Details

simplify4.9m (42.3%)

sample4.3m (37.3%)

Algorithm
56×intervals
16×halfpoints
Results
48.9s66153×body1280valid
34.0s17568×body2560valid
21.3s42037×body640valid
9.1s12312×body10240exit
9.0s94002×body80valid
7.3s20900×body320valid
6.0s64209×body80nan
2.7s10791×body160valid
2.0s47328×pre80true
1.1s704×body1280nan
367.0ms664×body640nan
330.0ms506×body5120valid
174.0ms387×body320nan
39.0ms191×body160nan

prune1.4m (11.8%)

series38.1s (5.5%)

Calls

341 calls:

803.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
640.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
581.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
417.0ms
(/ (- 1 (cos x)) (* x x))
400.0ms
(fma n (log n) 1)

rewrite12.0s (1.7%)

Algorithm
113×rewrite-expression-head
Calls

341 calls:

522.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
403.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
393.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))
303.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps)))) (/ (sin x) (cos x)))
189.0ms
(+ (/ 1 (+ x 1)) (+ (/ -2 x) (/ 1 (- x 1))))
Rules
11917×times-frac
11836×*-un-lft-identity
10985×add-sqr-sqrt
8160×add-cube-cbrt
5795×prod-diff
1672×pow1
1530×sqrt-prod
1490×difference-of-squares
1182×add-exp-log
963×distribute-lft-out--
957×add-cbrt-cube
808×div-inv
772×unpow-prod-down
667×distribute-lft-out
573×fma-neg
528×add-log-exp
490×associate-/r/
437×pow-prod-up
404×associate-/r*
344×log1p-expm1-u
338×pow-prod-down
337×expm1-log1p-u
335×insert-posit16
329×associate-*l*
293×prod-exp
291×associate-/l*
283×div-exp
270×log-prod
262×associate-+l+
261×distribute-rgt-neg-in sqr-pow
234×cbrt-unprod
226×associate-*r*
223×flip3-- flip--
196×cbrt-prod
186×pow-sqr
174×distribute-lft-neg-in
173×pow-plus
171×cbrt-undiv flip-+ flip3-+
125×fma-def
112×pow2
110×sqrt-div
82×unswap-sqr
75×diff-log
74×log-pow
69×frac-2neg clear-num sub-neg
63×sqrt-pow1
62×associate-+r+
60×pow1/2
55×1-exp
54×associate-*r/
52×pow-unpow
50×neg-mul-1
48×associate-*l/
47×*-commutative
43×associate-/l/
40×rec-exp
37×pow1/3
35×tan-quot
34×cbrt-div rem-sqrt-square fma-udef exp-prod
32×swap-sqr
31×frac-times
28×sum-log
26×distribute-rgt-in distribute-lft-in
25×pow-flip
23×log-div
21×+-commutative
20×div-sub rem-log-exp
17×inv-pow
16×hypot-def
15×difference-of-sqr-1 frac-add
12×expm1-udef
11×frac-sub
10×expm1-log1p neg-sub0
9×associate--l-
8×neg-log
6×pow-exp pow-to-exp associate-+l- log1p-udef
5×log1p-expm1
4×associate-+r- hypot-1-def pow-pow sin-mult
3×exp-diff associate--l+ pow3 associate--r+ sqr-sin distribute-rgt-out--
2×quot-tan sin-sum log1p-def cube-unmult sqrt-unprod +.c-commutative un-div-inv tan-sum exp-neg rem-square-sqrt cos-sum
1×diff-atan sin-cos-mult log-rec sub-div hypot-udef diff-sin rem-cbrt-cube diff-cos expm1-def

regimes4.3s (0.6%)

Accuracy

Total 24.5b remaining (17%)

Threshold costs 5.3b (3.6%)

5.2b81.1%quad2p (problem 3.2.1, positive)
4.8b82.5%quad2m (problem 3.2.1, negative)
4.7b82.8%quadm (p42, negative)
3.0b0%expq3 (problem 3.4.2)
1.5b87.4%2nthrt (problem 3.4.6)

localize4.2s (0.6%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)