Details

simplify7.0m (42.6%)

sample5.1m (30.7%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66504×body1280valid
40.5s17410×body2560valid
27.3s41582×body640valid
14.4s12605×body10240exit
13.1s94265×body80valid
9.2s20853×body320valid
6.1s63734×body80nan
3.3s10869×body160valid
2.8s47349×pre80true
1.2s638×body1280nan
609.0ms492×body5120valid
548.0ms372×body320nan
472.0ms631×body640nan
55.0ms210×body160nan

prune3.3m (20.0%)

series43.4s (4.4%)

Calls

360 calls:

1.1s
(sqrt (/ 1 (+ (hypot (sqrt x) 1) (sqrt x))))
959.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
797.0ms
(log (exp (* (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))) (cbrt (fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))))
733.0ms
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
706.0ms
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))

rewrite10.6s (1.1%)

Algorithm
116×rewrite-expression-head
Calls

360 calls:

443.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
416.0ms
(* x (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 1/3)))
294.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
272.0ms
(* (sqrt (/ (fma (- (exp x) 2) (- (exp x) 2) (/ (/ -1 (exp x)) (exp x))) (+ (- (exp x) 2) (/ -1 (exp x))))) (sqrt (- (- (exp x) 2) (/ -1 (exp x)))))
233.0ms
(* (sqrt (- (- (exp x) 2) (/ -1 (exp x)))) (sqrt (- (- (exp x) 2) (/ -1 (exp x)))))
Rules
12309×*-un-lft-identity
11413×times-frac
9239×add-sqr-sqrt
7492×add-cube-cbrt
4650×prod-diff
2470×sqrt-prod
1870×distribute-lft-out
1636×pow1
1297×add-exp-log
1068×add-cbrt-cube
1028×div-inv
660×distribute-lft-out--
571×difference-of-squares
542×add-log-exp
533×associate-/r/
528×associate--l+
503×associate-+l+
487×associate-*l*
486×distribute-rgt-in distribute-lft-in
474×associate-*r*
443×pow-prod-up
389×associate-/r*
365×associate-/l*
355×fma-neg
354×expm1-log1p-u
353×log1p-expm1-u
352×insert-posit16
307×prod-exp
301×div-exp
290×pow-prod-down
273×log-prod frac-sub pow-plus
253×flip-+ flip3-+
249×cbrt-unprod
246×cbrt-prod
235×flip3-- flip--
224×swap-sqr
214×unswap-sqr
205×cbrt-undiv
172×frac-times
170×distribute-rgt-neg-in
159×pow-sqr
157×distribute-rgt1-in distribute-rgt-out
150×distribute-lft-neg-in
148×sqrt-div
135×pow-flip
132×associate-/l/
127×associate-*l/
123×unpow-prod-down
119×associate-*r/
107×sqrt-pow1
104×pow-unpow
99×fma-def
97×pow2
84×frac-2neg clear-num
77×pow1/2 diff-log
74×associate-+r+ sub-neg
68×pow1/3
66×*-commutative
63×1-exp rec-exp
60×inv-pow
51×un-div-inv
50×neg-mul-1
49×log-pow
40×sqr-pow
35×difference-of-sqr-1
32×rem-sqrt-square
31×pow3
29×tan-quot
27×sum-log fma-udef
26×exp-prod
24×div-sub
18×+-commutative
17×cbrt-div
16×rem-log-exp log-div
14×frac-add
12×associate--l-
11×pow-exp pow-pow pow-to-exp
10×neg-sub0
sin-mult
neg-log hypot-def
associate-+l-
log1p-udef associate--r+
cos-mult
exp-sum
expm1-udef sin-sum sqrt-unprod sqr-sin hypot-udef rem-exp-log cos-sum
exp-diff associate-+r- sin-cos-mult cube-unmult log1p-expm1 sub-div +.c-commutative tan-sum frac-2neg-c exp-neg log1p-def rem-square-sqrt
expm1-log1p quot-tan diff-atan log-rec exp-to-pow distribute-rgt-out-- diff-sin +-inverses rem-cbrt-cube diff-cos expm1-def

regimes4.7s (0.5%)

Accuracy

Total 21.7b remaining (17.3%)

Threshold costs 4.0b (3.2%)

4.9b82.4%quadm (p42, negative)
4.8b82.6%quad2p (problem 3.2.1, positive)
4.0b-15.7%expq3 (problem 3.4.2)
1.5b93.6%quad2m (problem 3.2.1, negative)
1.3b88.5%2nthrt (problem 3.4.6)

localize4.1s (0.4%)

bsearch3.0s (0.3%)

end1.0ms (0.0%)