Details

analyze3.6s (11.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

501×	`unsub-neg_binary64_2118`
469×	`distribute-rgt-in_binary64_2074`
417×	`distribute-rgt-neg-in_binary64_2082`
332×	`distribute-lft-in_binary64_2073`
290×	`cancel-sign-sub-inv_binary64_2090`
267×	`distribute-lft-neg-in_binary64_2081`
266×	`neg-mul-1_binary64_2120`
265×	`neg-sub0_binary64_2119`
247×	`distribute-lft-neg-out_binary64_2083`
229×	`associate--r+_binary64_2060`
192×	`sub-neg_binary64_2117`
189×	`distribute-neg-in_binary64_2085`
168×	`*-commutative_binary64_2055`
153×	`distribute-rgt-neg-out_binary64_2084`
142×	`associate-r_binary64_2064`
140×	`associate-l_binary64_2065`
113×	`mul0-rgt_binary64_2107` `mul0-lft_binary64_2106`
102×	`+-commutative_binary64_2054`
93×	`remove-double-neg_binary64_2112`
47×	`*-lft-identity_binary64_2113`
46×	`*-rgt-identity_binary64_2114`
38×	`associate-+l-_binary64_2059`
35×	`associate--r-_binary64_2063`
31×	`sub0-neg_binary64_2111`
24×	`associate--l+_binary64_2061`
23×	`associate-+r+_binary64_2056`
17×	`associate-+r-_binary64_2058`
15×	`associate-+l+_binary64_2057`
14×	`cos-neg_binary64_2255` `mul-1-neg_binary64_2116` `+-rgt-identity_binary64_2109`
12×	`sin-neg_binary64_2254` `distribute-rgt-out--_binary64_2078` `associate--l-_binary64_2062`
8×	`cancel-sign-sub_binary64_2089`
5×	`+-lft-identity_binary64_2108` `distribute-lft-out--_binary64_2076`
3×	`distribute-neg-out_binary64_2086`
1×	`1-exp_binary64_2168` `swap-lambda1-lambda2` `swap-phi1-phi2`
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` `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` `--rgt-identity_binary64_2110` `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` `distribute-neg-frac_binary64_2088` `distribute-frac-neg_binary64_2087` `distribute-rgt1-in_binary64_2080` `distribute-lft1-in_binary64_2079` `distribute-rgt-out_binary64_2077` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	341
1	164	341
2	237	341
3	274	341
4	306	341
5	447	341
6	475	341
7	707	341
8	1046	341
9	1135	341
10	1279	341
11	1600	341
12	1905	341
13	2500	341
14	2503	341
15	2479	341
16	2493	341
17	2493	341
18	2893	341
19	2619	341
20	2619	341
21	2619	341
22	2619	341
23	2392	341
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 20 to 18 computations (10% saved)

sample223.0ms (0.7%)

Algorithm

1×

intervals

Results

155.0ms	186×	body	1024	valid
19.0ms	36×	body	512	valid
10.0ms	5×	body	2048	valid
5.0ms	15×	body	256	valid
2.0ms	14×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64_2117`
14×	`cancel-sign-sub-inv_binary64_2090`
10×	`distribute-rgt-in_binary64_2074` `*-commutative_binary64_2055`
9×	`neg-mul-1_binary64_2120`
8×	`associate--r+_binary64_2060`
7×	`unsub-neg_binary64_2118`
6×	`neg-sub0_binary64_2119` `associate--r-_binary64_2063`
5×	`distribute-neg-in_binary64_2085` `distribute-lft-neg-out_binary64_2083` `distribute-rgt-neg-in_binary64_2082` `distribute-lft-in_binary64_2073` `+-commutative_binary64_2054`
4×	`*-lft-identity_binary64_2113` `sub0-neg_binary64_2111` `associate-+l-_binary64_2059`
3×	`+-lft-identity_binary64_2108` `distribute-rgt-neg-out_binary64_2084` `associate-l_binary64_2065` `associate-r_binary64_2064` `associate-+l+_binary64_2057`
2×	`cos-neg_binary64_2255` `*-rgt-identity_binary64_2114`
1×	`1-exp_binary64_2168` `remove-double-neg_binary64_2112` `--rgt-identity_binary64_2110` `+-rgt-identity_binary64_2109` `distribute-lft-neg-in_binary64_2081` `associate--l+_binary64_2061` `associate-+r-_binary64_2058` `associate-+r+_binary64_2056`
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` `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` `mul-1-neg_binary64_2116` `/-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-neg-out_binary64_2086` `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_2062`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.2b

Counts

1 → 1

Compiler

Compiled 19 to 17 computations (10.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite120.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

Rules

11×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`add-sqr-sqrt_binary64_2146`
8×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`associate-r_binary64_2064`
4×	`cos-sum_binary64_2258` `add-log-exp_binary64_2163` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-l_binary64_2065`
3×	`cos-diff_binary64_2261` `cancel-sign-sub-inv_binary64_2090`
2×	`*-commutative_binary64_2055`
1×	`sub-neg_binary64_2117` `acos-asin_binary64_2305` `unswap-sqr_binary64_2092` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `cos-mult_binary64_2278` `associate-*l/_binary64_2067`

Counts

4 → 59

Calls

4 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 1775 to 321 computations (81.9% saved)

series1.2s (3.7%)

Error

16.9b

Counts

4 → 56

Calls

4 calls:

544.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
381.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
143.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
63.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3427 to 1985 computations (42.1% saved)

simplify146.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

461×	`unsub-neg_binary64_2118`
355×	`distribute-rgt-neg-in_binary64_2082`
336×	`neg-mul-1_binary64_2120`
325×	`neg-sub0_binary64_2119`
307×	`cancel-sign-sub-inv_binary64_2090`
293×	`distribute-lft-neg-in_binary64_2081`
254×	`associate-l_binary64_2065`
237×	`associate-r_binary64_2064`
206×	`sub-neg_binary64_2117`
148×	`*-commutative_binary64_2055`
146×	`distribute-lft-neg-out_binary64_2083`
128×	`distribute-lft-in_binary64_2073`
127×	`cancel-sign-sub_binary64_2089` `distribute-rgt-out--_binary64_2078`
102×	`distribute-rgt-in_binary64_2074`
98×	`distribute-rgt-out_binary64_2077`
96×	`distribute-rgt-neg-out_binary64_2084`
95×	`distribute-lft-out_binary64_2075`
92×	`distribute-lft-out--_binary64_2076`
81×	`sqr-pow_binary64_2096`
56×	`+-commutative_binary64_2054`
51×	`unswap-sqr_binary64_2092`
50×	`distribute-neg-out_binary64_2086`
37×	`exp-prod_binary64_2176`
34×	`cube-prod_binary64_2152`
33×	`log-prod_binary64_2210`
32×	`associate-+l-_binary64_2059` `associate-+l+_binary64_2057`
31×	`associate--l+_binary64_2061`
28×	`swap-sqr_binary64_2091`
25×	`associate-+r-_binary64_2058` `associate-+r+_binary64_2056`
23×	`*-rgt-identity_binary64_2114` `associate--r-_binary64_2063`
21×	`remove-double-neg_binary64_2112`
20×	`*-lft-identity_binary64_2113` `associate--r+_binary64_2060`
17×	`cube-unmult_binary64_2161` `+-rgt-identity_binary64_2109`
16×	`sub0-neg_binary64_2111`
14×	`pow-sqr_binary64_2097`
12×	`rem-sqrt-square_binary64_2137`
10×	`associate-/l*_binary64_2069`
9×	`unpow3_binary64_2190` `distribute-neg-in_binary64_2085`
8×	`unpow1/2_binary64_2188`
7×	`distribute-rgt1-in_binary64_2080`
6×	`cos-neg_binary64_2255` `pow-plus_binary64_2187`
5×	`difference-of-squares_binary64_2093`
4×	`sin-neg_binary64_2254` `cube-mult_binary64_2154` `distribute-lft1-in_binary64_2079`
3×	`unpow2_binary64_2189` `unpow1_binary64_2182`
2×	`exp-sum_binary64_2170` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106` `associate-/l/_binary64_2071` `associate-*r/_binary64_2066` `associate--l-_binary64_2062`
1×	`1-exp_binary64_2168` `exp-1-e_binary64_2167` `cube-neg_binary64_2151` `rem-3cbrt-lft_binary64_2149` `sqr-neg_binary64_2138` `rem-square-sqrt_binary64_2136` `count-2_binary64_2072`
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` `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` `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` `prod-exp_binary64_2173` `exp-diff_binary64_2172` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `rem-log-exp_binary64_2165` `rem-exp-log_binary64_2164` `cube-div_binary64_2153` `rem-3cbrt-rft_binary64_2150` `rem-cbrt-cube_binary64_2148` `rem-cube-cbrt_binary64_2147` `sqr-abs_binary64_2139` `times-frac_binary64_2130` `div-sub_binary64_2129` `mul-1-neg_binary64_2116` `/-rgt-identity_binary64_2115` `--rgt-identity_binary64_2110` `+-lft-identity_binary64_2108` `div0_binary64_2105` `-inverses_binary64_2104` `+-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-neg-frac_binary64_2088` `distribute-frac-neg_binary64_2087` `associate-/r/_binary64_2070` `associate-/r_binary64_2068` `associate-*l/_binary64_2067`

Counts

115 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	3285
1	455	2945
2	1391	2856
3	2404	2827
4	4491	2827
5	5008	2827

prune119.0ms (0.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	42	14	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	14	57

Error

2.8b

Counts

57 → 14

Compiler

Compiled 2028 to 596 computations (70.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite159.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

13×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-sqr-sqrt_binary64_2146`
9×	`add-cube-cbrt_binary64_2159` `-un-lft-identity_binary64_2124` `associate-r*_binary64_2064`
7×	`associate-l_binary64_2065`
6×	`cos-mult_binary64_2278`
5×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163`
3×	`-commutative_binary64_2055` `sin-mult_binary64_2279` `frac-times_binary64_2134` `associate-r/_binary64_2066`
2×	`unswap-sqr_binary64_2092` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`acos-asin_binary64_2305` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-*l/_binary64_2067`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2888 to 452 computations (84.3% saved)

series2.0s (6.2%)

Error

2.8b

Counts

4 → 55

Calls

4 calls:

1.0s	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
504.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
232.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
139.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5230 to 2677 computations (48.8% saved)

simplify203.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

781×	`cancel-sign-sub-inv_binary64_2090`
474×	`associate-r_binary64_2064`
461×	`associate-l_binary64_2065`
265×	`distribute-rgt-neg-in_binary64_2082`
241×	`distribute-lft-neg-in_binary64_2081`
234×	`neg-mul-1_binary64_2120` `neg-sub0_binary64_2119`
233×	`*-commutative_binary64_2055`
186×	`sub-neg_binary64_2117`
179×	`distribute-rgt-out_binary64_2077`
152×	`exp-prod_binary64_2176`
144×	`sqr-pow_binary64_2096`
94×	`distribute-rgt-in_binary64_2074`
91×	`distribute-lft-in_binary64_2073`
72×	`+-commutative_binary64_2054`
51×	`unsub-neg_binary64_2118`
47×	`distribute-rgt-out--_binary64_2078`
43×	`associate--l+_binary64_2061`
42×	`log-prod_binary64_2210` `cube-prod_binary64_2152`
35×	`-rgt-identity_binary64_2114` `-lft-identity_binary64_2113`
31×	`associate-+l+_binary64_2057`
29×	`associate--r+_binary64_2060`
28×	`distribute-neg-in_binary64_2085`
26×	`distribute-lft-neg-out_binary64_2083`
25×	`swap-sqr_binary64_2091` `associate-+r+_binary64_2056`
18×	`pow-sqr_binary64_2097`
17×	`unswap-sqr_binary64_2092`
15×	`unpow3_binary64_2190`
13×	`cube-unmult_binary64_2161`
12×	`unpow1/2_binary64_2188`
9×	`distribute-lft-out_binary64_2075`
8×	`exp-sum_binary64_2170` `cube-mult_binary64_2154`
7×	`distribute-rgt-neg-out_binary64_2084`
4×	`pow-plus_binary64_2187`
3×	`unpow2_binary64_2189` `unpow1_binary64_2182` `rem-sqrt-square_binary64_2137`
2×	`difference-of-squares_binary64_2093` `distribute-rgt1-in_binary64_2080`
1×	`1-exp_binary64_2168` `exp-1-e_binary64_2167` `distribute-lft1-in_binary64_2079` `associate-+l-_binary64_2059` `associate-+r-_binary64_2058`
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` `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` `prod-exp_binary64_2173` `exp-diff_binary64_2172` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `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` `rem-square-sqrt_binary64_2136` `times-frac_binary64_2130` `div-sub_binary64_2129` `mul-1-neg_binary64_2116` `/-rgt-identity_binary64_2115` `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` `difference-of-sqr--1_binary64_2095` `difference-of-sqr-1_binary64_2094` `cancel-sign-sub_binary64_2089` `distribute-neg-frac_binary64_2088` `distribute-frac-neg_binary64_2087` `distribute-neg-out_binary64_2086` `distribute-lft-out--_binary64_2076` `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--r-_binary64_2063` `associate--l-_binary64_2062`

Counts

127 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	5087
1	739	4497
2	2801	4418
3	4173	4418
4	4995	4418
5	4964	4418

prune200.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	94	13	107
Fresh	12	1	13
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Error

2.7b

Counts

121 → 14

Compiler

Compiled 4232 to 823 computations (80.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
0.3b	(.f64 (exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
0.6b	(log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

rewrite124.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

16×	`add-sqr-sqrt_binary64_2146`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`pow1_binary64_2185` `associate-l_binary64_2065`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`log-prod_binary64_2210`
6×	`associate-r_binary64_2064`
4×	`add-log-exp_binary64_2163` `exp-sum_binary64_2170`
3×	`unswap-sqr_binary64_2092`
2×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `*-commutative_binary64_2055`
1×	`acos-asin_binary64_2305` `log-pow_binary64_2213` `rem-log-exp_binary64_2165` `sin-mult_binary64_2279`

Counts

4 → 61

Calls

4 calls:

7.0ms	(.f64 (exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
6.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
2.0ms	(log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 2668 to 382 computations (85.7% saved)

series4.1s (12.8%)

Error

2.7b

Counts

4 → 47

Calls

4 calls:

2.3s	(.f64 (exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
1.4s	(log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
232.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
157.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 4674 to 2410 computations (48.4% saved)

simplify215.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

464×	`associate-*l/_binary64_2067`
390×	`cancel-sign-sub-inv_binary64_2090`
352×	`associate-l_binary64_2065`
275×	`distribute-rgt-neg-in_binary64_2082`
251×	`associate-r_binary64_2064`
250×	`*-commutative_binary64_2055`
240×	`associate-+l+_binary64_2057`
232×	`associate-/l/_binary64_2071`
219×	`distribute-lft-neg-in_binary64_2081`
199×	`sqr-pow_binary64_2096`
177×	`associate-+r+_binary64_2056`
159×	`unswap-sqr_binary64_2092`
151×	`associate-/l*_binary64_2069`
145×	`distribute-rgt-in_binary64_2074`
144×	`sub-neg_binary64_2117`
142×	`associate-/r/_binary64_2070`
136×	`distribute-lft-in_binary64_2073`
113×	`exp-sum_binary64_2170`
89×	`+-commutative_binary64_2054`
78×	`pow-sqr_binary64_2097`
74×	`neg-mul-1_binary64_2120`
73×	`distribute-rgt-out_binary64_2077`
67×	`neg-sub0_binary64_2119`
61×	`distribute-neg-in_binary64_2085`
60×	`distribute-lft-out_binary64_2075`
59×	`associate-/r*_binary64_2068`
51×	`log-prod_binary64_2210`
49×	`exp-prod_binary64_2176` `associate--r+_binary64_2060`
48×	`unsub-neg_binary64_2118`
38×	`associate-+l-_binary64_2059`
37×	`distribute-rgt-out--_binary64_2078`
36×	`associate-*r/_binary64_2066`
31×	`*-lft-identity_binary64_2113`
29×	`*-rgt-identity_binary64_2114`
26×	`distribute-lft-neg-out_binary64_2083`
23×	`rem-sqrt-square_binary64_2137`
22×	`times-frac_binary64_2130`
20×	`distribute-lft-out--_binary64_2076`
18×	`sub0-neg_binary64_2111` `swap-sqr_binary64_2091`
17×	`cube-prod_binary64_2152` `associate--l+_binary64_2061`
16×	`log-div_binary64_2211` `cube-unmult_binary64_2161` `cube-div_binary64_2153` `mul0-rgt_binary64_2107` `mul0-lft_binary64_2106`
14×	`distribute-rgt-neg-out_binary64_2084`
13×	`count-2_binary64_2072`
12×	`distribute-rgt1-in_binary64_2080` `associate-+r-_binary64_2058`
9×	`exp-to-pow_binary64_2186`
8×	`unpow1/2_binary64_2188` `exp-lft-sqr_binary64_2179` `remove-double-neg_binary64_2112` `--rgt-identity_binary64_2110` `+-rgt-identity_binary64_2109` `distribute-lft1-in_binary64_2079`
7×	`log-pow_binary64_2213`
6×	`pow-plus_binary64_2187` `exp-sqrt_binary64_2177` `rem-exp-log_binary64_2164`
5×	`associate--r-_binary64_2063`
4×	`unpow3_binary64_2190` `prod-exp_binary64_2173`
3×	`exp-lft-cube_binary64_2180` `distribute-neg-frac_binary64_2088`
2×	`cos-neg_binary64_2255` `unpow2_binary64_2189` `unpow1_binary64_2182` `/-rgt-identity_binary64_2115`
1×	`sin-neg_binary64_2254` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `rem-log-exp_binary64_2165` `cube-mult_binary64_2154` `+-lft-identity_binary64_2108`
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` `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-rec_binary64_2212` `pow-base-0_binary64_2208` `unpow1/3_binary64_2191` `pow-base-1_binary64_2184` `unpow0_binary64_2183` `unpow-1_binary64_2181` `exp-cbrt_binary64_2178` `div-exp_binary64_2175` `rec-exp_binary64_2174` `exp-diff_binary64_2172` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `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-square-sqrt_binary64_2136` `div-sub_binary64_2129` `mul-1-neg_binary64_2116` `div0_binary64_2105` `*-inverses_binary64_2104` `+-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` `associate--l-_binary64_2062`

Counts

108 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	4907
1	251	3985
2	599	3975
3	1096	3966
4	1457	3966
5	2327	3966
6	2875	3966
7	4820	3966

prune123.0ms (0.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	74	14	88

Error

2.7b

Counts

88 → 14

Compiler

Compiled 3075 to 545 computations (82.3% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.6b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

rewrite122.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

12×	`add-sqr-sqrt_binary64_2146`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`exp-prod_binary64_2176`
8×	`pow1_binary64_2185` `log-pow_binary64_2213`
7×	`associate-l_binary64_2065`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`add-log-exp_binary64_2163`
3×	`acos-asin_binary64_2305` `log-prod_binary64_2210` `associate-r_binary64_2064`
2×	`exp-diff_binary64_2172`
1×	`log-div_binary64_2211` `rem-log-exp_binary64_2165` `rem-exp-log_binary64_2164` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 2764 to 221 computations (92% saved)

series4.6s (14.3%)

Error

2.7b

Counts

4 → 51

Calls

4 calls:

2.3s	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
1.6s	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
405.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
219.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 5202 to 2575 computations (50.5% saved)

simplify354.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64_2130`
426×	`unswap-sqr_binary64_2092`
398×	`distribute-rgt-in_binary64_2074`
359×	`distribute-lft-in_binary64_2073`
340×	`log-prod_binary64_2210`
324×	`distribute-rgt-out_binary64_2077`
302×	`associate-l_binary64_2065`
273×	`*-commutative_binary64_2055`
223×	`associate-r_binary64_2064`
202×	`associate-+l+_binary64_2057`
181×	`associate-*l/_binary64_2067`
168×	`sqr-pow_binary64_2096`
133×	`log-pow_binary64_2213`
120×	`exp-prod_binary64_2176`
118×	`associate-*r/_binary64_2066`
104×	`log-div_binary64_2211`
97×	`associate-+r+_binary64_2056`
93×	`exp-sum_binary64_2170`
75×	`cube-prod_binary64_2152`
70×	`count-2_binary64_2072`
67×	`distribute-lft-out_binary64_2075`
64×	`associate-/l/_binary64_2071`
62×	`exp-to-pow_binary64_2186` `associate-/l*_binary64_2069`
58×	`pow-sqr_binary64_2097`
57×	`cube-div_binary64_2153`
49×	`unpow3_binary64_2190`
43×	`unsub-neg_binary64_2118`
40×	`swap-sqr_binary64_2091`
37×	`distribute-rgt1-in_binary64_2080`
35×	`pow-plus_binary64_2187`
31×	`*-rgt-identity_binary64_2114`
29×	`exp-sqrt_binary64_2177` `rem-sqrt-square_binary64_2137`
27×	`*-lft-identity_binary64_2113` `associate-/r/_binary64_2070`
26×	`cube-unmult_binary64_2161`
19×	`associate-/r*_binary64_2068`
18×	`log-rec_binary64_2212`
11×	`distribute-lft1-in_binary64_2079`
10×	`unpow1/2_binary64_2188` `rem-log-exp_binary64_2165` `+-commutative_binary64_2054`
9×	`cube-mult_binary64_2154`
8×	`exp-lft-sqr_binary64_2179`
7×	`rem-exp-log_binary64_2164`
5×	`prod-exp_binary64_2173`
3×	`sub-neg_binary64_2117`
1×	`unpow2_binary64_2189` `1-exp_binary64_2168` `exp-1-e_binary64_2167` `neg-mul-1_binary64_2120` `neg-sub0_binary64_2119` `/-rgt-identity_binary64_2115`
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` `pow-base-1_binary64_2184` `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` `exp-diff_binary64_2172` `exp-neg_binary64_2171` `e-exp-1_binary64_2169` `exp-0_binary64_2166` `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-square-sqrt_binary64_2136` `div-sub_binary64_2129` `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_2104` `+-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-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-rgt-out--_binary64_2078` `distribute-lft-out--_binary64_2076` `associate--r-_binary64_2063` `associate--l-_binary64_2062` `associate--l+_binary64_2061` `associate--r+_binary64_2060` `associate-+l-_binary64_2059` `associate-+r-_binary64_2058`

Counts

109 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	5911
1	159	4846
2	324	4846
3	450	4846
4	623	4840
5	1298	4840
6	2920	4840
7	4531	4840
8	4947	4840
9	4996	4840
10	4866	4840

prune100.0ms (0.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	89	14	103

Error

2.7b

Counts

103 → 14

Compiler

Compiled 2945 to 143 computations (95.1% saved)

regimes4.0s (12.6%)

Accuracy

Total 0.4b remaining (9.7%)

Threshold costs 0.4b (9.7%)

Compiler

Compiled 53784 to 31886 computations (40.7% saved)

bsearch0.0ms (0%)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64_2055`
2×	`+-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` `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` `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` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	43
1	31	43
2	31	43

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 104 to 88 computations (15.4% saved)

end0.0ms (0%)

sample10.2s (31.7%)

Algorithm

1×

intervals

Results

4.8s	5542×	body	1024	valid
735.0ms	1369×	body	512	valid
542.0ms	271×	body	2048	valid
168.0ms	522×	body	256	valid
48.0ms	296×	body	128	valid
4.0ms	5×	body	1024	invalid

Compiler

Compiled 4923 to 2926 computations (40.6% saved)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Details

analyze3.6s (11.2%)

sample223.0ms (0.7%)

simplify14.0ms (0%)

prune2.0ms (0%)

localize25.0ms (0.1%)

rewrite120.0ms (0.4%)

series1.2s (3.7%)

simplify146.0ms (0.5%)

prune119.0ms (0.4%)

localize25.0ms (0.1%)

rewrite159.0ms (0.5%)

series2.0s (6.2%)

simplify203.0ms (0.6%)

prune200.0ms (0.6%)

localize29.0ms (0.1%)

rewrite124.0ms (0.4%)

series4.1s (12.8%)

simplify215.0ms (0.7%)

prune123.0ms (0.4%)

localize32.0ms (0.1%)

rewrite122.0ms (0.4%)

series4.6s (14.3%)

simplify354.0ms (1.1%)

prune100.0ms (0.3%)

regimes4.0s (12.6%)

bsearch0.0ms (0%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample10.2s (31.7%)

Profiling

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31