Details

series7.6m (56.1%)

Calls

395 calls:

7.0m
(fma (pow 1 (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
682.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
571.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
541.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
525.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))

end2.9m (21.1%)

sample1.8m (13.2%)

Algorithm
56×intervals
16×halfpoints
Results
24.4s66812×body1280valid
16.9s17297×body2560valid
8.5s42549×body640valid
3.8s12689×body10240exit
2.9s93761×body80valid
2.6s20638×body320valid
1.7s63332×body80nan
867.0ms10586×body160valid
597.0ms47332×pre80true
284.0ms664×body1280nan
214.0ms690×body640nan
136.0ms465×body5120valid
67.0ms382×body320nan
22.0ms212×body160nan

prune51.6s (6.3%)

simplify11.9s (1.5%)

Algorithm
196×egg-herbie

rewrite8.4s (1.0%)

Algorithm
124×rewrite-expression-head
Calls

395 calls:

550.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
286.0ms
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
283.0ms
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
246.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
223.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
14863×*-un-lft-identity
13513×times-frac
12172×add-sqr-sqrt
9746×add-cube-cbrt
6501×prod-diff
3541×sqrt-prod
1622×distribute-lft-out
1426×associate--l+
1284×add-exp-log
1166×distribute-rgt-in distribute-lft-in
1002×difference-of-squares
990×add-cbrt-cube
965×distribute-lft-out--
900×unpow-prod-down
816×div-inv
780×associate-/r/
768×pow1
680×add-log-exp
627×associate-/l*
589×associate-+l+
567×associate-*r*
565×associate-*l*
550×associate-/r*
477×cube-prod
457×fma-neg
438×frac-sub
432×log-prod cbrt-prod
431×flip-- flip3--
402×distribute-rgt-neg-in
382×log1p-expm1-u
380×expm1-log1p-u
338×flip-+ flip3-+
330×div-exp
327×frac-times
310×sqr-pow
304×sqrt-div
267×distribute-lft-neg-in
254×prod-exp
226×associate-*r/
213×cbrt-undiv
209×log-pow
208×associate-*l/
190×unswap-sqr
174×exp-prod
168×fma-def
157×cbrt-unprod
146×exp-sum
139×unpow2
137×swap-sqr
127×sqrt-pow1
124×associate-/l/
115×sub-neg
107×diff-log
95×unpow3 cube-mult
89×pow-prod-down neg-mul-1
88×pow1/2
86×frac-2neg clear-num
82×pow-unpow
74×tan-quot
56×pow-exp
55×pow-to-exp
53×*-commutative
52×pow-prod-up
44×sum-log
42×cube-div
41×rec-exp 1-exp
40×rem-sqrt-square
32×pow1/3
30×+-commutative
29×frac-add
28×fma-udef
25×pow-pow div-sub neg-sub0
24×pow-sqr complex-mul-def pow-flip
23×log-div
20×inv-pow
18×rem-log-exp
17×pow-plus
16×neg-log
15×associate--l- cbrt-div
13×associate-+r+
10×exp-diff rem-cube-cbrt pow2
9×associate-+l-
8×sqrt-unprod hypot-def
7×exp-neg
6×difference-cubes *.c-commutative
5×sqrt-undiv exp-to-pow
4×pow-div rem-exp-log +.c-commutative associate--r+ complex-add-def cos-mult rem-cbrt-cube
3×un-div-inv associate-+r- difference-of-sqr-1 sin-mult distribute-rgt-out--
2×expm1-def sum-cubes sub-div expm1-log1p expm1-udef distribute-frac-neg distribute-rgt-out associate-*l*.c cos-sum sqr-cos tan-sum associate-+l+.c sin-sum log-rec
1×sin-cos-mult log1p-udef frac-2neg.c diff-atan log1p-expm1 distribute-neg-in diff-cos unsub-neg rem-square-sqrt diff-sin

regimes3.2s (0.4%)

Accuracy

Total 27.8b remaining (14.4%)

Threshold costs 7.0b (3.6%)

4.7b83.6%quadm (p42, negative)
4.0b85.8%quadp (p42, positive)
3.6b86.6%quad2m (problem 3.2.1, negative)
3.2b0%expq3 (problem 3.4.2)
1.5b82.5%2nthrt (problem 3.4.6)

localize1.9s (0.2%)

bsearch1.1s (0.1%)