Details

simplify5.3m (32.8%)

sample5.0m (31.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67113×body1280valid
37.5s17237×body2560valid
26.0s42016×body640valid
14.7s12757×body10240exit
10.9s93998×body80valid
9.6s20566×body320valid
6.5s62518×body80nan
4.1s10871×body160valid
1.9s47509×pre80true
749.0ms647×body1280nan
621.0ms708×body640nan
499.0ms438×body5120valid
170.0ms362×body320nan
86.0ms187×body160nan

prune4.7m (29.4%)

series38.4s (4.0%)

Calls

348 calls:

952.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
541.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
484.0ms
(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
471.0ms
(fma 1 (pow (+ 1 x) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
468.0ms
(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))

rewrite12.2s (1.3%)

Algorithm
113×rewrite-expression-head
Calls

348 calls:

403.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
219.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
188.0ms
(* (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2) (sin (* eps 1/2)))
183.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
155.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
Rules
138219×times-frac
70832×*-un-lft-identity
69660×add-sqr-sqrt
67811×add-cube-cbrt
34167×prod-diff
14071×sqrt-prod
8160×distribute-rgt-neg-in
8113×distribute-lft-neg-in
3522×div-inv
2679×neg-mul-1
2510×pow1
1154×add-exp-log
1001×add-cbrt-cube
894×distribute-lft-out
882×associate-/r/
804×pow-prod-up
718×difference-of-squares
694×fma-neg
648×distribute-lft-out--
528×add-log-exp
473×pow-prod-down
428×associate-*r*
427×associate-/l*
400×associate-/r*
345×associate-*l*
344×log1p-expm1-u pow-sqr
342×expm1-log1p-u
341×insert-posit16
314×pow-plus
283×prod-exp
272×associate-+l+
250×cbrt-unprod
234×div-exp log-prod
230×cbrt-prod
223×pow2
218×flip3-- flip--
174×cbrt-undiv
173×flip-+ flip3-+
134×sqrt-div
128×pow-unpow unpow-prod-down
102×unswap-sqr
98×log-pow
89×distribute-rgt-in distribute-lft-in
86×fma-def
77×associate-*r/
75×diff-log
72×sub-neg
70×sqrt-pow1 frac-2neg clear-num
66×pow-flip
65×pow1/2
57×*-commutative
54×cbrt-div
51×pow1/3
46×frac-times associate-/l/
43×exp-prod
41×sqr-pow associate-*l/
40×tan-quot
38×1-exp
37×rec-exp fma-udef
36×rem-sqrt-square
32×swap-sqr
31×div-sub
26×associate-+r+
25×sum-log difference-of-sqr-1
24×hypot-def
20×log-div
19×exp-sum inv-pow
17×+-commutative
16×frac-sub rem-log-exp
13×associate--r+
12×frac-add
11×associate--l- associate--l+ distribute-rgt-out--
10×neg-sub0
9×pow-pow
8×pow-exp distribute-neg-frac pow-to-exp
6×pow-div expm1-udef exp-diff
5×neg-log sub-div
4×cube-unmult distribute-rgt-neg-out hypot-1-def un-div-inv rem-exp-log sin-mult
3×expm1-log1p sin-sum sqrt-unprod sqr-sin associate-+l-
2×log1p-def exp-neg log1p-udef tan-sum hypot-udef unpow1/3 cos-sum +.c-commutative
1×diff-atan associate-+r- sqrt-undiv frac-2neg.c sin-cos-mult log1p-expm1 pow3 exp-to-pow diff-sin diff-cos expm1-def

localize4.2s (0.4%)

regimes4.0s (0.4%)

Accuracy

Total 23.7b remaining (19.4%)

Threshold costs 4.9b (4%)

4.8b83%quadm (p42, negative)
4.8b82.7%quad2m (problem 3.2.1, negative)
3.3b87.5%quad2p (problem 3.2.1, positive)
3.1b-7.4%expq3 (problem 3.4.2)
1.6b87.1%2nthrt (problem 3.4.6)

bsearch2.7s (0.3%)

end1.0ms (0.0%)