Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample37.0ms (0%)

Algorithm

1×

intervals

Results

16.0ms	67×	body	2048	valid
5.0ms	139×	body	128	valid
5.0ms	31×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`sub-neg_binary64_2117`
18×	`distribute-rgt-in_binary64_2074`
12×	`cancel-sign-sub-inv_binary64_2090` `+-commutative_binary64_2054`
11×	`neg-mul-1_binary64_2120` `distribute-lft-in_binary64_2073` `associate--r+_binary64_2060`
10×	`associate-+l-_binary64_2059`
9×	`neg-sub0_binary64_2119` `associate-+l+_binary64_2057`
8×	`distribute-neg-in_binary64_2085`
7×	`--rgt-identity_binary64_2110` `associate--l+_binary64_2061` `*-commutative_binary64_2055`
6×	`unsub-neg_binary64_2118` `sub0-neg_binary64_2111` `associate--r-_binary64_2063`
5×	`-rgt-identity_binary64_2114` `-lft-identity_binary64_2113`
4×	`+-rgt-identity_binary64_2109` `associate--l-_binary64_2062` `associate-+r+_binary64_2056`
3×	`distribute-lft-neg-out_binary64_2083` `distribute-rgt-neg-in_binary64_2082` `associate-+r-_binary64_2058`
2×	`remove-double-neg_binary64_2112` `+-lft-identity_binary64_2108` `distribute-rgt-neg-out_binary64_2084` `distribute-lft-neg-in_binary64_2081` `count-2_binary64_2072`
1×	`1-exp_binary64_2168` `mul-1-neg_binary64_2116` `distribute-neg-out_binary64_2086` `distribute-lft1-in_binary64_2079` `distribute-rgt-out_binary64_2077` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `associate-l_binary64_2065`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2387` `erf-erfc_binary64_2386` `erf-odd_binary64_2385` `if-if-and-not_binary64_2384` `if-if-and_binary64_2383` `if-if-or-not_binary64_2382` `if-if-or_binary64_2381` `if-not_binary64_2380` `if-same_binary64_2379` `if-false_binary64_2378` `if-true_binary64_2377` `not-gte_binary64_2376` `not-lte_binary64_2375` `not-gt_binary64_2374` `not-lt_binary64_2373` `gte-same_binary64_2372` `lte-same_binary64_2371` `gt-same_binary64_2370` `lt-same_binary64_2369` `sinh---cosh_binary64_2316` `sinh-+-cosh_binary64_2315` `sinh-cosh_binary64_2314` `tanh-def-c_binary64_2313` `tanh-def-b_binary64_2312` `tanh-def-a_binary64_2311` `cosh-def_binary64_2310` `sinh-def_binary64_2309` `tan-neg_binary64_2256` `cos-neg_binary64_2255` `sin-neg_binary64_2254` `tan-0_binary64_2253` `cos-0_binary64_2252` `sin-0_binary64_2251` `hang-m-tan_binary64_2250` `hang-p-tan_binary64_2249` `hang-m0-tan_binary64_2248` `hang-p0-tan_binary64_2247` `hang-0m-tan_binary64_2246` `hang-0p-tan_binary64_2245` `tan-+PI/2_binary64_2244` `tan-+PI_binary64_2243` `tan-PI_binary64_2242` `tan-PI/3_binary64_2241` `tan-PI/4_binary64_2240` `tan-PI/6_binary64_2239` `cos-+PI/2_binary64_2238` `cos-+PI_binary64_2237` `cos-PI_binary64_2236` `cos-PI/2_binary64_2235` `cos-PI/3_binary64_2234` `cos-PI/4_binary64_2233` `cos-PI/6_binary64_2232` `sin-+PI/2_binary64_2231` `sin-+PI_binary64_2230` `sin-PI_binary64_2229` `sin-PI/2_binary64_2228` `sin-PI/3_binary64_2227` `sin-PI/4_binary64_2226` `sin-PI/6_binary64_2225` `sub-1-sin_binary64_2224` `sub-1-cos_binary64_2223` `-1-add-sin_binary64_2222` `-1-add-cos_binary64_2221` `1-sub-sin_binary64_2220` `1-sub-cos_binary64_2219` `cos-sin-sum_binary64_2218` `log-E_binary64_2214` `log-pow_binary64_2213` `log-rec_binary64_2212` `log-div_binary64_2211` `log-prod_binary64_2210` `pow-base-0_binary64_2208` `unpow1/3_binary64_2191` `unpow3_binary64_2190` `unpow2_binary64_2189` `unpow1/2_binary64_2188` `pow-plus_binary64_2187` `exp-to-pow_binary64_2186` `pow-base-1_binary64_2184` `unpow0_binary64_2183` `unpow1_binary64_2182` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-lft-sqr_binary64_2179` `exp-cbrt_binary64_2178` `exp-sqrt_binary64_2177` `exp-prod_binary64_2176` `div-exp_binary64_2175` `rec-exp_binary64_2174` `prod-exp_binary64_2173` `exp-diff_binary64_2172` `exp-neg_binary64_2171` `exp-sum_binary64_2170` `e-exp-1_binary64_2169` `exp-1-e_binary64_2167` `exp-0_binary64_2166` `rem-log-exp_binary64_2165` `rem-exp-log_binary64_2164` `cube-unmult_binary64_2161` `cube-mult_binary64_2154` `cube-div_binary64_2153` `cube-prod_binary64_2152` `cube-neg_binary64_2151` `rem-3cbrt-rft_binary64_2150` `rem-3cbrt-lft_binary64_2149` `rem-cbrt-cube_binary64_2148` `rem-cube-cbrt_binary64_2147` `sqr-abs_binary64_2139` `sqr-neg_binary64_2138` `rem-sqrt-square_binary64_2137` `rem-square-sqrt_binary64_2136` `times-frac_binary64_2130` `div-sub_binary64_2129` `/-rgt-identity_binary64_2115` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `div0_binary64_2105` `-inverses_binary64_2104` `+-inverses_binary64_2103` `lft-mult-inverse_binary64_2102` `rgt-mult-inverse_binary64_2101` `remove-double-div_binary64_2100` `pow-sqr_binary64_2097` `sqr-pow_binary64_2096` `difference-of-sqr--1_binary64_2095` `difference-of-sqr-1_binary64_2094` `difference-of-squares_binary64_2093` `unswap-sqr_binary64_2092` `swap-sqr_binary64_2091` `cancel-sign-sub_binary64_2089` `distribute-neg-frac_binary64_2088` `distribute-frac-neg_binary64_2087` `distribute-rgt1-in_binary64_2080` `distribute-rgt-out--_binary64_2078` `distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `associate-r*_binary64_2064`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	33	15
4	41	15
5	51	15
6	66	15
7	103	15
8	101	15
9	100	15
10	95	15
11	96	15
12	97	15
13	98	15
14	99	15
15	101	15
16	101	15

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

14.4b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(hypot.f64 1 x)
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite116.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

14.4b

Rules

26×	`*-un-lft-identity_binary64_2124`
24×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159`
12×	`sqrt-prod_binary64_2140`
9×	`times-frac_binary64_2130`
7×	`cancel-sign-sub-inv_binary64_2090`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`difference-of-squares_binary64_2093`
3×	`distribute-lft-out_binary64_2075` `distribute-lft-out--_binary64_2076` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`sqrt-div_binary64_2141`
1×	`diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137`

Counts

4 → 75

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

Compiler

Compiled 1401 to 1270 computations (9.4% saved)

series166.0ms (0.2%)

Error

14.4b

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
54.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
30.0ms	(/.f64 1/2 (hypot.f64 1 x))
7.0ms	(hypot.f64 1 x)

Compiler

Compiled 396 to 385 computations (2.8% saved)

simplify1.3min (99.4%)

Algorithm

1×	egg-herbie

Rules

552×	`unsub-neg_binary64_2118`
418×	`cancel-sign-sub-inv_binary64_2090`
352×	`distribute-rgt-in_binary64_2074`
284×	`distribute-lft-in_binary64_2073`
269×	`times-frac_binary64_2130`
230×	`*-commutative_binary64_2055`
191×	`associate-/l*_binary64_2069`
171×	`sub-neg_binary64_2117`
159×	`associate-l_binary64_2065`
148×	`associate-r_binary64_2064`
132×	`associate-/r*_binary64_2068`
111×	`neg-mul-1_binary64_2120`
110×	`sqr-pow_binary64_2096`
104×	`neg-sub0_binary64_2119`
90×	`associate-+l+_binary64_2057`
89×	`unswap-sqr_binary64_2092`
88×	`associate-*l/_binary64_2067`
87×	`associate-/l/_binary64_2071`
85×	`associate-+r+_binary64_2056`
79×	`distribute-rgt-out_binary64_2077`
76×	`associate-/r/_binary64_2070`
71×	`div-sub_binary64_2129`
67×	`distribute-lft-neg-out_binary64_2083`
65×	`exp-prod_binary64_2176` `+-commutative_binary64_2054`
63×	`distribute-rgt-neg-out_binary64_2084` `associate-*r/_binary64_2066`
61×	`distribute-rgt-neg-in_binary64_2082`
55×	`pow-sqr_binary64_2097`
53×	`associate-+l-_binary64_2059`
52×	`distribute-lft-neg-in_binary64_2081`
46×	`*-lft-identity_binary64_2113`
44×	`*-rgt-identity_binary64_2114`
38×	`mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `distribute-lft-out_binary64_2075`
37×	`sub0-neg_binary64_2111`
36×	`associate-+r-_binary64_2058`
30×	`swap-sqr_binary64_2091`
28×	`log-prod_binary64_2210` `/-rgt-identity_binary64_2115`
26×	`exp-sum_binary64_2170`
25×	`cancel-sign-sub_binary64_2089`
23×	`cube-prod_binary64_2152` `associate--r+_binary64_2060`
20×	`distribute-rgt-out--_binary64_2078`
19×	`+-rgt-identity_binary64_2109`
16×	`difference-of-squares_binary64_2093`
15×	`distribute-neg-in_binary64_2085`
13×	`exp-diff_binary64_2172` `distribute-neg-frac_binary64_2088` `distribute-rgt1-in_binary64_2080`
11×	`cube-unmult_binary64_2161`
9×	`--rgt-identity_binary64_2110`
8×	`unpow3_binary64_2190` `pow-plus_binary64_2187` `difference-of-sqr-1_binary64_2094`
7×	`log-div_binary64_2211` `cube-div_binary64_2153` `rem-sqrt-square_binary64_2137`
6×	`remove-double-neg_binary64_2112`
5×	`pow-base-1_binary64_2184` `cube-mult_binary64_2154` `sqr-neg_binary64_2138` `mul-1-neg_binary64_2116` `distribute-lft-out--_binary64_2076` `associate--l+_binary64_2061`
4×	`div0_binary64_2105` `difference-of-sqr--1_binary64_2095`
3×	`count-2_binary64_2072`
2×	`log-rec_binary64_2212` `rem-square-sqrt_binary64_2136` `+-lft-identity_binary64_2108` `distribute-neg-out_binary64_2086` `associate--r-_binary64_2063`
1×	`log-pow_binary64_2213` `unpow1/2_binary64_2188` `div-exp_binary64_2175` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `cube-neg_binary64_2151` `rem-3cbrt-lft_binary64_2149` `rem-cbrt-cube_binary64_2148` `*-inverses_binary64_2104` `rgt-mult-inverse_binary64_2101` `remove-double-div_binary64_2100`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2387` `erf-erfc_binary64_2386` `erf-odd_binary64_2385` `if-if-and-not_binary64_2384` `if-if-and_binary64_2383` `if-if-or-not_binary64_2382` `if-if-or_binary64_2381` `if-not_binary64_2380` `if-same_binary64_2379` `if-false_binary64_2378` `if-true_binary64_2377` `not-gte_binary64_2376` `not-lte_binary64_2375` `not-gt_binary64_2374` `not-lt_binary64_2373` `gte-same_binary64_2372` `lte-same_binary64_2371` `gt-same_binary64_2370` `lt-same_binary64_2369` `sinh---cosh_binary64_2316` `sinh-+-cosh_binary64_2315` `sinh-cosh_binary64_2314` `tanh-def-c_binary64_2313` `tanh-def-b_binary64_2312` `tanh-def-a_binary64_2311` `cosh-def_binary64_2310` `sinh-def_binary64_2309` `tan-neg_binary64_2256` `cos-neg_binary64_2255` `sin-neg_binary64_2254` `tan-0_binary64_2253` `cos-0_binary64_2252` `sin-0_binary64_2251` `hang-m-tan_binary64_2250` `hang-p-tan_binary64_2249` `hang-m0-tan_binary64_2248` `hang-p0-tan_binary64_2247` `hang-0m-tan_binary64_2246` `hang-0p-tan_binary64_2245` `tan-+PI/2_binary64_2244` `tan-+PI_binary64_2243` `tan-PI_binary64_2242` `tan-PI/3_binary64_2241` `tan-PI/4_binary64_2240` `tan-PI/6_binary64_2239` `cos-+PI/2_binary64_2238` `cos-+PI_binary64_2237` `cos-PI_binary64_2236` `cos-PI/2_binary64_2235` `cos-PI/3_binary64_2234` `cos-PI/4_binary64_2233` `cos-PI/6_binary64_2232` `sin-+PI/2_binary64_2231` `sin-+PI_binary64_2230` `sin-PI_binary64_2229` `sin-PI/2_binary64_2228` `sin-PI/3_binary64_2227` `sin-PI/4_binary64_2226` `sin-PI/6_binary64_2225` `sub-1-sin_binary64_2224` `sub-1-cos_binary64_2223` `-1-add-sin_binary64_2222` `-1-add-cos_binary64_2221` `1-sub-sin_binary64_2220` `1-sub-cos_binary64_2219` `cos-sin-sum_binary64_2218` `log-E_binary64_2214` `pow-base-0_binary64_2208` `unpow1/3_binary64_2191` `unpow2_binary64_2189` `exp-to-pow_binary64_2186` `unpow0_binary64_2183` `unpow1_binary64_2182` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-lft-sqr_binary64_2179` `exp-cbrt_binary64_2178` `exp-sqrt_binary64_2177` `rec-exp_binary64_2174` `prod-exp_binary64_2173` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `rem-log-exp_binary64_2165` `rem-exp-log_binary64_2164` `rem-3cbrt-rft_binary64_2150` `rem-cube-cbrt_binary64_2147` `sqr-abs_binary64_2139` `+-inverses_binary64_2103` `lft-mult-inverse_binary64_2102` `distribute-frac-neg_binary64_2087` `distribute-lft1-in_binary64_2079` `associate--l-_binary64_2062`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	120	1444
1	243	1377
2	494	1377
3	1426	1374
4	3285	1353

Details

analyze2.0ms (0%)

sample37.0ms (0%)

simplify105.0ms (0.1%)

prune7.0ms (0%)

localize7.0ms (0%)

rewrite116.0ms (0.2%)

series166.0ms (0.2%)

simplify1.3min (99.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	33	15
4	41	15
5	51	15
6	66	15
7	103	15
8	101	15
9	100	15
10	95	15
11	96	15
12	97	15
13	98	15
14	99	15
15	101	15
16	101	15

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	33	15
4	41	15
5	51	15
6	66	15
7	103	15
8	101	15
9	100	15
10	95	15
11	96	15
12	97	15
13	98	15
14	99	15
15	101	15
16	101	15

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	33	15
4	41	15
5	51	15
6	66	15
7	103	15
8	101	15
9	100	15
10	95	15
11	96	15
12	97	15
13	98	15
14	99	15
15	101	15
16	101	15