Details

sample1.9m (49.5%)

Algorithm
56×intervals
16×halfpoints
Results
24.4s67365×body1280valid
16.8s17378×body2560valid
8.3s42313×body640valid
4.0s13130×body10240exit
3.1s93461×body80valid
2.6s20779×body320valid
1.6s62665×body80nan
832.0ms10432×body160valid
562.0ms47482×pre80true
281.0ms632×body1280nan
215.0ms680×body640nan
138.0ms473×body5120valid
70.0ms372×body320nan
22.0ms200×body160nan

prune44.6s (19.8%)

series40.8s (18.1%)

Calls

392 calls:

1.1s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
997.0ms
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
960.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
949.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
935.0ms
(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)))

simplify11.5s (5.1%)

rewrite10.6s (4.7%)

Algorithm
123×rewrite-expression-head
Calls

392 calls:

324.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
322.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
319.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
220.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
178.0ms
(- (pow (pow (+ x 1.0) 1.0) (/ 1 n)) (pow x (/ 1.0 n)))
Rules
9367×*-un-lft-identity
8491×add-sqr-sqrt
7315×times-frac
6539×add-cube-cbrt
4976×prod-diff
2012×sqrt-prod
1872×unpow-prod-down
1175×add-exp-log
964×distribute-lft-out
879×difference-of-squares
866×add-cbrt-cube
832×associate-+l+
773×cube-prod
752×pow1
747×sqr-pow
664×add-log-exp
626×associate-*r*
597×associate-*l*
500×fma-neg
491×div-inv
473×distribute-lft-out--
461×associate-/l*
383×associate-/r/
378×log1p-expm1-u
377×expm1-log1p-u
369×cbrt-prod
335×distribute-rgt-neg-in
319×associate-/r*
292×log-pow
287×unpow2
279×div-exp
253×distribute-lft-neg-in
248×prod-exp
239×unswap-sqr
226×flip-+ flip3-+
180×flip-- flip3--
176×exp-prod
173×log-prod
167×sqrt-div
155×cbrt-undiv
150×unpow3 cube-mult
138×cbrt-unprod
134×fma-def
131×sqrt-pow1
117×distribute-rgt-in distribute-lft-in
115×swap-sqr
110×associate-*l/
107×pow-exp
106×diff-log
100×sub-neg
97×pow-to-exp
94×pow1/2 exp-sum
85×neg-mul-1
83×cbrt-div
81×pow-prod-down
77×pow-unpow
73×pow1/3
70×associate-/l/ associate-*r/
67×frac-2neg clear-num
55×*-commutative frac-times
54×pow-prod-up
41×sum-log
39×rem-sqrt-square tan-quot
37×fma-udef
34×1-exp
28×+-commutative rec-exp
27×pow-flip
25×inv-pow
24×frac-add pow-sqr complex-mul-def
21×log-div
20×div-sub
19×associate--l+
18×pow-pow neg-sub0
16×associate--l-
15×rem-cube-cbrt frac-sub
14×neg-log
13×pow-plus
12×difference-cubes
11×associate-+r+ associate-+l- rem-log-exp
8×associate--r+
7×exp-diff sqrt-unprod pow2
6×*.c-commutative distribute-rgt-out exp-to-pow
5×rem-exp-log sin-mult
4×pow-div 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 distribute-lft1-in associate-+r- exp-neg rem-square-sqrt associate-*l*.c cos-sum sqr-cos tan-sum associate-+l+.c 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

regimes3.4s (1.5%)

Accuracy

Total 30.5b remaining (14.8%)

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)

localize2.2s (1.0%)

bsearch847.0ms (0.4%)

end1.0ms (0.0%)