Details

sample1.9m (53.3%)

Algorithm
56×intervals
16×halfpoints
Results
24.6s66750×body1280valid
16.8s17347×body2560valid
8.5s42645×body640valid
3.9s12758×body10240exit
2.9s93425×body80valid
2.6s20878×body320valid
1.7s63396×body80nan
874.0ms10548×body160valid
550.0ms47348×pre80true
281.0ms622×body1280nan
198.0ms606×body640nan
136.0ms484×body5120valid
65.0ms351×body320nan
18.0ms175×body160nan

prune37.5s (17.6%)

series35.6s (16.7%)

Calls

365 calls:

959.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
684.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
658.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (- (tan x)))
509.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
444.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify10.6s (5.0%)

Algorithm
192×egg-herbie

rewrite9.4s (4.4%)

Algorithm
120×rewrite-expression-head
Calls

365 calls:

336.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
296.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))
116.0ms
(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
109.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
98.0ms
(/ 1 (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
Rules
8674×*-un-lft-identity
7974×add-sqr-sqrt
7136×times-frac
6014×add-cube-cbrt
4052×prod-diff
2405×sqrt-prod
1391×add-exp-log
1008×add-cbrt-cube
896×unpow-prod-down
781×difference-of-squares
687×distribute-lft-out
634×distribute-lft-out--
627×pow1
621×add-log-exp
531×fma-neg
499×log-prod
446×associate-/l*
438×associate-*r*
414×div-inv
400×associate-/r/
384×prod-exp
368×cube-prod
367×associate-*l*
351×sqr-pow
350×expm1-log1p-u
349×log1p-expm1-u
346×associate-/r*
340×distribute-rgt-neg-in
329×div-exp
275×cbrt-prod
270×distribute-lft-neg-in
251×flip-- flip3-- associate-+l+
235×unswap-sqr
226×cbrt-unprod
220×cbrt-undiv
170×sqrt-div
144×flip-+ flip3-+
134×unpow2
113×diff-log
104×sqrt-pow1
101×sub-neg
93×pow-exp
92×pow-to-exp
81×pow-unpow
80×pow1/2 neg-mul-1
74×associate-/l/
73×log-pow
72×unpow3 cube-mult
70×frac-2neg clear-num
69×pow-prod-down
68×fma-def
54×associate-*r/
46×*-commutative associate-*l/ swap-sqr
42×1-exp
39×rec-exp
38×rem-log-exp
37×rem-sqrt-square
36×fma-udef
33×frac-times
30×log-div
29×tan-quot
27×associate-+r+ sum-log
24×complex-mul-def
22×pow-prod-up
21×pow-flip div-sub frac-sub
20×neg-sub0
18×exp-prod
17×+-commutative cbrt-div
16×inv-pow pow1/3 exp-sum
15×associate--l-
14×pow-sqr pow-pow
13×neg-log
12×distribute-rgt-in distribute-lft-in
11×cos-mult
10×frac-add expm1-udef associate--l+
associate--r- sub-div
sin-mult
cube-div difference-cubes sqrt-unprod pow2 pow-plus hypot-def *.c-commutative associate-+l-
distribute-rgt-out--
rem-cube-cbrt sqrt-undiv sum-cubes associate-+r- +.c-commutative associate--r+ complex-add-def log-rec
rem-exp-log exp-diff unpow-prod-up difference-of-sqr-1 rem-square-sqrt
expm1-def log1p-udef frac-2neg.c exp-neg sin-sum log1p-expm1 pow-sub expm1-log1p associate-*l*.c sqr-cos tan-sum cos-sum associate-+l+.c pow-neg
sin-cos-mult sqrt-pow2 e-exp-1 un-div-inv diff-atan diff-cos distribute-frac-neg distribute-rgt-out diff-sin exp-to-pow rem-cbrt-cube

regimes2.9s (1.3%)

Accuracy

Total 29.3b remaining (10.8%)

Threshold costs 6.7b (2.5%)

4.9b82.6%quad2m (problem 3.2.1, negative)
4.9b82.7%quadm (p42, negative)
4.4b49.5%expq3 (problem 3.4.2)
4.4b83.5%quad2p (problem 3.2.1, positive)
1.6b81.5%2nthrt (problem 3.4.6)

localize1.9s (0.9%)

bsearch1.6s (0.8%)

end1.0ms (0.0%)