Details

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66872×body1280valid
37.6s17140×body2560valid
29.5s42745×body640valid
14.4s12897×body10240exit
11.6s93579×body80valid
9.1s20405×body320valid
6.7s62508×body80nan
2.7s11077×body160valid
1.9s47424×pre80true
787.0ms645×body1280nan
542.0ms468×body5120valid
519.0ms703×body640nan
219.0ms396×body320nan
100.0ms218×body160nan

simplify3.6m

prune2.3m

series35.1s

Calls

389 calls:

Slowest
528.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
524.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))
492.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (tan x))
480.0ms
(/ (- x (sin x)) (- x (tan x)))
389.0ms
(* (+ (* (/ (* (* x x) x) 91125) (* (* x x) x)) 1/27) (/ x (+ 1/9 (* (- (/ (* x x) 45) 1/3) (/ (* x x) 45)))))

rewrite14.6s

Algorithm
119×rewrite-expression-head
Calls

389 calls:

Slowest
661.0ms
(/ (+ (* 1/60 (* (* x (* x x)) (* x x))) (+ (* 1/3 (* x (* x x))) (* 2 x))) (/ 2 (sin y)))
402.0ms
(* (+ (* (/ (* (* x x) x) 91125) (* (* x x) x)) 1/27) (/ x (+ 1/9 (* (- (/ (* x x) 45) 1/3) (/ (* x x) 45)))))
374.0ms
(- (exp (+ (* (+ b a) eps) (+ (* (+ b a) eps) (* (+ b a) eps)))) 1)
373.0ms
(* (* (* (* a x) (* a x)) (* a x)) 1/6)
343.0ms
(* (* (* (* eps a) (* eps a)) a) eps)
Rules
6469×times-frac
5932×*-un-lft-identity
4911×add-sqr-sqrt
3625×add-cube-cbrt
2714×sqrt-prod
1459×add-exp-log
1321×pow1
1294×add-cbrt-cube
822×distribute-lft-out
663×add-log-exp
572×associate-/l*
503×associate-*l*
467×difference-of-squares
461×prod-exp
416×cbrt-unprod
406×associate-*r*
403×pow-prod-down
377×insert-posit16
358×distribute-lft-out--
345×associate-/r*
286×associate-/r/
264×div-inv
247×div-exp
243×flip-+
242×flip3-+
218×flip--
217×flip3-- sqrt-div
210×associate-*l/
209×log-prod
180×cbrt-undiv
136×unswap-sqr
123×pow-prod-up
122×cbrt-prod
101×sub-neg
100×exp-prod
98×diff-log
91×sqrt-pow1
87×*-commutative
81×pow-unpow
77×frac-times
75×pow1/2
74×associate-/l/
73×log-pow
69×frac-2neg clear-num pow-sqr
64×frac-add
63×associate-*r/
58×unpow-prod-down
57×pow-plus
56×tan-quot
53×sum-log
51×swap-sqr
40×1-exp
39×rec-exp
37×+-commutative
36×rem-sqrt-square log-div
35×pow1/3 cbrt-div difference-of-sqr-1
34×frac-sub pow2
33×pow-flip
29×distribute-rgt-in distribute-lft-in
27×associate--l+
25×associate-+r+ sqr-pow
22×associate--r+
21×rem-log-exp
19×associate-+l+ inv-pow
18×div-sub
15×associate--l-
13×distribute-rgt-neg-in complex-mul-def
10×neg-sub0 pow-exp pow-to-exp
pow-pow
associate-+l-
un-div-inv
pow-div exp-diff distribute-lft1-in neg-log distribute-rgt-out
sin-sum pow3 sqrt-unprod exp-to-pow distribute-rgt-out--
exp-sum exp-neg sin-mult
sin-cos-mult *.c-commutative log-rec sub-div sqr-sin +.c-commutative cube-unmult rem-exp-log
associate-*l*.c tan-sum frac-2neg-c rem-square-sqrt cos-sum complex-add-def
diff-atan cos-mult associate-+r- sqrt-pow2 +-inverses associate-+l+.c diff-sin rem-cbrt-cube diff-cos unsub-neg associate--r-

localize4.8s

regimes4.5s

Accuracy

Total 29.3b remaining (16.4%)

Threshold costs 5.7b (3.2%)

5.0b45.9%expq3 (problem 3.4.2)
5.0b81.9%quad2p (problem 3.2.1, positive)
4.9b81.9%quadp (p42, positive)
4.4b84.3%quadm (p42, negative)
2.9b88.7%quad2m (problem 3.2.1, negative)

bsearch3.2s

end1.0ms