Details

sample1.9m (50.5%)

Algorithm
56×intervals
16×halfpoints
Results
24.0s67365×body1280valid
16.7s17378×body2560valid
8.1s42313×body640valid
4.0s13130×body10240exit
2.8s93461×body80valid
2.5s20779×body320valid
1.6s62665×body80nan
805.0ms10432×body160valid
540.0ms47482×pre80true
276.0ms632×body1280nan
211.0ms680×body640nan
128.0ms473×body5120valid
74.0ms372×body320nan
22.0ms200×body160nan

prune40.6s (18.4%)

series40.2s (18.2%)

Calls

391 calls:

1.1s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
981.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))
967.0ms
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
916.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
905.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify11.4s (5.2%)

rewrite11.3s (5.1%)

Algorithm
123×rewrite-expression-head
Calls

391 calls:

322.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
321.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
316.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
310.0ms
(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
235.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
Rules
9243×*-un-lft-identity
8317×add-sqr-sqrt
6905×times-frac
6364×add-cube-cbrt
5036×prod-diff
1946×sqrt-prod
1591×unpow-prod-down
1108×add-exp-log
957×distribute-lft-out
897×difference-of-squares
840×add-cbrt-cube
832×associate-+l+
773×cube-prod
719×pow1
678×sqr-pow
670×add-log-exp
602×associate-*r*
506×fma-neg
500×distribute-lft-out--
474×div-inv
428×associate-/l*
400×associate-*l*
383×associate-/r/
377×log1p-expm1-u
376×expm1-log1p-u
344×distribute-rgt-neg-in
322×log-pow
315×associate-/r*
284×cbrt-prod
259×exp-prod
249×distribute-lft-neg-in
238×prod-exp
236×div-exp
222×flip-+ flip3-+
220×unpow2
218×unswap-sqr
181×flip-- flip3--
179×log-prod
167×sqrt-div
150×unpow3 cube-mult
145×cbrt-undiv
131×cbrt-unprod
128×fma-def
126×sqrt-pow1
116×distribute-rgt-in pow-unpow distribute-lft-in
115×swap-sqr
109×diff-log associate-*l/
101×sub-neg
94×exp-sum
92×pow-exp
87×pow1/2
84×pow-to-exp
83×neg-mul-1
81×cbrt-div
75×pow-prod-down
72×pow1/3
69×associate-/l/
68×associate-*r/
64×frac-2neg clear-num
54×frac-times
52×*-commutative
50×pow-prod-up
41×sum-log
40×rem-sqrt-square
39×tan-quot
35×fma-udef
28×1-exp
26×+-commutative
25×rec-exp
24×frac-add complex-mul-def
23×associate--l+
22×pow-sqr
21×pow-pow log-div
20×div-sub neg-sub0
18×distribute-rgt-out
16×associate--l-
15×rem-cube-cbrt frac-sub
14×neg-log
12×difference-cubes rem-log-exp
11×associate-+r+ associate-+l-
9×exp-to-pow
8×rem-exp-log distribute-lft1-in pow-flip associate--r+
7×exp-diff sqrt-unprod pow2 pow-plus
6×inv-pow *.c-commutative
5×sin-mult
4×cube-div +.c-commutative complex-add-def hypot-def cos-mult distribute-rgt-out--
3×un-div-inv difference-of-sqr-1
2×expm1-def associate-+r- exp-neg pow-sub rem-square-sqrt associate-*l*.c cos-sum sqr-cos tan-sum associate-+l+.c pow-neg sin-sum
1×sub0-neg sin-cos-mult frac-2neg.c diff-atan sub-div diff-cos expm1-log1p distribute-frac-neg distribute-rgt-neg-out expm1-udef rem-cbrt-cube diff-sin

regimes2.9s (1.3%)

Accuracy

Total 31.2b remaining (15%)

Threshold costs 6.7b (3.2%)

4.4b83.7%quadp (p42, positive)
4.2b85.2%quadm (p42, negative)
4.2b82.6%quad2p (problem 3.2.1, positive)
4.2b85.2%quad2m (problem 3.2.1, negative)
3.2b0%expq3 (problem 3.4.2)

localize1.9s (0.9%)

bsearch1.1s (0.5%)

end1.0ms (0.0%)