Details

analyze432.0ms (5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample38.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	204×	body	128	valid
8.0ms	19×	body	2048	valid
5.0ms	15×	body	4096	valid
2.0ms	10×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64_2055`
2×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `+-commutative_binary64_2054`
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` `1-exp_binary64_2168` `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` `neg-mul-1_binary64_2120` `neg-sub0_binary64_2119` `unsub-neg_binary64_2118` `sub-neg_binary64_2117` `mul-1-neg_binary64_2116` `/-rgt-identity_binary64_2115` `-rgt-identity_binary64_2114` `-lft-identity_binary64_2113` `remove-double-neg_binary64_2112` `sub0-neg_binary64_2111` `--rgt-identity_binary64_2110` `+-rgt-identity_binary64_2109` `+-lft-identity_binary64_2108` `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-inv_binary64_2090` `cancel-sign-sub_binary64_2089` `distribute-neg-frac_binary64_2088` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-neg-in_binary64_2085` `distribute-rgt-neg-out_binary64_2084` `distribute-lft-neg-out_binary64_2083` `distribute-rgt-neg-in_binary64_2082` `distribute-lft-neg-in_binary64_2081` `distribute-rgt1-in_binary64_2080` `distribute-lft1-in_binary64_2079` `distribute-rgt-out--_binary64_2078` `distribute-rgt-out_binary64_2077` `distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075` `count-2_binary64_2072` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `associate-l_binary64_2065` `associate-r*_binary64_2064` `associate--r-_binary64_2063` `associate--l-_binary64_2062` `associate--l+_binary64_2061` `associate--r+_binary64_2060` `associate-+l-_binary64_2059` `associate-+r-_binary64_2058` `associate-+l+_binary64_2057` `associate-+r+_binary64_2056`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	23	23
2	25	23

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

35.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
28.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite65.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

35.7b

Rules

8×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
7×	`*-un-lft-identity_binary64_2124`
6×	`add-sqr-sqrt_binary64_2146`
5×	`add-cube-cbrt_binary64_2159`
4×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `flip3-+_binary64_2127` `sqrt-div_binary64_2141` `flip-+_binary64_2098` `sqrt-prod_binary64_2140`
3×	`sqrt-pow1_binary64_2142`
2×	`pow1/2_binary64_2204` `associate-*r/_binary64_2066` `sum-log_binary64_2215` `+-commutative_binary64_2054`
1×	`rem-sqrt-square_binary64_2137` `pow-prod-down_binary64_2195` `distribute-lft-out_binary64_2075`

Counts

4 → 51

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1296 to 455 computations (64.9% saved)

series269.0ms (3.1%)

Error

7.3b

Counts

4 → 65

Calls

4 calls:

64.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
61.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
54.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
42.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2734 to 2349 computations (14.1% saved)

simplify255.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

495×	`associate-r_binary64_2064`
472×	`associate-l_binary64_2065`
236×	`sub-neg_binary64_2117`
225×	`cancel-sign-sub-inv_binary64_2090`
188×	`*-commutative_binary64_2055`
144×	`distribute-rgt-in_binary64_2074`
142×	`sqr-pow_binary64_2096`
119×	`associate-/r*_binary64_2068`
117×	`distribute-rgt-neg-in_binary64_2082`
116×	`neg-sub0_binary64_2119` `distribute-lft-in_binary64_2073` `associate-/l*_binary64_2069` `associate-+l+_binary64_2057`
104×	`neg-mul-1_binary64_2120`
98×	`+-commutative_binary64_2054`
95×	`unswap-sqr_binary64_2092`
93×	`times-frac_binary64_2130` `pow-sqr_binary64_2097`
91×	`distribute-lft-neg-in_binary64_2081`
89×	`associate-+r+_binary64_2056`
68×	`associate-*l/_binary64_2067`
64×	`associate-*r/_binary64_2066`
58×	`associate-+l-_binary64_2059`
54×	`associate--l+_binary64_2061`
53×	`difference-of-squares_binary64_2093`
50×	`pow-plus_binary64_2187`
49×	`associate-+r-_binary64_2058`
40×	`+-rgt-identity_binary64_2109`
39×	`unsub-neg_binary64_2118`
38×	`distribute-neg-frac_binary64_2088`
30×	`div-sub_binary64_2129`
27×	`distribute-lft-neg-out_binary64_2083`
25×	`associate-/r/_binary64_2070`
24×	`sub0-neg_binary64_2111`
21×	`cube-unmult_binary64_2161`
18×	`distribute-rgt-out_binary64_2077` `associate-/l/_binary64_2071` `associate--r+_binary64_2060`
17×	`exp-prod_binary64_2176`
12×	`cube-prod_binary64_2152`
11×	`distribute-lft-out_binary64_2075`
10×	`distribute-rgt-out--_binary64_2078`
9×	`unpow3_binary64_2190` `mul-1-neg_binary64_2116`
7×	`rem-sqrt-square_binary64_2137`
6×	`distribute-neg-in_binary64_2085`
5×	`cube-mult_binary64_2154`
4×	`exp-sum_binary64_2170` `distribute-rgt-neg-out_binary64_2084` `distribute-lft-out--_binary64_2076`
3×	`unpow2_binary64_2189` `unpow1_binary64_2182` `rem-square-sqrt_binary64_2136`
2×	`prod-exp_binary64_2173` `exp-diff_binary64_2172` `-rgt-identity_binary64_2114` `-inverses_binary64_2104` `+-inverses_binary64_2103` `count-2_binary64_2072`
1×	`log-prod_binary64_2210` `1-exp_binary64_2168` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `rgt-mult-inverse_binary64_2101` `distribute-rgt1-in_binary64_2080`
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` `pow-base-0_binary64_2208` `unpow1/3_binary64_2191` `unpow1/2_binary64_2188` `exp-to-pow_binary64_2186` `pow-base-1_binary64_2184` `unpow0_binary64_2183` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-lft-sqr_binary64_2179` `exp-cbrt_binary64_2178` `exp-sqrt_binary64_2177` `div-exp_binary64_2175` `rec-exp_binary64_2174` `exp-neg_binary64_2171` `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-div_binary64_2153` `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` `/-rgt-identity_binary64_2115` `*-lft-identity_binary64_2113` `remove-double-neg_binary64_2112` `--rgt-identity_binary64_2110` `+-lft-identity_binary64_2108` `div0_binary64_2105` `lft-mult-inverse_binary64_2102` `remove-double-div_binary64_2100` `difference-of-sqr--1_binary64_2095` `difference-of-sqr-1_binary64_2094` `swap-sqr_binary64_2091` `cancel-sign-sub_binary64_2089` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-lft1-in_binary64_2079` `associate--r-_binary64_2063` `associate--l-_binary64_2062`

Counts

116 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2197
1	476	2108
2	1499	2062
3	4315	2059

prune161.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	190	9	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	9	200

Error

4.9b

Counts

200 → 9

Compiler

Compiled 5230 to 2862 computations (45.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
28.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

20×	`add-sqr-sqrt_binary64_2146`
18×	`sqrt-prod_binary64_2140`
14×	`*-un-lft-identity_binary64_2124`
10×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
7×	`associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `sqrt-div_binary64_2141` `associate-l_binary64_2065`
4×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `unswap-sqr_binary64_2092`
3×	`pow-prod-down_binary64_2195`
2×	`rem-sqrt-square_binary64_2137` `associate-*r/_binary64_2066` `distribute-lft-out_binary64_2075`
1×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `sqrt-unprod_binary64_2144` `*-commutative_binary64_2055` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 75

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
5.0ms	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
3.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2015 to 692 computations (65.7% saved)

series268.0ms (3.1%)

Error

4.9b

Counts

4 → 54

Calls

4 calls:

67.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
63.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
57.0ms	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
44.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2652 to 2317 computations (12.6% saved)

simplify326.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

527×	`times-frac_binary64_2130`
277×	`cancel-sign-sub-inv_binary64_2090`
258×	`associate-/r*_binary64_2068`
246×	`associate-/l*_binary64_2069`
204×	`associate-*l/_binary64_2067`
195×	`associate-r_binary64_2064`
177×	`associate-l_binary64_2065`
173×	`distribute-rgt-neg-in_binary64_2082`
144×	`associate-*r/_binary64_2066`
138×	`distribute-lft-neg-in_binary64_2081`
133×	`distribute-rgt-in_binary64_2074`
108×	`distribute-lft-in_binary64_2073`
103×	`*-commutative_binary64_2055`
98×	`unswap-sqr_binary64_2092`
93×	`+-commutative_binary64_2054`
92×	`associate-+l+_binary64_2057`
89×	`sub-neg_binary64_2117`
80×	`sqr-pow_binary64_2096`
68×	`associate-/l/_binary64_2071` `associate-/r/_binary64_2070`
66×	`associate-+r+_binary64_2056`
57×	`neg-sub0_binary64_2119`
55×	`exp-prod_binary64_2176` `distribute-neg-frac_binary64_2088`
51×	`neg-mul-1_binary64_2120`
48×	`associate--l+_binary64_2061` `associate-+r-_binary64_2058`
46×	`associate-+l-_binary64_2059`
44×	`pow-plus_binary64_2187` `pow-sqr_binary64_2097`
35×	`log-prod_binary64_2210` `cube-div_binary64_2153`
31×	`distribute-lft-neg-out_binary64_2083`
26×	`log-div_binary64_2211`
21×	`unsub-neg_binary64_2118`
20×	`*-lft-identity_binary64_2113` `associate--r+_binary64_2060`
19×	`distribute-rgt-out_binary64_2077`
17×	`*-rgt-identity_binary64_2114`
16×	`difference-of-squares_binary64_2093`
15×	`cube-prod_binary64_2152`
14×	`unpow3_binary64_2190`
13×	`exp-sqrt_binary64_2177`
11×	`cube-unmult_binary64_2161` `distribute-rgt-out--_binary64_2078` `distribute-lft-out_binary64_2075`
10×	`distribute-neg-in_binary64_2085`
8×	`cube-mult_binary64_2154` `mul-1-neg_binary64_2116` `/-rgt-identity_binary64_2115`
7×	`rem-sqrt-square_binary64_2137`
5×	`log-pow_binary64_2213` `swap-sqr_binary64_2091`
4×	`distribute-lft-out--_binary64_2076`
3×	`unpow2_binary64_2189` `unpow1_binary64_2182` `exp-lft-sqr_binary64_2179` `exp-diff_binary64_2172` `rem-square-sqrt_binary64_2136`
2×	`log-rec_binary64_2212` `pow-base-1_binary64_2184` `prod-exp_binary64_2173` `+-rgt-identity_binary64_2109` `*-inverses_binary64_2104` `distribute-rgt-neg-out_binary64_2084` `count-2_binary64_2072`
1×	`exp-sum_binary64_2170` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `rem-log-exp_binary64_2165` `+-inverses_binary64_2103` `distribute-lft1-in_binary64_2079`
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` `unpow1/2_binary64_2188` `exp-to-pow_binary64_2186` `unpow0_binary64_2183` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-cbrt_binary64_2178` `div-exp_binary64_2175` `rec-exp_binary64_2174` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `rem-exp-log_binary64_2164` `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` `div-sub_binary64_2129` `remove-double-neg_binary64_2112` `sub0-neg_binary64_2111` `--rgt-identity_binary64_2110` `+-lft-identity_binary64_2108` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `div0_binary64_2105` `lft-mult-inverse_binary64_2102` `rgt-mult-inverse_binary64_2101` `remove-double-div_binary64_2100` `difference-of-sqr--1_binary64_2095` `difference-of-sqr-1_binary64_2094` `cancel-sign-sub_binary64_2089` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-rgt1-in_binary64_2080` `associate--r-_binary64_2063` `associate--l-_binary64_2062`

Counts

129 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2729
1	540	2649
2	1929	2595
3	4810	2595

prune134.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	161	9	170

Error

4.7b

Counts

170 → 9

Compiler

Compiled 4508 to 2777 computations (38.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.9b	(sqrt.f64 (.f64 2 (.f64 im im)))

rewrite111.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

51×	`add-sqr-sqrt_binary64_2146`
50×	`sqrt-prod_binary64_2140`
38×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
26×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
11×	`pow1_binary64_2185`
9×	`associate-/r*_binary64_2068`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `distribute-lft-out--_binary64_2076`
4×	`sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `associate-/l*_binary64_2069`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090`
2×	`pow1/2_binary64_2204` `flip3--_binary64_2128` `flip--_binary64_2099` `associate-/r/_binary64_2070`
1×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `sqrt-undiv_binary64_2145` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`

Counts

4 → 108

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3656 to 1176 computations (67.8% saved)

series277.0ms (3.2%)

Error

1.5b

Counts

4 → 57

Calls

4 calls:

87.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
69.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
64.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
13.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 3087 to 2435 computations (21.1% saved)

simplify414.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

487×	`times-frac_binary64_2130`
371×	`associate-/l*_binary64_2069`
303×	`associate-/r*_binary64_2068`
238×	`cancel-sign-sub-inv_binary64_2090`
190×	`associate-*l/_binary64_2067`
156×	`associate-*r/_binary64_2066`
147×	`associate-/l/_binary64_2071`
135×	`associate-/r/_binary64_2070`
130×	`distribute-rgt-neg-in_binary64_2082`
123×	`sub-neg_binary64_2117`
104×	`distribute-lft-neg-in_binary64_2081`
98×	`distribute-rgt-in_binary64_2074` `associate-r_binary64_2064`
82×	`associate-l_binary64_2065`
81×	`*-commutative_binary64_2055`
79×	`associate-+l-_binary64_2059`
77×	`distribute-lft-in_binary64_2073`
70×	`sqr-pow_binary64_2096`
66×	`unswap-sqr_binary64_2092`
65×	`neg-sub0_binary64_2119`
63×	`distribute-lft-neg-out_binary64_2083`
61×	`neg-mul-1_binary64_2120`
59×	`associate--l+_binary64_2061`
58×	`+-commutative_binary64_2054`
51×	`distribute-neg-frac_binary64_2088`
41×	`associate--r+_binary64_2060`
40×	`pow-sqr_binary64_2097`
27×	`unsub-neg_binary64_2118`
24×	`associate-+l+_binary64_2057`
23×	`distribute-rgt-neg-out_binary64_2084`
21×	`distribute-neg-in_binary64_2085`
20×	`difference-of-squares_binary64_2093`
19×	`pow-plus_binary64_2187`
18×	`exp-prod_binary64_2176` `*-rgt-identity_binary64_2114`
15×	`div-sub_binary64_2129`
13×	`distribute-rgt-out_binary64_2077`
12×	`cube-prod_binary64_2152`
11×	`associate-+r+_binary64_2056`
10×	`div-exp_binary64_2175` `rem-sqrt-square_binary64_2137` `associate-+r-_binary64_2058`
9×	`prod-exp_binary64_2173` `distribute-lft-out_binary64_2075`
8×	`cube-unmult_binary64_2161` `distribute-rgt-out--_binary64_2078`
7×	`unpow3_binary64_2190` `+-rgt-identity_binary64_2109`
6×	`mul-1-neg_binary64_2116` `/-rgt-identity_binary64_2115` `associate--l-_binary64_2062`
5×	`log-div_binary64_2211` `cube-mult_binary64_2154` `rem-square-sqrt_binary64_2136` `swap-sqr_binary64_2091`
4×	`distribute-lft-out--_binary64_2076`
3×	`log-prod_binary64_2210` `unpow2_binary64_2189` `unpow1_binary64_2182` `rec-exp_binary64_2174` `exp-sum_binary64_2170` `cancel-sign-sub_binary64_2089`
2×	`exp-diff_binary64_2172` `cube-div_binary64_2153` `*-lft-identity_binary64_2113` `sub0-neg_binary64_2111` `count-2_binary64_2072` `associate--r-_binary64_2063`
1×	`log-rec_binary64_2212` `1-exp_binary64_2168` `rem-log-exp_binary64_2165` `rem-3cbrt-lft_binary64_2149` `*-inverses_binary64_2104` `+-inverses_binary64_2103` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-rgt1-in_binary64_2080`
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` `pow-base-0_binary64_2208` `unpow1/3_binary64_2191` `unpow1/2_binary64_2188` `exp-to-pow_binary64_2186` `pow-base-1_binary64_2184` `unpow0_binary64_2183` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-lft-sqr_binary64_2179` `exp-cbrt_binary64_2178` `exp-sqrt_binary64_2177` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-1-e_binary64_2167` `exp-0_binary64_2166` `rem-exp-log_binary64_2164` `cube-neg_binary64_2151` `rem-3cbrt-rft_binary64_2150` `rem-cbrt-cube_binary64_2148` `rem-cube-cbrt_binary64_2147` `sqr-abs_binary64_2139` `sqr-neg_binary64_2138` `remove-double-neg_binary64_2112` `--rgt-identity_binary64_2110` `+-lft-identity_binary64_2108` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `div0_binary64_2105` `lft-mult-inverse_binary64_2102` `rgt-mult-inverse_binary64_2101` `remove-double-div_binary64_2100` `difference-of-sqr--1_binary64_2095` `difference-of-sqr-1_binary64_2094` `distribute-lft1-in_binary64_2079`

Counts

165 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	4901
1	607	4730
2	1809	4678

prune304.0ms (3.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	324	3	327
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	325	11	336

Error

1.5b

Counts

336 → 11

Compiler

Compiled 11530 to 5149 computations (55.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (sqrt.f64 2) (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.4b	(*.f64 (sqrt.f64 2) (fabs.f64 im))
28.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite94.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

30×	`add-sqr-sqrt_binary64_2146`
22×	`sqrt-prod_binary64_2140`
19×	`*-un-lft-identity_binary64_2124`
13×	`add-cube-cbrt_binary64_2159`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`times-frac_binary64_2130` `associate-/r*_binary64_2068`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `difference-of-squares_binary64_2093`
4×	`sqrt-div_binary64_2141`
3×	`associate-r_binary64_2064` `cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076`
2×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `flip3--_binary64_2128` `flip--_binary64_2099` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137` `pow-prod-down_binary64_2195` `-commutative_binary64_2055` `diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/l_binary64_2069`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 (.f64 (sqrt.f64 2) (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(*.f64 (sqrt.f64 2) (fabs.f64 im))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2639 to 894 computations (66.1% saved)

series240.0ms (2.8%)

Error

0.4b

Counts

4 → 55

Calls

4 calls:

67.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
65.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
52.0ms	(/.f64 (.f64 (sqrt.f64 2) (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
12.0ms	(*.f64 (sqrt.f64 2) (fabs.f64 im))

Compiler

Compiled 2949 to 2343 computations (20.5% saved)

simplify342.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64_2068`
451×	`associate-*l/_binary64_2067`
413×	`associate-/r/_binary64_2070`
371×	`associate-/l/_binary64_2071`
211×	`cancel-sign-sub-inv_binary64_2090`
162×	`associate-r_binary64_2064`
148×	`associate-l_binary64_2065`
127×	`distribute-rgt-neg-in_binary64_2082`
122×	`associate-/l*_binary64_2069`
119×	`sub-neg_binary64_2117`
102×	`distribute-lft-neg-in_binary64_2081`
100×	`unswap-sqr_binary64_2092`
99×	`distribute-rgt-in_binary64_2074`
88×	`*-commutative_binary64_2055`
82×	`sqr-pow_binary64_2096`
80×	`distribute-lft-in_binary64_2073`
74×	`times-frac_binary64_2130`
58×	`neg-sub0_binary64_2119`
55×	`distribute-lft-neg-out_binary64_2083` `+-commutative_binary64_2054`
54×	`neg-mul-1_binary64_2120`
53×	`distribute-neg-frac_binary64_2088`
44×	`pow-sqr_binary64_2097`
36×	`difference-of-squares_binary64_2093`
31×	`associate-*r/_binary64_2066`
30×	`div-sub_binary64_2129`
29×	`exp-prod_binary64_2176` `*-rgt-identity_binary64_2114`
28×	`associate--l+_binary64_2061`
27×	`log-div_binary64_2211`
25×	`unsub-neg_binary64_2118` `associate--r+_binary64_2060`
24×	`distribute-rgt-neg-out_binary64_2084` `associate-+l+_binary64_2057`
21×	`cube-prod_binary64_2152`
20×	`pow-plus_binary64_2187`
19×	`cube-div_binary64_2153` `/-rgt-identity_binary64_2115` `distribute-neg-in_binary64_2085`
15×	`log-prod_binary64_2210`
13×	`*-lft-identity_binary64_2113` `distribute-rgt-out_binary64_2077`
11×	`associate-+r+_binary64_2056`
10×	`associate-+r-_binary64_2058`
9×	`cube-unmult_binary64_2161` `swap-sqr_binary64_2091` `distribute-rgt-out--_binary64_2078`
8×	`rem-sqrt-square_binary64_2137`
7×	`unpow3_binary64_2190` `mul-1-neg_binary64_2116` `+-rgt-identity_binary64_2109` `distribute-lft-out_binary64_2075`
5×	`cube-mult_binary64_2154` `distribute-lft-out--_binary64_2076`
4×	`log-rec_binary64_2212` `rem-square-sqrt_binary64_2136`
3×	`unpow2_binary64_2189` `unpow1_binary64_2182` `exp-sum_binary64_2170` `*-inverses_binary64_2104` `cancel-sign-sub_binary64_2089` `associate-+l-_binary64_2059`
2×	`div-exp_binary64_2175` `exp-diff_binary64_2172` `sub0-neg_binary64_2111` `distribute-frac-neg_binary64_2087` `count-2_binary64_2072`
1×	`exp-sqrt_binary64_2177` `rec-exp_binary64_2174` `prod-exp_binary64_2173` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `rem-log-exp_binary64_2165` `rem-3cbrt-lft_binary64_2149` `sqr-abs_binary64_2139` `+-inverses_binary64_2103` `distribute-neg-out_binary64_2086` `distribute-rgt1-in_binary64_2080` `distribute-lft1-in_binary64_2079`
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` `pow-base-0_binary64_2208` `unpow1/3_binary64_2191` `unpow1/2_binary64_2188` `exp-to-pow_binary64_2186` `pow-base-1_binary64_2184` `unpow0_binary64_2183` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-lft-sqr_binary64_2179` `exp-cbrt_binary64_2178` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `rem-exp-log_binary64_2164` `cube-neg_binary64_2151` `rem-3cbrt-rft_binary64_2150` `rem-cbrt-cube_binary64_2148` `rem-cube-cbrt_binary64_2147` `sqr-neg_binary64_2138` `remove-double-neg_binary64_2112` `--rgt-identity_binary64_2110` `+-lft-identity_binary64_2108` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `div0_binary64_2105` `lft-mult-inverse_binary64_2102` `rgt-mult-inverse_binary64_2101` `remove-double-div_binary64_2100` `difference-of-sqr--1_binary64_2095` `difference-of-sqr-1_binary64_2094` `associate--r-_binary64_2063` `associate--l-_binary64_2062`

Counts

144 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3368
1	624	3160
2	2226	3113

prune188.0ms (2.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	229	5	234
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	232	13	245

Error

0.4b

Counts

245 → 13

Compiler

Compiled 6950 to 3421 computations (50.8% saved)

regimes1.8s (20.8%)

Accuracy

Total 17.6b remaining (98.8%)

Threshold costs 0b (0%)

Compiler

Compiled 18350 to 13080 computations (28.7% saved)

bsearch97.0ms (1.1%)

Steps

Iters	Range		Point
8	2.1156893573738586e+131	1.1424125478528636e+134	5.269431306839334e+131
7	4.2006160234821056e-219	5.8950658576936505e-217	1.0165515961308099e-218
9	-8.607074320350157e-281	-3.069974748620384e-288	-3.7129649888112956e-283
6	-2.7270574680747332e+127	-3.477530920783191e+126	-7.202903839708791e+126

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64_2055`
13×	`+-commutative_binary64_2054`
10×	`sub-neg_binary64_2117`
8×	`neg-mul-1_binary64_2120` `neg-sub0_binary64_2119`
3×	`unsub-neg_binary64_2118`
2×	`distribute-neg-in_binary64_2085` `distribute-rgt-neg-in_binary64_2082` `distribute-lft-neg-in_binary64_2081`
1×	`distribute-neg-frac_binary64_2088` `distribute-neg-out_binary64_2086`
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` `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` `tan-0_binary64_2253` `cos-0_binary64_2252` `sin-0_binary64_2251` `unpow1_binary64_2182` `e-exp-1_binary64_2169` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `exp-0_binary64_2166` `sqr-abs_binary64_2139` `sqr-neg_binary64_2138` `mul-1-neg_binary64_2116` `/-rgt-identity_binary64_2115` `-rgt-identity_binary64_2114` `-lft-identity_binary64_2113` `remove-double-neg_binary64_2112` `sub0-neg_binary64_2111` `--rgt-identity_binary64_2110` `+-rgt-identity_binary64_2109` `+-lft-identity_binary64_2108` `cancel-sign-sub-inv_binary64_2090` `cancel-sign-sub_binary64_2089` `distribute-frac-neg_binary64_2087` `distribute-rgt-neg-out_binary64_2084` `distribute-lft-neg-out_binary64_2083`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	145
1	81	143
2	100	143
3	115	143
4	125	143
5	130	143
6	131	143

Proof

(if real (<= f64 h0 -7202903839708791454515804731480427612697800613685522411864547062448064380545122088651033242300552505006115190744660318791663616) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (neg f64 h0) h0)))) (if real (<= f64 h0 -7770456921274543/20927902484106783612273926739453160362527437728623703270385749772858418967283908642445280836244059729054583455420959898929436431361178008664032378075583153913934702685203576143400536338012443636480379262017668896452308479037888217888995203019681763505021868120481527671211777014946532005541417320448) (* f64 1/2 (/ f64 (* f64 (sqrt f64 (sqrt f64 2)) (=> (* f64 (sqrt f64 (sqrt f64 2)) (fabs f64 h1)))) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 4040229746560629/397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 (neg f64 (+ f64 (* f64 1/2 (/ f64 (pow f64 h0 2) h1)) h1)) h0)))) (if real (<= f64 h0 526943130683933404140511674407486271206865862546582166602289282604173309459688309700453239666867942764432737980502176033213987684352) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0))))))))
*-commutative_binary64_2055 =>
(if real (<= f64 h0 -7202903839708791454515804731480427612697800613685522411864547062448064380545122088651033242300552505006115190744660318791663616) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (neg f64 h0) h0)))) (if real (<= f64 h0 -7770456921274543/20927902484106783612273926739453160362527437728623703270385749772858418967283908642445280836244059729054583455420959898929436431361178008664032378075583153913934702685203576143400536338012443636480379262017668896452308479037888217888995203019681763505021868120481527671211777014946532005541417320448) (* f64 1/2 (/ f64 (* f64 (sqrt f64 (sqrt f64 2)) (* f64 (fabs f64 h1) (sqrt f64 (sqrt f64 2)))) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 4040229746560629/397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 (neg f64 (+ f64 (* f64 1/2 (/ f64 (pow f64 h0 2) h1)) h1)) h0)))) (if real (<= f64 h0 526943130683933404140511674407486271206865862546582166602289282604173309459688309700453239666867942764432737980502176033213987684352) (* f64 1/2 (sqrt f64 (* f64 2 (=> (+ f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0))))))))
+-commutative_binary64_2054 =>
(if real (<= f64 h0 -7202903839708791454515804731480427612697800613685522411864547062448064380545122088651033242300552505006115190744660318791663616) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (neg f64 h0) h0)))) (if real (<= f64 h0 -7770456921274543/20927902484106783612273926739453160362527437728623703270385749772858418967283908642445280836244059729054583455420959898929436431361178008664032378075583153913934702685203576143400536338012443636480379262017668896452308479037888217888995203019681763505021868120481527671211777014946532005541417320448) (* f64 1/2 (/ f64 (* f64 (sqrt f64 (sqrt f64 2)) (* f64 (fabs f64 h1) (sqrt f64 (sqrt f64 2)))) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 4040229746560629/397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136) (* f64 1/2 (sqrt f64 (* f64 2 (=> (+ f64 (neg f64 (+ f64 (* f64 1/2 (/ f64 (pow f64 h0 2) h1)) h1)) h0))))) (if real (<= f64 h0 526943130683933404140511674407486271206865862546582166602289282604173309459688309700453239666867942764432737980502176033213987684352) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0))))))))
+-commutative_binary64_2054 =>
(if real (<= f64 h0 -7202903839708791454515804731480427612697800613685522411864547062448064380545122088651033242300552505006115190744660318791663616) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (neg f64 h0) h0)))) (if real (<= f64 h0 -7770456921274543/20927902484106783612273926739453160362527437728623703270385749772858418967283908642445280836244059729054583455420959898929436431361178008664032378075583153913934702685203576143400536338012443636480379262017668896452308479037888217888995203019681763505021868120481527671211777014946532005541417320448) (* f64 1/2 (/ f64 (* f64 (sqrt f64 (sqrt f64 2)) (* f64 (fabs f64 h1) (sqrt f64 (sqrt f64 2)))) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 4040229746560629/397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136) (* f64 1/2 (sqrt f64 (* f64 2 (=> (+ f64 h0 (neg f64 (+ f64 (* f64 1/2 (/ f64 (pow f64 h0 2) h1)) h1))))))) (if real (<= f64 h0 526943130683933404140511674407486271206865862546582166602289282604173309459688309700453239666867942764432737980502176033213987684352) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0))))))))
unsub-neg_binary64_2118 =>
(if real (<= f64 h0 -7202903839708791454515804731480427612697800613685522411864547062448064380545122088651033242300552505006115190744660318791663616) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (neg f64 h0) h0)))) (if real (<= f64 h0 -7770456921274543/20927902484106783612273926739453160362527437728623703270385749772858418967283908642445280836244059729054583455420959898929436431361178008664032378075583153913934702685203576143400536338012443636480379262017668896452308479037888217888995203019681763505021868120481527671211777014946532005541417320448) (* f64 1/2 (/ f64 (* f64 (sqrt f64 (sqrt f64 2)) (* f64 (fabs f64 h1) (sqrt f64 (sqrt f64 2)))) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 4040229746560629/397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136) (* f64 1/2 (sqrt f64 (* f64 2 (- f64 h0 (=> (+ f64 (* f64 1/2 (/ f64 (pow f64 h0 2) h1)) h1)))))) (if real (<= f64 h0 526943130683933404140511674407486271206865862546582166602289282604173309459688309700453239666867942764432737980502176033213987684352) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0))))))))
+-commutative_binary64_2054 =>
(if real (<= f64 h0 -7202903839708791454515804731480427612697800613685522411864547062448064380545122088651033242300552505006115190744660318791663616) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (neg f64 h0) h0)))) (if real (<= f64 h0 -7770456921274543/20927902484106783612273926739453160362527437728623703270385749772858418967283908642445280836244059729054583455420959898929436431361178008664032378075583153913934702685203576143400536338012443636480379262017668896452308479037888217888995203019681763505021868120481527671211777014946532005541417320448) (* f64 1/2 (/ f64 (* f64 (sqrt f64 (sqrt f64 2)) (* f64 (fabs f64 h1) (sqrt f64 (sqrt f64 2)))) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 4040229746560629/397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136) (* f64 1/2 (sqrt f64 (* f64 2 (- f64 h0 (+ f64 h1 (* f64 1/2 (/ f64 (pow f64 h0 2) h1))))))) (if real (<= f64 h0 526943130683933404140511674407486271206865862546582166602289282604173309459688309700453239666867942764432737980502176033213987684352) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0))))))))

end0.0ms (0%)

sample2.7s (31.1%)

Algorithm

1×

intervals

Results

390.0ms	6092×	body	128	valid
203.0ms	634×	body	2048	valid
200.0ms	499×	body	4096	valid
107.0ms	409×	body	1024	valid
43.0ms	231×	body	512	valid
19.0ms	135×	body	256	valid

Compiler

Compiled 2558 to 1828 computations (28.5% saved)

Details

analyze432.0ms (5%)

sample38.0ms (0.4%)

simplify42.0ms (0.5%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite65.0ms (0.7%)

series269.0ms (3.1%)

simplify255.0ms (2.9%)

prune161.0ms (1.8%)

localize11.0ms (0.1%)

rewrite71.0ms (0.8%)

series268.0ms (3.1%)

simplify326.0ms (3.7%)

prune134.0ms (1.5%)

localize13.0ms (0.1%)

rewrite111.0ms (1.3%)

series277.0ms (3.2%)

simplify414.0ms (4.7%)

prune304.0ms (3.5%)

localize15.0ms (0.2%)

rewrite94.0ms (1.1%)

series240.0ms (2.8%)

simplify342.0ms (3.9%)

prune188.0ms (2.2%)

regimes1.8s (20.8%)

bsearch97.0ms (1.1%)

simplify20.0ms (0.2%)

end0.0ms (0%)

sample2.7s (31.1%)

Profiling