Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample29.0ms (0.1%)

Algorithm

1×

intervals

Results

6.0ms	181×	body	128	valid
5.0ms	38×	body	1024	valid
4.0ms	256×	pre	128	true
2.0ms	19×	body	512	valid
1.0ms	6×	body	2048	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify3.3s (13.6%)

Algorithm

1×	egg-herbie

Rules

975×	`unsub-neg_binary64_2118`
519×	`associate-/r/_binary64_2070`
401×	`exp-prod_binary64_2176`
334×	`div-sub_binary64_2129`
285×	`sub-neg_binary64_2117`
161×	`neg-mul-1_binary64_2120`
137×	`neg-sub0_binary64_2119`
102×	`distribute-rgt-in_binary64_2074`
91×	`*-commutative_binary64_2055`
87×	`associate-/l*_binary64_2069`
77×	`swap-sqr_binary64_2091`
70×	`distribute-lft-in_binary64_2073`
69×	`exp-diff_binary64_2172`
66×	`remove-double-neg_binary64_2112`
64×	`distribute-rgt-neg-out_binary64_2084`
63×	`distribute-lft-neg-out_binary64_2083`
62×	`distribute-neg-frac_binary64_2088`
59×	`exp-sum_binary64_2170` `distribute-rgt-neg-in_binary64_2082` `associate-+l-_binary64_2059`
58×	`cancel-sign-sub-inv_binary64_2090`
50×	`pow-plus_binary64_2187`
49×	`associate-r_binary64_2064`
45×	`distribute-lft-neg-in_binary64_2081` `distribute-rgt1-in_binary64_2080` `associate--r+_binary64_2060`
44×	`times-frac_binary64_2130`
42×	`div0_binary64_2105` `associate-l_binary64_2065`
40×	`+-commutative_binary64_2054`
39×	`sqr-neg_binary64_2138`
38×	`sub0-neg_binary64_2111`
35×	`distribute-frac-neg_binary64_2087`
33×	`associate--r-_binary64_2063`
32×	`associate-+r-_binary64_2058`
29×	`exp-neg_binary64_2171` `distribute-neg-in_binary64_2085`
26×	`associate--l-_binary64_2062`
25×	`associate-/l/_binary64_2071` `associate--l+_binary64_2061`
24×	`distribute-neg-out_binary64_2086`
21×	`associate-/r*_binary64_2068`
20×	`distribute-rgt-out_binary64_2077`
19×	`*-lft-identity_binary64_2113` `associate-+l+_binary64_2057` `associate-+r+_binary64_2056`
17×	`mul0-lft_binary64_2106`
16×	`mul0-rgt_binary64_2107`
13×	`cube-prod_binary64_2152` `+-rgt-identity_binary64_2109` `pow-sqr_binary64_2097` `sqr-pow_binary64_2096`
12×	`/-rgt-identity_binary64_2115` `associate-*r/_binary64_2066`
10×	`exp-lft-sqr_binary64_2179` `distribute-rgt-out--_binary64_2078`
9×	`-rgt-identity_binary64_2114` `--rgt-identity_binary64_2110` `associate-l/_binary64_2067`
8×	`cube-unmult_binary64_2161` `unswap-sqr_binary64_2092`
7×	`+-lft-identity_binary64_2108`
5×	`cube-div_binary64_2153` `distribute-lft1-in_binary64_2079` `count-2_binary64_2072`
4×	`pow-base-1_binary64_2184` `exp-sqrt_binary64_2177` `rem-sqrt-square_binary64_2137` `distribute-lft-out--_binary64_2076`
3×	`+-inverses_binary64_2103` `distribute-lft-out_binary64_2075`
2×	`cube-neg_binary64_2151` `*-inverses_binary64_2104` `cancel-sign-sub_binary64_2089`
1×	`unpow3_binary64_2190` `prod-exp_binary64_2173` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `mul-1-neg_binary64_2116` `difference-of-sqr--1_binary64_2095`
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` `unpow2_binary64_2189` `unpow1/2_binary64_2188` `exp-to-pow_binary64_2186` `unpow0_binary64_2183` `unpow1_binary64_2182` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-cbrt_binary64_2178` `div-exp_binary64_2175` `rec-exp_binary64_2174` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `rem-log-exp_binary64_2165` `rem-exp-log_binary64_2164` `cube-mult_binary64_2154` `rem-3cbrt-rft_binary64_2150` `rem-3cbrt-lft_binary64_2149` `rem-cbrt-cube_binary64_2148` `rem-cube-cbrt_binary64_2147` `sqr-abs_binary64_2139` `rem-square-sqrt_binary64_2136` `lft-mult-inverse_binary64_2102` `rgt-mult-inverse_binary64_2101` `remove-double-div_binary64_2100` `difference-of-sqr-1_binary64_2094` `difference-of-squares_binary64_2093`

Counts

1 → 3

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	63	19
4	108	19
5	217	19
6	484	19
7	1122	19
8	2559	1
9	73	1

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	0	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Error

18.9b

Counts

4 → 1

Compiler

Compiled 40 to 31 computations (22.5% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.6b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite119.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

18.2b

Rules

58×	`*-un-lft-identity_binary64_2124`
26×	`add-sqr-sqrt_binary64_2146`
25×	`times-frac_binary64_2130`
19×	`distribute-lft-out_binary64_2075`
14×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
5×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-sub_binary64_2129` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070`
1×	`sum-log_binary64_2215` `associate-+l-_binary64_2059` `+-commutative_binary64_2054` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

2 → 65

Calls

2 calls:

18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1500 to 803 computations (46.5% saved)

series653.0ms (2.7%)

Error

0.0b

Counts

2 → 48

Calls

2 calls:

321.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
220.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 3988 to 3205 computations (19.6% saved)

simplify664.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

506×	`cancel-sign-sub-inv_binary64_2090`
486×	`distribute-rgt-in_binary64_2074`
424×	`sub-neg_binary64_2117`
412×	`distribute-lft-in_binary64_2073`
176×	`associate-+r+_binary64_2056`
175×	`+-commutative_binary64_2054`
171×	`associate-+l+_binary64_2057`
169×	`times-frac_binary64_2130`
160×	`distribute-neg-in_binary64_2085`
156×	`associate--r+_binary64_2060`
151×	`associate--l+_binary64_2061`
133×	`associate-/r*_binary64_2068`
122×	`associate-/l*_binary64_2069`
79×	`*-commutative_binary64_2055`
69×	`neg-mul-1_binary64_2120` `neg-sub0_binary64_2119` `sqr-pow_binary64_2096`
67×	`distribute-neg-frac_binary64_2088`
57×	`unsub-neg_binary64_2118`
53×	`distribute-rgt-neg-in_binary64_2082`
45×	`associate-r_binary64_2064`
43×	`associate-*l/_binary64_2067`
42×	`div-sub_binary64_2129`
40×	`associate-*r/_binary64_2066`
36×	`distribute-lft-neg-in_binary64_2081` `distribute-rgt-out_binary64_2077`
32×	`associate-/l/_binary64_2071`
31×	`pow-sqr_binary64_2097`
30×	`associate-l_binary64_2065`
22×	`*-rgt-identity_binary64_2114`
21×	`distribute-rgt-out--_binary64_2078`
20×	`distribute-lft-neg-out_binary64_2083`
18×	`associate-/r/_binary64_2070`
17×	`prod-exp_binary64_2173`
16×	`pow-plus_binary64_2187` `div-exp_binary64_2175`
15×	`/-rgt-identity_binary64_2115`
14×	`distribute-rgt1-in_binary64_2080`
11×	`cube-div_binary64_2153`
10×	`cube-prod_binary64_2152`
9×	`log-div_binary64_2211` `unpow3_binary64_2190` `unswap-sqr_binary64_2092`
8×	`log-prod_binary64_2210` `cube-unmult_binary64_2161`
7×	`cube-mult_binary64_2154` `distribute-lft-out_binary64_2075`
6×	`swap-sqr_binary64_2091`
5×	`log-pow_binary64_2213` `unpow2_binary64_2189` `distribute-rgt-neg-out_binary64_2084`
4×	`unpow1_binary64_2182` `exp-prod_binary64_2176` `rec-exp_binary64_2174` `distribute-lft1-in_binary64_2079`
3×	`pow-base-1_binary64_2184` `exp-diff_binary64_2172` `*-lft-identity_binary64_2113` `associate--r-_binary64_2063` `associate-+l-_binary64_2059`
2×	`difference-of-squares_binary64_2093` `associate-+r-_binary64_2058`
1×	`log-rec_binary64_2212` `exp-sqrt_binary64_2177` `exp-sum_binary64_2170` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `rem-log-exp_binary64_2165` `mul-1-neg_binary64_2116` `remove-double-neg_binary64_2112` `*-inverses_binary64_2104` `cancel-sign-sub_binary64_2089` `distribute-lft-out--_binary64_2076` `associate--l-_binary64_2062`
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-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-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` `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_2103` `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-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `count-2_binary64_2072`

Counts

113 → 257

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	4119
1	865	3906
2	3264	3732

prune556.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	255	3	258

Error

0.0b

Counts

258 → 3

Compiler

Compiled 9010 to 5480 computations (39.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
2.0b	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (+.f64 (/.f64 (/.f64 4 alpha) alpha) (.f64 2 (/.f64 beta (/.f64 (*.f64 alpha alpha) beta)))))
4.4b	(/.f64 beta (/.f64 (*.f64 alpha alpha) beta))
9.3b	(/.f64 (*.f64 alpha alpha) beta)

rewrite607.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

65×	`times-frac_binary64_2130`
57×	`add-sqr-sqrt_binary64_2146`
49×	`*-un-lft-identity_binary64_2124`
45×	`add-cube-cbrt_binary64_2159`
29×	`cancel-sign-sub-inv_binary64_2090`
23×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
22×	`frac-add_binary64_2132`
21×	`frac-sub_binary64_2133`
16×	`add-log-exp_binary64_2163`
15×	`associate-*r/_binary64_2066`
14×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
13×	`associate-l_binary64_2065`
10×	`associate-/r*_binary64_2068` `flip3-+_binary64_2127` `flip-+_binary64_2098`
9×	`div-inv_binary64_2121` `flip3--_binary64_2128` `flip--_binary64_2099`
8×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-times_binary64_2134`
6×	`pow1_binary64_2185` `associate-r_binary64_2064`
4×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-/l_binary64_2069` `sum-log_binary64_2215` `diff-log_binary64_2216` `associate-l/_binary64_2067`
3×	`sub-neg_binary64_2117` `difference-of-squares_binary64_2093`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `distribute-lft-out--_binary64_2076` `unswap-sqr_binary64_2092`
1×	`associate-/r/_binary64_2070` `associate--l+_binary64_2061` `associate--r+_binary64_2060` `pow-prod-down_binary64_2195` `*-commutative_binary64_2055`

Counts

4 → 178

Calls

4 calls:

25.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (+.f64 (/.f64 (/.f64 4 alpha) alpha) (.f64 2 (/.f64 beta (/.f64 (*.f64 alpha alpha) beta)))))
14.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
6.0ms	(/.f64 beta (/.f64 (*.f64 alpha alpha) beta))
5.0ms	(/.f64 (*.f64 alpha alpha) beta)

Compiler

Compiled 9268 to 5150 computations (44.4% saved)

series1.1s (4.5%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

648.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (+.f64 (/.f64 (/.f64 4 alpha) alpha) (.f64 2 (/.f64 beta (/.f64 (*.f64 alpha alpha) beta)))))
159.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
122.0ms	(/.f64 beta (/.f64 (*.f64 alpha alpha) beta))
108.0ms	(/.f64 (*.f64 alpha alpha) beta)

Compiler

Compiled 2762 to 2128 computations (23% saved)

simplify709.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

441×	`associate-*l/_binary64_2067`
431×	`distribute-rgt-in_binary64_2074`
420×	`distribute-lft-in_binary64_2073`
170×	`associate-/l*_binary64_2069`
163×	`associate-/r/_binary64_2070`
153×	`*-commutative_binary64_2055`
121×	`associate-/l/_binary64_2071`
117×	`distribute-rgt-neg-in_binary64_2082`
109×	`cancel-sign-sub-inv_binary64_2090`
106×	`times-frac_binary64_2130`
87×	`distribute-lft-neg-out_binary64_2083`
85×	`neg-sub0_binary64_2119`
84×	`neg-mul-1_binary64_2120`
81×	`sub-neg_binary64_2117`
74×	`distribute-lft-neg-in_binary64_2081`
71×	`associate-/r*_binary64_2068`
54×	`associate-l_binary64_2065`
49×	`distribute-neg-in_binary64_2085`
47×	`associate-r_binary64_2064`
45×	`associate-*r/_binary64_2066`
43×	`distribute-rgt-neg-out_binary64_2084`
34×	`distribute-neg-frac_binary64_2088`
30×	`+-commutative_binary64_2054`
28×	`sqr-pow_binary64_2096`
19×	`unswap-sqr_binary64_2092`
14×	`unpow3_binary64_2190`
11×	`cube-div_binary64_2153` `div-sub_binary64_2129`
10×	`log-div_binary64_2211` `cube-mult_binary64_2154`
9×	`/-rgt-identity_binary64_2115` `pow-sqr_binary64_2097`
7×	`exp-prod_binary64_2176` `*-rgt-identity_binary64_2114` `swap-sqr_binary64_2091`
6×	`log-prod_binary64_2210` `div-exp_binary64_2175` `cube-prod_binary64_2152` `difference-of-squares_binary64_2093` `distribute-rgt-out_binary64_2077`
5×	`associate--l+_binary64_2061` `associate--r+_binary64_2060` `associate-+r+_binary64_2056`
4×	`cube-unmult_binary64_2161` `distribute-rgt-out--_binary64_2078`
3×	`*-lft-identity_binary64_2113`
2×	`unpow2_binary64_2189` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `exp-sum_binary64_2170` `rem-3cbrt-lft_binary64_2149` `rem-square-sqrt_binary64_2136` `mul-1-neg_binary64_2116` `associate-+r-_binary64_2058`
1×	`exp-lft-sqr_binary64_2179` `rec-exp_binary64_2174` `1-exp_binary64_2168` `unsub-neg_binary64_2118` `*-inverses_binary64_2104` `distribute-rgt1-in_binary64_2080` `distribute-lft-out_binary64_2075` `count-2_binary64_2072` `associate--r-_binary64_2063` `associate-+l-_binary64_2059` `associate-+l+_binary64_2057`
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` `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` `unpow1_binary64_2182` `unpow-1_binary64_2181` `exp-lft-cube_binary64_2180` `exp-cbrt_binary64_2178` `exp-sqrt_binary64_2177` `exp-diff_binary64_2172` `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-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` `rem-sqrt-square_binary64_2137` `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_2103` `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-lft1-in_binary64_2079` `distribute-lft-out--_binary64_2076` `associate--l-_binary64_2062`

Counts

212 → 608

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	475	8140
1	1624	7732

prune3.3s (13.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	608	0	608
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	608	3	611

Error

0.0b

Counts

611 → 3

Compiler

Compiled 39225 to 21064 computations (46.3% saved)

localize64.0ms (0.3%)

Local error

Found 4 expressions with local error:

15.1b	(/.f64 (pow.f64 alpha 4) (*.f64 beta beta))
16.3b	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
17.9b	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
19.6b	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))

rewrite3.7s (15.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

152×	`times-frac_binary64_2130`
123×	`unpow-prod-down_binary64_2203`
96×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
54×	`add-exp-log_binary64_2162`
41×	`sqr-pow_binary64_2096`
30×	`div-exp_binary64_2175` `cube-prod_binary64_2152`
27×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
18×	`add-cbrt-cube_binary64_2160`
16×	`pow-to-exp_binary64_2193` `pow-exp_binary64_2192`
10×	`unpow3_binary64_2190` `cube-mult_binary64_2154`
6×	`cbrt-undiv_binary64_2158` `prod-exp_binary64_2173`
4×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`
2×	`cbrt-unprod_binary64_2157`

Counts

4 → 282

Calls

4 calls:

9.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
8.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
7.0ms	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))
6.0ms	(/.f64 (pow.f64 alpha 4) (*.f64 beta beta))

Compiler

Compiled 33292 to 21491 computations (35.4% saved)

series1.0s (4.2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

237.0ms	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))
232.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
213.0ms	(/.f64 (pow.f64 alpha 4) (*.f64 beta beta))
203.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

Compiler

Compiled 7848 to 5455 computations (30.5% saved)

simplify513.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

482×	`times-frac_binary64_2130`
397×	`associate-/l*_binary64_2069`
357×	`log-prod_binary64_2210`
284×	`associate-/r*_binary64_2068`
256×	`log-div_binary64_2211`
159×	`associate-/l/_binary64_2071`
112×	`sqr-pow_binary64_2096`
103×	`log-pow_binary64_2213`
99×	`associate-r_binary64_2064`
98×	`distribute-rgt-neg-in_binary64_2082`
96×	`distribute-lft-neg-in_binary64_2081`
93×	`swap-sqr_binary64_2091`
89×	`associate-l_binary64_2065`
83×	`cube-prod_binary64_2152`
80×	`pow-sqr_binary64_2097` `cancel-sign-sub-inv_binary64_2090`
78×	`associate-/r/_binary64_2070`
52×	`associate-*l/_binary64_2067`
43×	`cube-div_binary64_2153`
41×	`unswap-sqr_binary64_2092`
36×	`pow-plus_binary64_2187` `distribute-rgt-in_binary64_2074`
33×	`/-rgt-identity_binary64_2115`
32×	`associate-*r/_binary64_2066` `associate--r+_binary64_2060`
31×	`distribute-lft-in_binary64_2073` `associate-+l+_binary64_2057`
29×	`associate--l+_binary64_2061`
28×	`sub-neg_binary64_2117`
26×	`neg-mul-1_binary64_2120`
24×	`neg-sub0_binary64_2119`
23×	`exp-prod_binary64_2176` `cube-unmult_binary64_2161` `associate-+r+_binary64_2056`
22×	`distribute-neg-frac_binary64_2088`
21×	`rem-sqrt-square_binary64_2137`
17×	`-rgt-identity_binary64_2114` `-commutative_binary64_2055` `+-commutative_binary64_2054`
16×	`div-exp_binary64_2175` `prod-exp_binary64_2173`
14×	`distribute-neg-in_binary64_2085`
12×	`log-rec_binary64_2212` `associate-+l-_binary64_2059`
11×	`unpow3_binary64_2190`
9×	`cube-mult_binary64_2154` `count-2_binary64_2072`
8×	`associate--l-_binary64_2062`
6×	`pow-base-1_binary64_2184`
5×	`div-sub_binary64_2129` `distribute-lft-neg-out_binary64_2083` `associate-+r-_binary64_2058`
4×	`rec-exp_binary64_2174`
3×	`distribute-rgt-neg-out_binary64_2084` `distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075`
2×	`rem-cbrt-cube_binary64_2148` `rem-cube-cbrt_binary64_2147` `rem-square-sqrt_binary64_2136` `*-lft-identity_binary64_2113` `distribute-rgt-out_binary64_2077`
1×	`unpow2_binary64_2189` `unpow1_binary64_2182` `1-exp_binary64_2168` `rem-log-exp_binary64_2165` `unsub-neg_binary64_2118` `*-inverses_binary64_2104` `distribute-rgt-out--_binary64_2078` `associate--r-_binary64_2063`
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-lft-sqr_binary64_2179` `exp-cbrt_binary64_2178` `exp-sqrt_binary64_2177` `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-exp-log_binary64_2164` `cube-neg_binary64_2151` `rem-3cbrt-rft_binary64_2150` `rem-3cbrt-lft_binary64_2149` `sqr-abs_binary64_2139` `sqr-neg_binary64_2138` `mul-1-neg_binary64_2116` `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_2103` `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` `difference-of-squares_binary64_2093` `cancel-sign-sub_binary64_2089` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-rgt1-in_binary64_2080` `distribute-lft1-in_binary64_2079`

Counts

306 → 372

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	354	5493
1	512	5283
2	3111	5283
3	4529	5263

prune5.1s (20.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	372	3	375

Error

0.0b

Counts

375 → 3

Compiler

Compiled 43523 to 27726 computations (36.3% saved)

regimes754.0ms (3.1%)

Accuracy

Total 0.3b remaining (91.3%)

Threshold costs 0.3b (91.3%)

Compiler

Compiled 7692 to 5831 computations (24.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64_2054`
16×	`sub-neg_binary64_2117` `*-commutative_binary64_2055`
13×	`neg-mul-1_binary64_2120` `neg-sub0_binary64_2119`
5×	`distribute-rgt-neg-in_binary64_2082`
4×	`distribute-neg-frac_binary64_2088` `distribute-lft-neg-in_binary64_2081`
2×	`unsub-neg_binary64_2118` `cancel-sign-sub-inv_binary64_2090` `distribute-neg-in_binary64_2085`
1×	`1-exp_binary64_2168` `distribute-lft-neg-out_binary64_2083`
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` `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_binary64_2089` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-rgt-neg-out_binary64_2084`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	93
1	53	93
2	72	93
3	98	93
4	121	93
5	137	93
6	145	93
7	147	93

Proof

(if real (<= f64 (/ f64 (- f64 h0 h1) (+ f64 (+ f64 h1 h0) 2)) -2251799813685007/2251799813685248) (/ f64 (+ f64 (* f64 2 (/ f64 h0 h1)) (- f64 (- f64 (/ f64 2 h1) (* f64 6 (/ f64 h0 (* f64 h1 h1)))) (+ f64 (/ f64 (/ f64 4 h1) h1) (* f64 2 (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))))) 2) (/ f64 (exp f64 (log f64 (+ f64 (/ f64 (- f64 h0 h1) (+ f64 (=> (+ f64 h1 h0)) 2)) 1))) 2))
+-commutative_binary64_2054 =>
(if real (<= f64 (/ f64 (- f64 h0 h1) (+ f64 (=> (+ f64 h1 h0)) 2)) -2251799813685007/2251799813685248) (/ f64 (+ f64 (* f64 2 (/ f64 h0 h1)) (- f64 (- f64 (/ f64 2 h1) (* f64 6 (/ f64 h0 (* f64 h1 h1)))) (+ f64 (/ f64 (/ f64 4 h1) h1) (* f64 2 (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))))) 2) (/ f64 (exp f64 (log f64 (+ f64 (/ f64 (- f64 h0 h1) (+ f64 (+ f64 h0 h1) 2)) 1))) 2))
+-commutative_binary64_2054 =>
(if real (<= f64 (/ f64 (- f64 h0 h1) (+ f64 (+ f64 h0 h1) 2)) -2251799813685007/2251799813685248) (/ f64 (+ f64 (* f64 2 (/ f64 h0 h1)) (- f64 (- f64 (/ f64 2 h1) (* f64 6 (/ f64 h0 (* f64 h1 h1)))) (+ f64 (/ f64 (/ f64 4 h1) h1) (* f64 2 (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))))) 2) (/ f64 (exp f64 (log f64 (+ f64 (/ f64 (- f64 h0 h1) (+ f64 (+ f64 h0 h1) 2)) 1))) 2))

end0.0ms (0%)

sample2.0s (8.4%)

Algorithm

1×

intervals

Results

190.0ms	5975×	body	128	valid
141.0ms	1035×	body	1024	valid
137.0ms	8000×	pre	128	true
54.0ms	593×	body	512	valid
19.0ms	304×	body	256	valid
18.0ms	93×	body	2048	valid

Compiler

Compiled 1545 to 1164 computations (24.7% saved)

Details

analyze3.0ms (0%)

sample29.0ms (0.1%)

simplify3.3s (13.6%)

prune4.0ms (0%)

localize8.0ms (0%)

rewrite119.0ms (0.5%)

series653.0ms (2.7%)

simplify664.0ms (2.7%)

prune556.0ms (2.3%)

localize20.0ms (0.1%)

rewrite607.0ms (2.5%)

series1.1s (4.5%)

simplify709.0ms (2.9%)

prune3.3s (13.6%)

localize64.0ms (0.3%)

rewrite3.7s (15.3%)

series1.0s (4.2%)

simplify513.0ms (2.1%)

prune5.1s (20.9%)

regimes754.0ms (3.1%)

bsearch3.0ms (0%)

simplify10.0ms (0%)

end0.0ms (0%)

sample2.0s (8.4%)

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