Details

simplify5.5m (43.3%)

sample4.4m (34.4%)

Algorithm
56×intervals
16×halfpoints
Results
51.2s66810×body1280valid
31.6s17396×body2560valid
18.9s41741×body640valid
9.8s12737×body10240exit
8.7s93751×body80valid
6.1s21173×body320valid
5.3s63286×body80nan
2.0s10876×body160valid
1.4s47298×pre80true
480.0ms623×body1280nan
447.0ms675×body640nan
311.0ms415×body5120valid
122.0ms397×body320nan
33.0ms196×body160nan

prune1.6m (12.2%)

series50.5s (6.6%)

Calls

385 calls:

2.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (log1p (expm1 (fma (* eps (* a (* (* a eps) (* a eps)))) 1/6 (* (* (* a eps) (* a eps)) 1/2))))) (- (exp (* b eps)) 1.0)))
1.7s
(log (* (cbrt (exp (* 0.022222222222222223 (* x x)))) (cbrt (exp (* 0.022222222222222223 (* x x))))))
1.6s
(- (fma (fma (/ (tan x) (/ (cos eps) (sin eps))) (/ (tan x) (/ (cos eps) (sin eps))) (/ (tan x) (/ (cos eps) (sin eps)))) (/ (+ (tan x) (tan eps)) (- 1 (* (/ (tan x) (/ (cos eps) (sin eps))) (* (/ (* (sin eps) (tan x)) (cos eps)) (/ (* (sin eps) (tan x)) (cos eps)))))) (/ (+ (tan x) (tan eps)) (- 1 (* (/ (tan x) (/ (cos eps) (sin eps))) (* (/ (* (sin eps) (tan x)) (cos eps)) (/ (* (sin eps) (tan x)) (cos eps))))))) (tan x))
1.3s
(log (cbrt (exp (* 0.022222222222222223 (* x x)))))
1.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma eps a (fma (* 1/6 (* eps (* eps eps))) (* a (* a a)) (* (* 1/2 (* eps eps)) (* a a)))) (- (exp (* b eps)) 1.0)))

rewrite13.7s (1.8%)

Algorithm
122×rewrite-expression-head
Calls

385 calls:

574.0ms
(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
438.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
248.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
221.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
211.0ms
(* eps (* a (* (* a eps) (* a eps))))
Rules
10298×*-un-lft-identity
8637×times-frac
8119×add-sqr-sqrt
6970×add-cube-cbrt
5120×prod-diff
2768×pow1
2506×sqrt-prod
1400×distribute-lft-out
1254×add-exp-log
1191×add-cbrt-cube
826×pow-prod-up
783×unpow-prod-down
671×add-log-exp
634×div-inv
611×pow-prod-down
595×fma-neg
506×difference-of-squares
460×distribute-lft-out--
424×associate-/r/
383×prod-exp
375×expm1-log1p-u log1p-expm1-u
370×associate-*l/
367×pow-plus
366×cbrt-unprod
356×pow-sqr
354×associate-/l*
349×flip-+
334×flip3-+
309×associate-/r*
307×distribute-rgt-neg-in
291×distribute-lft-neg-in
284×flip--
274×associate-*r*
269×flip3--
265×sqr-pow
250×associate-+l+
246×associate-*r/
243×associate-*l*
236×associate-+r+
221×pow2
193×div-exp
182×sqrt-div
179×cbrt-undiv
170×log-prod
154×cbrt-prod
149×fma-def
133×frac-sub
128×frac-times
119×associate-/l/
114×cube-prod diff-log
107×sub-neg
97×neg-mul-1
89×frac-add
87×swap-sqr
82×log-pow
79×unswap-sqr
67×frac-2neg clear-num
63×sqrt-pow1
57×*-commutative
56×pow-unpow
49×exp-prod
46×cbrt-div
45×pow1/2
41×associate--l+
40×distribute-rgt-in distribute-lft-in
39×rem-sqrt-square
37×log-div
35×tan-quot
33×div-sub
31×sum-log
29×pow1/3 associate--r+
28×fma-udef
26×unpow3 cube-mult
23×+-commutative
22×rem-log-exp
21×difference-cubes
17×cube-unmult
15×exp-to-pow complex-mul-def
10×associate--l- 1-exp rec-exp
9×neg-sub0 pow3
8×pow-flip
7×exp-sum
6×pow-exp pow-pow pow-to-exp exp-lft-cube
5×expm1-log1p expm1-udef cos-mult neg-log
4×exp-diff log1p-expm1 *.c-commutative sin-mult un-div-inv rem-exp-log hypot-def log1p-udef
3×+.c-commutative inv-pow exp-neg associate-+l- cos-sum sqr-cos
2×associate-*l*.c sin-sum associate-+r- complex-def-add complex-add-def tan-sum associate--r-
1×quot-tan diff-atan distribute-rgt-out-- rem-cube-cbrt sin-cos-mult sqrt-unprod sub-div frac-2neg.c distribute-lft-in.c rem-square-sqrt distribute-rgt-in.c diff-sin associate-+l+.c diff-cos unsub-neg

localize5.7s (0.7%)

regimes5.5s (0.7%)

Accuracy

Total 33.2b remaining (24.3%)

Threshold costs 5.4b (4%)

7.4b72.8%quadm (p42, negative)
4.6b84.1%quad2m (problem 3.2.1, negative)
4.2b85.5%quadp (p42, positive)
4.2b85.5%quad2p (problem 3.2.1, positive)
3.3b0%expq3 (problem 3.4.2)

bsearch2.0s (0.3%)

end1.0ms (0.0%)