Details

sample1.9m (50.8%)

Algorithm
56×intervals
16×halfpoints
Results
24.0s67012×body1280valid
16.9s17044×body2560valid
8.2s42141×body640valid
3.8s12509×body10240exit
2.9s94055×body80valid
2.6s20886×body320valid
1.6s63211×body80nan
837.0ms10595×body160valid
548.0ms47296×pre80true
304.0ms655×body1280nan
219.0ms674×body640nan
118.0ms414×body5120valid
59.0ms322×body320nan
23.0ms184×body160nan

prune42.0s (18.9%)

series39.9s (18.0%)

Calls

383 calls:

1.1s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
982.0ms
(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
964.0ms
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
943.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
935.0ms
(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify10.7s (4.8%)

rewrite10.4s (4.7%)

Algorithm
122×rewrite-expression-head
Calls

383 calls:

308.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
179.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
179.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
176.0ms
(* (/ (- x (sin x)) (- (pow x 3) (pow (tan x) 3))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
142.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
Rules
12824×*-un-lft-identity
12801×times-frac
11535×add-sqr-sqrt
8228×add-cube-cbrt
4008×prod-diff
3576×sqrt-prod
1860×unpow-prod-down
1632×difference-of-squares
1628×cube-prod
1576×cbrt-prod
1250×distribute-lft-out
1175×add-exp-log
1119×distribute-lft-out--
931×add-cbrt-cube
825×associate-*l*
771×associate-/l*
756×pow1
705×sqr-pow
614×add-log-exp
510×div-inv
446×fma-neg
407×associate-/r*
395×distribute-rgt-neg-in
373×expm1-log1p-u
368×log1p-expm1-u log-prod
366×associate-/r/
337×associate-*r*
299×associate-+l+
256×prod-exp div-exp
201×distribute-lft-neg-in unswap-sqr
196×unpow3 cube-mult
195×flip-- flip3--
193×flip-+ flip3-+
191×pow-unpow
185×cbrt-undiv
173×log-pow
155×cbrt-unprod exp-sum
137×sqrt-div
108×associate-*l/
107×tan-quot
103×pow-prod-down
100×diff-log sub-neg
90×fma-def
86×sqrt-pow1
74×exp-prod
72×frac-2neg swap-sqr clear-num
71×associate-/l/
70×frac-times
69×associate-*r/
67×neg-mul-1
61×pow-to-exp pow-exp
60×*-commutative
53×pow1/2
49×difference-cubes
47×distribute-rgt-in distribute-lft-in
42×log-div unpow2
39×pow1/3
37×fma-udef
30×1-exp
29×div-sub
27×rem-sqrt-square rec-exp
26×sum-log
25×rem-log-exp
24×pow-pow complex-mul-def
23×cbrt-div
21×pow-flip
19×pow-prod-up associate-+r+
17×sum-cubes neg-sub0
16×+-commutative
15×pow-sqr
14×frac-sub
13×associate--l- neg-log hypot-def
12×cube-div rem-cube-cbrt
11×frac-add pow-plus
10×pow-div
associate-+l-
exp-diff pow2 associate--l+
inv-pow cos-mult
associate--r+ distribute-rgt-out-- *.c-commutative
log1p-udef associate-+r- log1p-expm1 rem-cbrt-cube expm1-udef
rem-exp-log sqrt-unprod sub-div +.c-commutative complex-add-def sin-mult
sin-cos-mult un-div-inv expm1-log1p
associate-+l+.c expm1-def exp-neg difference-of-sqr-1 associate-*l*.c cos-sum tan-sum exp-to-pow sin-sum
diff-atan diff-cos rem-square-sqrt frac-2neg.c diff-sin

regimes3.1s (1.4%)

Accuracy

Total 32.0b remaining (11.4%)

Threshold costs 5.9b (2.1%)

5.1b41.4%expq3 (problem 3.4.2)
4.7b82.1%quadp (p42, positive)
4.4b84.4%quadm (p42, negative)
4.3b84.6%quad2m (problem 3.2.1, negative)
3.3b87%quad2p (problem 3.2.1, positive)

localize1.9s (0.9%)

bsearch1.3s (0.6%)

end1.0ms (0.0%)