Details

sample2.1m (53.0%)

Algorithm
56×intervals
16×halfpoints
Results
30.7s67691×body1280valid
19.7s17547×body2560valid
11.6s41768×body640valid
5.2s93846×body80valid
3.7s20352×body320valid
2.9s62612×body80nan
1.3s10543×body160valid
777.0ms13293×body80overflowed
759.0ms47569×pre80true
607.0ms654×body1280nan
280.0ms632×body640nan
199.0ms431×body5120valid
97.0ms362×body320nan
32.0ms193×body160nan

series44.0s (18.7%)

Calls

386 calls:

1.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
1.4s
(- (fma 0.3333333333333333 (/ 1 (* (- 1 (log (/ 1 N))) (pow N 3))) (* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))) (fma 5.551115123125783e-17 (/ 1 (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))) (fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))))
1.3s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))
1.0s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
970.0ms
(cbrt (* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

prune40.6s (17.3%)

simplify11.2s (4.8%)

Algorithm
194×egg-herbie

rewrite8.4s (3.6%)

Algorithm
122×rewrite-expression-head
Calls

386 calls:

2.4s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))
232.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
135.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
98.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
83.0ms
(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
Rules
10741×*-un-lft-identity
9611×add-sqr-sqrt
9333×times-frac
7042×add-cube-cbrt
4677×prod-diff
1964×sqrt-prod
1396×unpow-prod-down
1354×add-exp-log
1111×difference-of-squares
992×add-cbrt-cube
941×distribute-lft-out--
938×distribute-lft-out
859×cbrt-prod
735×pow1
673×associate-*l*
668×cube-prod
649×associate-/l*
648×add-log-exp
528×fma-neg
520×div-inv
497×sqr-pow
439×associate-/r/
378×distribute-rgt-neg-in
373×associate-/r*
372×log1p-expm1-u
371×expm1-log1p-u
354×div-exp
341×associate-*r*
315×prod-exp
281×flip-- flip3--
247×associate-+l+
246×unswap-sqr
224×flip-+ flip3-+
219×cbrt-undiv
195×distribute-lft-neg-in
194×log-prod
173×cbrt-unprod
127×associate-*l/
120×diff-log cbrt-div sqrt-pow1
116×unpow3 cube-mult
114×pow-unpow sub-neg
110×swap-sqr
107×pow-prod-down
103×sqrt-div
100×log-pow
97×exp-sum
90×fma-def frac-times
86×pow-exp
85×pow1/2
82×pow-to-exp
77×frac-add log-div
75×associate-*r/
72×tan-quot
70×unpow2
69×exp-prod frac-2neg clear-num
68×associate-/l/
65×neg-mul-1
56×*-commutative
54×pow-prod-up
43×1-exp
42×pow1/3
40×fma-udef rec-exp
34×distribute-rgt-in distribute-lft-in
28×rem-sqrt-square div-sub
27×frac-sub
24×pow-pow pow-sqr sum-log complex-mul-def
18×associate--r-
17×associate-+r+
15×neg-sub0 associate--l+
14×associate--l- +-commutative
13×cube-div rem-cube-cbrt pow-plus rem-log-exp
11×neg-log
10×pow-flip
associate--r+
difference-cubes inv-pow
sqrt-unprod
exp-diff pow2 *.c-commutative associate-+l-
pow-div log1p-udef log1p-expm1 +.c-commutative complex-add-def expm1-udef
sin-cos-mult un-div-inv associate-+r- expm1-log1p rem-exp-log sin-mult cos-mult distribute-rgt-out--
associate-+l+.c expm1-def exp-neg sub-div difference-of-sqr-1 rem-square-sqrt associate-*l*.c cos-sum tan-sum rem-cbrt-cube frac-2neg.c exp-to-pow sin-sum
diff-atan diff-cos distribute-frac-neg distribute-rgt-neg-out diff-sin log-rec

regimes3.0s (1.3%)

Accuracy

Total 26.1b remaining (10.8%)

Threshold costs 5.7b (2.4%)

5.8b31.2%expq3 (problem 3.4.2)
4.6b83.7%quad2m (problem 3.2.1, negative)
4.6b83.9%quadm (p42, negative)
1.4b82.9%2nthrt (problem 3.4.6)
1.4b94.2%quad2p (problem 3.2.1, positive)

localize2.0s (0.8%)

bsearch1.3s (0.5%)

end1.0ms (0.0%)