
147×sqrt-div
135×sqr-pow
129×cube-prod
92×*-commutative
91×sub-neg
89×sqrt-pow1
86×associate-/l/
79×swap-sqr
74×distribute-rgt-in distribute-lft-in
71×log-prod
69×pow1/2
66×diff-log
58×clear-num frac-2neg
49×distribute-rgt-neg-in
48×pow-prod-up
47×log-pow
44×+-commutative
43×1-exp
42×pow-unpow
37×unpow2
34×rec-exp
33×distribute-lft-neg-in
32×exp-sum
31×pow-to-exp pow-exp
30×exp-prod
29×associate-+l+
26×rem-sqrt-square
25×associate-+r+ pow1/3
24×pow-sqr
22×difference-cubes pow-plus div-sub
20×pow-pow
19×pow3
18×frac-sub
16×log-div
15×pow2 distribute-rgt-out associate--l+
12×cube-div distribute-rgt-out--
11×unpow3 cube-mult neg-mul-1
10×neg-sub0 rem-log-exp
distribute-lft-neg-out
neg-log
associate--l- sqrt-unprod
un-div-inv distribute-lft1-in rem-cbrt-cube associate--r+
inv-pow pow-flip associate-+l-
distribute-rgt1-in associate-+r- rem-square-sqrt distribute-frac-neg
exp-diff rem-cube-cbrt unsub-neg rem-exp-log sub-div count-2 exp-to-pow
sqrt-pow2 cube-unmult +-inverses associate--r-

simplify10.1s (8.6%)

Algorithm
181×egg-herbie

regimes3.1s (2.6%)

Accuracy

Total 31.7b remaining (7.4%)

Threshold costs 3.7b (0.9%)

12.1b47.5%Compound Interest
5.0b82.9%The quadratic formula (r1)
4.5b78.3%Kahan p9 Example
2.4b21.9%Complex division, real part
1.5b93.9%The quadratic formula (r2)

localize1.5s (1.2%)

bsearch782.0ms (0.7%)

end1.0ms (0.0%)