Details

simplify5.3m (43.2%)

sample4.3m (34.9%)

Algorithm
56×intervals
16×halfpoints
Results
47.2s67068×body1280valid
34.1s17482×body2560valid
17.8s42210×body640valid
10.3s13034×body10240exit
9.5s93334×body80valid
6.2s20810×body320valid
4.5s63525×body80nan
1.9s10561×body160valid
1.8s47297×pre80true
958.0ms655×body1280nan
417.0ms650×body640nan
406.0ms411×body5120valid
104.0ms326×body320nan
79.0ms207×body160nan

prune1.4m (11.9%)

series47.5s (6.5%)

Calls

369 calls:

1.9s
(/ (/ (- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.7s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
1.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* 1/6 (* (* a a) a)) (* eps (* eps eps)) (fma eps a (* (* (* a a) 1/2) (* eps eps)))) (- (exp (* b eps)) 1.0)))
917.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
629.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite13.0s (1.8%)

Algorithm
119×rewrite-expression-head
Calls

369 calls:

484.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
457.0ms
(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
381.0ms
(- (cbrt (+ x 1.0)) (cbrt x))
371.0ms
(* (sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))))
370.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))
Rules
9842×*-un-lft-identity
7950×times-frac
6993×add-sqr-sqrt
5700×add-cube-cbrt
3322×prod-diff
3128×sqrt-prod
1749×distribute-lft-out
1459×pow1
1084×add-exp-log
996×unpow-prod-down
984×add-cbrt-cube
585×add-log-exp
522×difference-of-squares
514×div-inv
508×distribute-lft-out--
479×associate-/l*
443×fma-neg
414×associate-/r*
395×associate-/r/
359×expm1-log1p-u
357×log1p-expm1-u
346×sqr-pow
316×associate-*r* associate-*l*
315×pow-prod-down
265×pow-prod-up
261×log-prod
259×sqrt-div
242×swap-sqr
237×associate-+l+
228×prod-exp
222×cbrt-unprod
219×div-exp
209×associate-*r/
205×flip-+ flip3-+
197×flip3-- flip--
166×cbrt-undiv
164×distribute-rgt-neg-in
162×cbrt-prod
150×distribute-lft-neg-in
123×pow-sqr
115×cube-prod
107×tan-quot unswap-sqr
103×sub-neg
98×diff-log
91×pow-plus
85×associate-/l/
80×frac-times associate-*l/
74×frac-2neg clear-num
71×log-pow
66×pow2
62×fma-def
57×*-commutative
50×sqrt-pow1 neg-mul-1 pow1/2
45×frac-sub pow-unpow
44×div-sub
37×cbrt-div rem-sqrt-square fma-udef
36×distribute-rgt-in distribute-lft-in
30×pow1/3
27×unpow3 cube-mult
24×log-div
21×associate--l+ rem-log-exp
18×sum-log
17×cube-unmult
15×complex-mul-def
14×1-exp rec-exp
13×+-commutative frac-add
12×pow-exp
11×pow-to-exp
9×neg-sub0
8×pow-flip sub-div associate--l- inv-pow hypot-def pow-div
7×cos-sum
6×sin-mult pow-pow
5×cos-mult sin-sum associate-+r- exp-sum exp-prod
4×*.c-commutative distribute-frac-neg sqrt-unprod associate--r+ distribute-rgt-out--
3×rem-cube-cbrt neg-log +.c-commutative cube-div difference-cubes
2×expm1-log1p expm1-udef associate-*l*.c log1p-expm1 complex-def-add tan-sum complex-add-def unsub-neg log1p-udef
1×exp-diff diff-atan frac-2neg.c sin-cos-mult pow3 exp-to-pow rem-exp-log distribute-lft-in.c associate-+l- rem-square-sqrt distribute-rgt-in.c diff-sin associate-+l+.c rem-cbrt-cube diff-cos

regimes5.8s (0.8%)

Accuracy

Total 27.5b remaining (19.5%)

Threshold costs 5.1b (3.7%)

4.5b84.1%quadp (p42, positive)
4.5b84.2%quad2p (problem 3.2.1, positive)
4.4b84.5%quad2m (problem 3.2.1, negative)
4.3b84.9%quadm (p42, negative)
3.5b0%expq3 (problem 3.4.2)

localize5.4s (0.7%)

bsearch1.9s (0.3%)

end1.0ms (0.0%)