Details

sample2.0m (57.4%)

Algorithm
56×intervals
16×halfpoints
Results
29.2s67679×body1280valid
17.4s17819×body2560valid
9.6s42071×body640valid
4.9s12904×body10240exit
3.2s2217×body1280nan
3.0s92644×body80valid
2.9s20341×body320valid
1.9s64089×body80nan
1.8s1823×body640nan
976.0ms10532×body160valid
532.0ms47497×pre80true
474.0ms906×body320nan
139.0ms435×body5120valid
135.0ms460×body160nan

prune36.6s (17.2%)

series32.7s (15.4%)

Calls

360 calls:

868.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))
525.0ms
(* (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)))
523.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
401.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
361.0ms
(/ (* 1.0 (log (* (exp 1.0) (exp (- x x))))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))

simplify10.4s (4.9%)

Algorithm
190×egg-herbie

rewrite5.1s (2.4%)

Algorithm
118×rewrite-expression-head
Calls

360 calls:

245.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
111.0ms
(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
89.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
66.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
57.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
Rules
7722×*-un-lft-identity
6961×add-sqr-sqrt
6156×times-frac
5435×add-cube-cbrt
3561×prod-diff
1640×sqrt-prod
1147×unpow-prod-down
1042×add-exp-log
780×add-cbrt-cube
697×distribute-lft-out
661×pow1
593×add-log-exp
581×cbrt-prod
535×associate-*r*
532×difference-of-squares
501×associate-*l*
463×distribute-lft-out--
427×fma-neg
420×sqr-pow
388×associate-/l*
380×div-inv
349×log1p-expm1-u
345×expm1-log1p-u
344×associate-/r*
326×associate-/r/
277×log-prod
256×associate-+l+
252×distribute-rgt-neg-in
248×div-exp
220×unswap-sqr
205×flip-- flip3--
195×prod-exp
185×flip-+ flip3-+
180×distribute-lft-neg-in
146×cbrt-undiv
139×sqrt-div
127×unpow2
117×cbrt-unprod
113×exp-sum
111×log-pow
103×fma-def sqrt-pow1
98×diff-log
96×swap-sqr
95×sub-neg
90×distribute-rgt-in distribute-lft-in
89×associate-*l/
81×exp-prod
77×pow1/2
75×pow-prod-down
74×pow1/3
73×pow-unpow
70×pow-exp
67×pow-to-exp
64×frac-2neg clear-num
63×associate-/l/ cbrt-div cube-prod
60×neg-mul-1
50×*-commutative frac-times associate-*r/
38×tan-quot pow-prod-up
36×log-div
35×1-exp rec-exp
33×rem-sqrt-square
28×pow-sqr sum-log
24×fma-udef complex-mul-def
23×associate-+r+
22×div-sub
20×rem-log-exp
18×+-commutative
16×pow-pow neg-sub0
15×pow-flip
14×unpow3 cube-mult
13×inv-pow
12×associate--l- frac-add neg-log associate-+l-
11×pow2 pow-plus
10×rem-cube-cbrt frac-sub associate--l+
7×cube-div exp-diff
6×*.c-commutative
5×rem-exp-log log1p-udef sqrt-unprod hypot-def sin-mult distribute-rgt-out--
4×pow-div log1p-expm1 +.c-commutative expm1-log1p complex-add-def rem-square-sqrt expm1-udef exp-to-pow associate--r+
3×cos-mult associate-+r- log-rec
2×associate-+l+.c expm1-def exp-neg difference-of-sqr-1 un-div-inv associate-*l*.c tan-sum cos-sum sin-sum
1×sin-cos-mult rem-cbrt-cube difference-cubes diff-atan sub-div diff-cos unsub-neg frac-2neg.c diff-sin

regimes2.8s (1.3%)

Accuracy

Total 29.1b remaining (13.4%)

Threshold costs 6.6b (3%)

4.7b-47%expq3 (problem 3.4.2)
4.4b87.2%quad2m (problem 3.2.1, negative)
4.3b87.3%quadm (p42, negative)
2.9b89.8%quadp (p42, positive)
2.9b89.9%quad2p (problem 3.2.1, positive)

localize1.9s (0.9%)

bsearch991.0ms (0.5%)

end1.0ms (0.0%)