Details

simplify4.4m (38.9%)

sample4.3m (38.0%)

Algorithm
56×intervals
16×halfpoints
Results
51.4s66832×body1280valid
30.4s17421×body2560valid
19.7s41742×body640valid
10.3s12653×body10240exit
8.8s93899×body80valid
6.2s21068×body320valid
5.9s63893×body80nan
1.9s10867×body160valid
1.5s47209×pre80true
594.0ms664×body1280nan
394.0ms455×body5120valid
386.0ms707×body640nan
128.0ms388×body320nan
38.0ms208×body160nan

prune1.5m (12.8%)

series45.0s (6.6%)

Calls

373 calls:

1.2s
(expm1 (log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
645.0ms
(log1p (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
553.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
534.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
532.0ms
(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

rewrite13.1s (1.9%)

Algorithm
120×rewrite-expression-head
Calls

373 calls:

522.0ms
(- (+ (/ (/ (sin x) x) (cos x)) (/ (* (/ (sin x) x) (/ (sin x) x)) (* (cos x) (cos x)))) (/ (sin x) x))
406.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
317.0ms
(* (cbrt (- (- (exp x) 2.0) (/ -1 (exp x)))) (cbrt (- (- (exp x) 2.0) (/ -1 (exp x)))))
259.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
251.0ms
(+ (* (* a (* (* a x) (* a x))) x) (* (* a x) (* a x)))
Rules
9441×*-un-lft-identity
8928×times-frac
8402×add-sqr-sqrt
7007×add-cube-cbrt
4824×prod-diff
2314×sqrt-prod
1147×add-exp-log
1129×pow1
980×add-cbrt-cube
726×distribute-lft-out
629×add-log-exp
603×div-inv
554×fma-neg
508×difference-of-squares
471×distribute-lft-out--
404×associate-*r*
395×associate-/r/
366×expm1-log1p-u
364×log1p-expm1-u
357×associate-/r*
356×associate-*l*
330×log-prod
318×associate-/l*
286×flip3-- flip--
282×prod-exp
267×associate-+l+
250×pow-prod-down
239×sqrt-div
232×cbrt-unprod
226×div-exp
217×cbrt-prod
212×unpow-prod-down
185×flip-+ flip3-+
183×distribute-rgt-neg-in
177×log-pow
154×distribute-lft-neg-in
151×cbrt-undiv
141×pow-unpow
123×unswap-sqr
119×fma-def
117×cube-prod associate-*l/
115×diff-log
112×sub-neg
111×swap-sqr
87×sqrt-pow1
84×pow-prod-up
82×associate-*r/
81×sqr-pow
80×associate--l+
76×frac-times exp-sum
74×frac-2neg clear-num
71×distribute-rgt-in pow1/2 distribute-lft-in
67×cbrt-div log-div
60×*-commutative
59×associate-/l/
58×exp-prod
54×pow-sqr
52×frac-sub
51×neg-mul-1
43×distribute-rgt-out
39×1-exp rec-exp fma-udef
38×associate-+r+
36×pow-plus
32×rem-sqrt-square
30×unpow3 cube-mult
28×pow2
27×tan-quot
24×frac-add
23×associate--l- pow1/3 rem-log-exp pow-flip
22×sum-log
21×div-sub
17×+-commutative
15×associate--r+
14×distribute-rgt1-in complex-mul-def
12×exp-diff
10×inv-pow rem-exp-log
9×pow-exp pow-to-exp
7×neg-sub0 neg-log pow-pow
6×quot-tan
5×sqrt-unprod distribute-neg-frac
4×cos-mult log1p-expm1 un-div-inv hypot-def sqr-cos log1p-udef
3×expm1-udef cube-unmult *.c-commutative +.c-commutative exp-to-pow associate-+l- difference-cubes associate--r-
2×expm1-log1p sin-sum associate-+r- sin-cos-mult pow3 tan-sum rem-square-sqrt cos-sum associate-*l*.c distribute-neg-in complex-add-def
1×diff-atan distribute-rgt-out-- rem-cube-cbrt distribute-rgt-neg-out sub-div diff-sin associate-+l+.c diff-cos unsub-neg

regimes5.6s (0.8%)

Accuracy

Total 29.8b remaining (20.5%)

Threshold costs 6.5b (4.5%)

4.9b82.6%quadp (p42, positive)
4.8b83.3%quad2p (problem 3.2.1, positive)
3.7b87%quad2m (problem 3.2.1, negative)
3.6b87.4%quadm (p42, negative)
3.3b0%expq3 (problem 3.4.2)

localize5.3s (0.8%)

bsearch1.7s (0.3%)

end1.0ms (0.0%)