Details

prune39.5s (31.2%)

sample31.7s (25.0%)

Algorithm
73×intervals
Results
9.6s294704×body80valid
4.9s13761×body1280valid
2.7s3880×body2560valid
1.8s9386×body640valid
1.8s16929×body160valid
1.4s100590×pre80true
1.0s2168×body10240exit
731.0ms6802×body320valid
558.0ms19557×body80nan
65.0ms229×body5120valid
3.0ms100×pre80false

series29.0s (22.9%)

Calls

275 calls:

1.2s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
980.0ms
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
608.0ms
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
594.0ms
(* 100.0 (* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) n)))
577.0ms
(/ 1.0 (+ 2.0 (* (fma (sqrt 2.0) (sqrt 2.0) (- (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))

simplify10.9s (8.6%)

Algorithm
172×egg-herbie

rewrite10.2s (8.1%)

Algorithm
102×rewrite-expression-head
Calls

275 calls:

595.0ms
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
582.0ms
(* 100.0 (* (* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0)))) n))
357.0ms
(* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))
324.0ms
(+ (* (* (* 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) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
283.0ms
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
Rules
17285×times-frac
14193×*-un-lft-identity
12228×add-sqr-sqrt
9842×add-cube-cbrt
5333×prod-diff
1797×distribute-rgt-neg-in
1768×distribute-lft-neg-in
1595×add-exp-log
1354×distribute-lft-out
1203×add-cbrt-cube
1071×unpow-prod-down
985×difference-of-squares
973×distribute-rgt-in distribute-lft-in
928×div-inv
886×distribute-lft-out--
687×sqrt-prod
685×associate-*r*
611×associate-/l*
591×associate-/r/
557×pow1
539×add-log-exp
516×prod-exp
449×div-exp
441×associate-*l*
374×sqr-pow
366×flip-+ flip3-+
357×cube-prod
352×associate-/r*
319×cbrt-unprod
298×cbrt-undiv
275×log1p-expm1-u expm1-log1p-u
259×fma-neg
252×neg-mul-1
176×cbrt-prod
169×flip3-- flip--
165×frac-times
160×associate-*r/
139×unswap-sqr
136×associate-+l+
115×associate-*l/
113×pow-prod-down
112×frac-sub
106×fma-def
104×sum-log
91×unpow3 cube-mult
88×1-exp
81×exp-neg
75×sub-neg
73×neg-sub0
72×swap-sqr
70×associate-/l/
67×clear-num frac-2neg
63×*-commutative
62×exp-diff
61×pow-unpow
56×cbrt-div
55×unpow2
52×diff-log
44×rec-exp
42×fma-udef
41×sqrt-div
39×pow-exp
31×pow-to-exp
24×un-div-inv +-commutative
22×rem-sqrt-square div-sub
21×pow1/3 log-prod
20×pow1/2 exp-sum sqrt-pow1
19×associate-+r+
17×cube-div
16×frac-add
15×pow-flip
13×associate--r+
12×pow-prod-up
11×pow-sqr pow-plus
10×pow2 log-pow
inv-pow
associate--l- neg-log pow-pow
log-div
rem-cbrt-cube
rem-cube-cbrt distribute-lft-neg-out distribute-neg-in distribute-frac-neg hypot-def exp-prod sum-cubes associate-+l- rem-log-exp
associate--l+
sub0-neg associate-+r-
sub-div unsub-neg associate--r- distribute-rgt-out-- sqrt-undiv distribute-neg-frac exp-to-pow

regimes3.2s (2.5%)

Accuracy

Total 34.8b remaining (12.2%)

Threshold costs 3.4b (1.2%)

10.5b52.3%Compound Interest
7.4b35.1%Complex division, real part
4.4b84.7%The quadratic formula (r2)
4.0b52.8%Complex division, imag part
3.8b86.7%The quadratic formula (r1)

localize1.3s (1.0%)

bsearch840.0ms (0.7%)

end1.0ms (0.0%)