Details

sample5.0m (53.0%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66452×body1280valid
38.5s17807×body2560valid
27.3s42516×body640valid
14.0s12638×body10240exit
11.6s93562×body80valid
9.3s20261×body320valid
7.6s63772×body80nan
2.6s10801×body160valid
2.2s47279×pre80true
729.0ms616×body1280nan
629.0ms652×body640nan
481.0ms478×body5120valid
174.0ms329×body320nan
56.0ms182×body160nan

simplify2.3m (25.0%)

prune1.2m (13.4%)

series31.1s (5.5%)

Calls

315 calls:

631.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
608.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
551.0ms
(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)))))
526.0ms
(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)))))
504.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite6.8s (1.2%)

Algorithm
109×rewrite-expression-head
Calls

315 calls:

189.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
174.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
126.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
124.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
115.0ms
(* (/ 1 (sqrt (+ 1 x))) (+ (/ 1 (sqrt (+ 1 x))) (pow x -1/2)))
Rules
10918×times-frac
9912×*-un-lft-identity
9497×add-sqr-sqrt
7454×add-cube-cbrt
4624×prod-diff
2194×sqrt-prod
1201×add-exp-log
1165×pow1
892×add-cbrt-cube
872×difference-of-squares
694×div-inv
653×distribute-lft-out
610×associate-*r*
513×distribute-lft-out--
478×add-log-exp
426×fma-neg
402×associate-*l*
375×distribute-rgt-neg-in
348×distribute-lft-neg-in
345×associate-/r/
335×associate-/r*
327×div-exp
312×log1p-expm1-u
310×expm1-log1p-u
308×insert-posit16
290×cbrt-prod
280×unpow-prod-down
279×prod-exp
268×associate-/l*
264×pow-prod-up
249×associate-+l+
213×pow-prod-down
211×pow-unpow
198×cbrt-unprod
181×log-prod
174×cbrt-undiv
155×flip-+ flip3-+
152×distribute-rgt-out
147×flip3-- flip--
132×sqrt-pow1
130×sqrt-div
116×neg-mul-1 unswap-sqr
100×pow-sqr
96×sqr-pow
88×pow1/2
78×pow-plus
70×1-exp
69×rec-exp
68×diff-log
62×frac-2neg clear-num
60×sub-neg
58×fma-def
56×*-commutative
54×pow2
46×swap-sqr
44×cbrt-div
40×associate-/l/
38×pow1/3 associate-*l/
36×associate-*r/
33×rem-sqrt-square
32×frac-times
30×log-pow
28×fma-udef
27×tan-quot pow-flip
22×div-sub
21×sum-log
18×frac-add
17×cube-unmult
16×inv-pow log-div
14×rem-log-exp
13×difference-of-sqr-1
12×distribute-rgt1-in frac-sub distribute-lft1-in +-commutative hypot-def
10×expm1-udef
9×neg-sub0 pow-exp pow-to-exp
8×associate--l-
7×distribute-rgt-in pow-pow distribute-lft-in
6×expm1-log1p exp-sum neg-log exp-prod
4×exp-diff associate-+r+ pow3 sqrt-unprod sin-mult associate--r+ log1p-def count-2
3×associate--l+ log1p-udef sqr-sin un-div-inv
2×quot-tan sin-sum log1p-expm1 +.c-commutative tan-sum exp-to-pow exp-neg associate-+l- rem-square-sqrt cos-sum rem-cbrt-cube
1×diff-atan cos-mult frac-2neg.c sin-cos-mult sub-div hypot-1-def distribute-rgt-out-- rem-exp-log diff-sin diff-cos expm1-def

regimes4.5s (0.8%)

Accuracy

Total 24.4b remaining (17.4%)

Threshold costs 4.4b (3.1%)

4.7b82.9%quadm (p42, negative)
4.6b83.4%quad2m (problem 3.2.1, negative)
4.5b83.4%quad2p (problem 3.2.1, positive)
3.2b0%expq3 (problem 3.4.2)
3.0b75.3%2nthrt (problem 3.4.6)

localize3.9s (0.7%)

bsearch1.6s (0.3%)

end1.0ms (0.0%)