Date:	Wednesday, September 16th, 2020
Commit:	eff2405d on multiprecision
Hostname:	warfa with Racket 7.8
Seed:	2020260
Parameters:	256 points for 4 iterations
Flags:	`setup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback` default

Details

sample6.7min (40.8%)

Algorithm

319×

intervals

Results

1.5min	191474×	body	1024	valid
1.5min	12961×	body	8192	exit
46.9s	861549×	body	128	valid
44.3s	69747×	body	2048	valid
22.9s	94412×	body	512	valid
9.6s	73851×	body	256	valid
8.8s	5295×	body	1024	overflowed
7.4s	317503×	pre	128	true
6.7s	34357×	body	128	overflowed
6.0s	14522×	body	1024	nan
5.5s	67008×	body	128	nan
5.4s	50304×	body	128	invalid
4.5s	7099×	body	4096	valid
4.4s	1272×	body	4096	invalid
2.6s	2829×	body	512	overflowed
2.5s	1193×	body	2048	invalid
2.4s	5710×	body	1024	invalid
2.0s	7377×	body	512	nan
1.1s	3668×	body	512	invalid
934.0ms	1210×	body	8192	valid
632.0ms	4096×	body	2048	nan
627.0ms	3730×	body	256	nan
623.0ms	1397×	body	256	overflowed
420.0ms	2106×	body	256	invalid
228.0ms	407×	body	2048	overflowed
12.0ms	14×	body	4096	nan
6.0ms	240×	pre	128	false

series4.7min (28.7%)

Calls

1735 calls:

7.9s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
3.8s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
3.7s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
3.5s	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))

analyze2.0min (12.2%)

Algorithm

159×	search
2×	random

Search

True	Other	False	Iter
0%	80.2%	19.8%	0
4.7%	75.5%	19.8%	1
8.4%	70.8%	20.8%	2
17.6%	58.7%	23.7%	3
22.5%	51.4%	26.1%	4
27.4%	45.5%	27.1%	5
30.1%	41.4%	28.5%	6
32.6%	37.3%	30.1%	7
34.6%	34.3%	31.1%	8
37.1%	30.7%	32.1%	9
38.6%	28.4%	33%	10
40%	26.4%	33.6%	11
41.3%	24.5%	34.3%	12
43.2%	21.6%	35.2%	13
43.7%	20.7%	35.6%	14

prune1.1min (6.6%)

Filtered: 58223 candidates to 37425 candidates (35.7%)

simplify1.0min (6.2%)

Algorithm

859×	egg-herbie

rewrite25.5s (2.6%)

Algorithm

543×	rewrite-expression-head

Calls

1735 calls:

366.0ms	(-.f64 (pow.f64 (/.f64 (pow.f64 x0 3) (pow.f64 (-.f64 1 x1) 6)) 3) (pow.f64 (pow.f64 x0 3) 3))
242.0ms	(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 4 (+.f64 1 t)) -8) (+.f64 1 t)) 6) (+.f64 (/.f64 (+.f64 (/.f64 4 (+.f64 1 t)) -8) (+.f64 1 t)) 5))
142.0ms	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) c0) (sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))))
121.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
105.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

Rules

31461×	`times-frac_binary64`
25471×	`*-un-lft-identity_binary64`
23831×	`add-sqr-sqrt_binary64`
16667×	`add-cube-cbrt_binary64`
10117×	`add-exp-log_binary64`
7084×	`add-cbrt-cube_binary64`
6358×	`sqrt-prod_binary64`
4207×	`pow1_binary64`
3674×	`cbrt-prod_binary64`
3560×	`prod-exp_binary64`
3378×	`associate-r_binary64`
2933×	`difference-of-squares_binary64`
2817×	`distribute-lft-out_binary64`
2731×	`add-log-exp_binary64`
2502×	`div-exp_binary64`
2324×	`unpow-prod-down_binary64`
2226×	`associate-/r*_binary64`
2143×	`cbrt-unprod_binary64`
1972×	`associate-l_binary64`
1932×	`div-inv_binary64`
1686×	`associate-/l*_binary64`
1604×	`distribute-lft-out--_binary64`
1545×	`cbrt-undiv_binary64`
1541×	`flip--_binary64`
1540×	`flip3--_binary64`
1473×	`associate-*l/_binary64`
1394×	`associate-*r/_binary64`
1232×	`frac-times_binary64`
1205×	`associate-/r/_binary64`
1096×	`pow-prod-down_binary64`
1068×	`flip-+_binary64`
1067×	`flip3-+_binary64`
1025×	`sqrt-div_binary64`
1006×	`sqr-pow_binary64`
860×	`pow-exp_binary64`
785×	`cube-prod_binary64`
768×	`cbrt-div_binary64`
705×	`unswap-sqr_binary64`
639×	`frac-add_binary64`
624×	`log-prod_binary64`
592×	`sqrt-pow1_binary64`
558×	`pow-to-exp_binary64`
450×	`exp-prod_binary64`
423×	`*-commutative_binary64`
373×	`clear-num_binary64` `frac-2neg_binary64`
340×	`sub-neg_binary64`
329×	`pow-unpow_binary64`
308×	`log-pow_binary64`
299×	`associate-/l/_binary64`
294×	`sum-log_binary64`
267×	`pow1/2_binary64`
264×	`rec-exp_binary64`
254×	`diff-log_binary64`
246×	`swap-sqr_binary64`
232×	`pow1/3_binary64`
205×	`rem-sqrt-square_binary64`
167×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
166×	`difference-of-sqr-1_binary64`
165×	`frac-sub_binary64`
140×	`+-commutative_binary64`
136×	`tan-quot_binary64`
130×	`log-div_binary64`
122×	`pow-pow_binary64`
109×	`unpow3_binary64`
103×	`unpow2_binary64`
102×	`exp-diff_binary64`
96×	`div-sub_binary64`
94×	`pow-prod-up_binary64`
91×	`pow-flip_binary64`
90×	`cube-mult_binary64`
89×	`exp-neg_binary64`
84×	`associate-+r+_binary64`
73×	`neg-sub0_binary64`
71×	`associate--l+_binary64`
66×	`pow-sqr_binary64`
62×	`sin-mult_binary64`
59×	`rem-log-exp_binary64` `inv-pow_binary64`
55×	`associate--r+_binary64`
49×	`difference-of-sqr--1_binary64`
45×	`exp-sum_binary64`
43×	`pow-plus_binary64`
40×	`distribute-rgt-out_binary64` `cube-div_binary64`
39×	`cos-mult_binary64` `associate-+l+_binary64`
35×	`distribute-rgt-neg-in_binary64`
32×	`pow2_binary64`
30×	`distribute-lft-neg-in_binary64` `distribute-rgt-out--_binary64`
26×	`un-div-inv_binary64`
24×	`neg-mul-1_binary64`
21×	`rem-exp-log_binary64` `cos-diff_binary64` `rem-cube-cbrt_binary64`
20×	`associate--l-_binary64`
18×	`rem-cbrt-cube_binary64`
17×	`sin-diff_binary64` `sub-div_binary64`
16×	`sin-cos-mult_binary64`
15×	`cosh-undef_binary64`
14×	`cos-sum_binary64`
12×	`distribute-rgt1-in_binary64` `acos-asin_binary64`
11×	`associate-+r-_binary64` `asin-acos_binary64` `associate--r-_binary64`
10×	`sinh-undef_binary64`
7×	`sqrt-unprod_binary64` `sinh-def_binary64`
6×	`unpow-prod-up_binary64` `exp-to-pow_binary64` `distribute-frac-neg_binary64` `sin-sum_binary64`
5×	`sqrt-undiv_binary64` `associate-+l-_binary64`
4×	`sqrt-pow2_binary64` `tan-sum_binary64` `pow-sub_binary64`
3×	`acos-neg_binary64` `sum-cubes_binary64` `sqr-sin-a_binary64`
2×	`distribute-rgt-neg-out_binary64` `pow3_binary64` `cos-2_binary64` `distribute-lft1-in_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64`
1×	`difference-cubes_binary64` `remove-double-div_binary64` `count-2_binary64` `tanh-def-a_binary64` `tanh-undef_binary64` `pow-neg_binary64` `unpow1/3_binary64` `sqr-cos-a_binary64` `neg-log_binary64` `diff-sin_binary64` `tanh-def-b_binary64` `mul0-rgt_binary64` `diff-atan_binary64` `tanh-def-c_binary64` `diff-cos_binary64` `distribute-lft-neg-out_binary64`

regimes15.4s (1.6%)

Accuracy

Total 127.6b remaining (20.1%)

Threshold costs 23.3b (3.7%)

8.4b	30.7%	Toniolo and Linder, Equation (13)
7.1b	49.6%	Cubic critical, narrow range
6.5b	25.9%	Henrywood and Agarwal, Equation (12)
6.1b	69.9%	Compound Interest
5.9b	48.8%	Quotient of products

Details

sample6.7min (40.8%)

series4.7min (28.7%)

analyze2.0min (12.2%)

prune1.1min (6.6%)

simplify1.0min (6.2%)

rewrite25.5s (2.6%)

regimes15.4s (1.6%)

localize7.7s (0.8%)

bsearch5.7s (0.6%)

end4.0ms (0.0%)

Profiling