Details

analyze159.0ms (1.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5240	106
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

Compiler

Compiled 174 to 47 computations (73% saved)

sample48.0ms (0.5%)

Algorithm

1×

intervals

Results

34.0ms

256×

body

128

valid

Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5240	106

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.4b

Counts

2 → 1

Compiler

Compiled 142 to 114 computations (19.7% saved)

localize44.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 x x) 1737369620307813/2251799813685248)
0.1b	(.f64 3782789308857969/36028797018963968 (.f64 x x))
13.6b	(.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))
27.9b	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))))

rewrite981.0ms (10.9%)

Algorithm

1×	rewrite-expression-head

Error

28.3b

Rules

29×	`add-sqr-sqrt_binary64_2146`
22×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
21×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
19×	`times-frac_binary64_2130` `associate-r_binary64_2064`
16×	`pow1_binary64_2185`
8×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
7×	`pow-prod-down_binary64_2195` `associate-l_binary64_2065`
4×	`add-log-exp_binary64_2163` `associate-/r/_binary64_2070` `unswap-sqr_binary64_2092`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `*-commutative_binary64_2055`
2×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `associate-/l/_binary64_2071`
1×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-*r/_binary64_2066`

Counts

4 → 103

Calls

4 calls:

35.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))))
31.0ms	(.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))
6.0ms	(.f64 (.f64 x x) 1737369620307813/2251799813685248)
6.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

Compiler

Compiled 11202 to 8727 computations (22.1% saved)

series457.0ms (5.1%)

Error

Counts

4 → 26

Calls

4 calls:

181.0ms	(.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))
147.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (.f64 x x) 1737369620307813/2251799813685248)) (.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12))))
42.0ms	(.f64 (.f64 x x) 1737369620307813/2251799813685248)
40.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

Compiler

Compiled 1938 to 1620 computations (16.4% saved)

simplify144.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4899	8920
1	4899	8920

prune836.0ms (9.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	3	130

Error

Counts

130 → 3

Compiler

Compiled 11071 to 8647 computations (21.9% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
0.1b	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

13×	`add-sqr-sqrt_binary64_2146`
12×	`associate-r_binary64_2064`
7×	`add-exp-log_binary64_2162`
6×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160` `unpow-prod-down_binary64_2203` `unswap-sqr_binary64_2092` `cube-prod_binary64_2152`
3×	`prod-exp_binary64_2173` `associate-l_binary64_2065`
2×	`pow1_binary64_2185` `sqr-pow_binary64_2096`
1×	`pow-to-exp_binary64_2193` `pow-exp_binary64_2192` `cbrt-unprod_binary64_2157` `unpow3_binary64_2190` `cube-mult_binary64_2154` `*-commutative_binary64_2055` `diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `cancel-sign-sub-inv_binary64_2090`

Counts

2 → 43

Calls

2 calls:

7.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))
3.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))

Compiler

Compiled 594 to 447 computations (24.7% saved)

series100.0ms (1.1%)

Error

Counts

2 → 9

Calls

2 calls:

62.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
34.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 148 to 122 computations (17.6% saved)

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5192	542

prune38.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Error

Counts

55 → 3

Compiler

Compiled 609 to 443 computations (27.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)) (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)))
0.1b	(/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 7))
0.1b	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
0.6b	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite418.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

80×	`times-frac_binary64_2130`
67×	`*-un-lft-identity_binary64_2124`
61×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
36×	`unpow-prod-down_binary64_2203`
26×	`associate-/r*_binary64_2068`
19×	`add-exp-log_binary64_2162`
12×	`cube-prod_binary64_2152` `sqr-pow_binary64_2096`
10×	`add-cbrt-cube_binary64_2160`
9×	`div-exp_binary64_2175` `associate-/l*_binary64_2069`
6×	`add-log-exp_binary64_2163`
4×	`pow1_binary64_2185` `unpow3_binary64_2190` `cube-mult_binary64_2154`
3×	`pow-to-exp_binary64_2193` `pow-exp_binary64_2192` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`
2×	`distribute-lft-out_binary64_2075`
1×	`sum-log_binary64_2215` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098` `+-commutative_binary64_2054`

Counts

4 → 169

Calls

4 calls:

51.0ms	(+.f64 (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)) (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)))
8.0ms	(/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 7))
6.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))
5.0ms	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))

Compiler

Compiled 4941 to 4006 computations (18.9% saved)

series226.0ms (2.5%)

Error

Counts

4 → 15

Calls

4 calls:

89.0ms	(+.f64 (/.f64 1660320414109913/6603827387272392 (pow.f64 x 3)) (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5)))
46.0ms	(/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 7))
38.0ms	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
36.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

Compiler

Compiled 882 to 748 computations (15.2% saved)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5158	2562

prune328.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	184	3	187

Error

Counts

187 → 3

Compiler

Compiled 4925 to 3944 computations (19.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 8))
0.2b	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 4))
0.3b	(/.f64 1/2 (*.f64 x x))
15.4b	(.f64 x (+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 6)) (+.f64 (/.f64 1/2 (.f64 x x)) (+.f64 (/.f64 1660320414109913/6603827387272392 (pow.f64 x 4)) (/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 8))))))

rewrite406.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

49×	`*-un-lft-identity_binary64_2124`
45×	`times-frac_binary64_2130`
42×	`add-sqr-sqrt_binary64_2146`
40×	`add-cube-cbrt_binary64_2159`
24×	`unpow-prod-down_binary64_2203`
21×	`add-exp-log_binary64_2162`
15×	`add-cbrt-cube_binary64_2160` `associate-/r*_binary64_2068`
9×	`frac-add_binary64_2132` `associate-/l*_binary64_2069`
8×	`div-exp_binary64_2175` `sqr-pow_binary64_2096`
7×	`associate-*r/_binary64_2066`
6×	`pow1_binary64_2185` `associate-r_binary64_2064` `distribute-lft-out_binary64_2075`
4×	`add-log-exp_binary64_2163` `cbrt-undiv_binary64_2158`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-l_binary64_2065` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`
2×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `pow-to-exp_binary64_2193` `pow-exp_binary64_2192`
1×	`pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `*-commutative_binary64_2055`

Counts

4 → 141

Calls

4 calls:

63.0ms	(.f64 x (+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 6)) (+.f64 (/.f64 1/2 (.f64 x x)) (+.f64 (/.f64 1660320414109913/6603827387272392 (pow.f64 x 4)) (/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 8))))))
5.0ms	(/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 8))
5.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 4))
5.0ms	(/.f64 1/2 (*.f64 x x))

Compiler

Compiled 5206 to 3859 computations (25.9% saved)

series186.0ms (2.1%)

Error

Counts

4 → 18

Calls

4 calls:

65.0ms	(.f64 x (+.f64 (/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 6)) (+.f64 (/.f64 1/2 (.f64 x x)) (+.f64 (/.f64 1660320414109913/6603827387272392 (pow.f64 x 4)) (/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 8))))))
40.0ms	(/.f64 90075934112096643708144967800859671858474104609/7999901474247532368018484521926651180403835008 (pow.f64 x 8))
36.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 4))
26.0ms	(/.f64 1/2 (*.f64 x x))

Compiler

Compiled 964 to 791 computations (17.9% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4977	2894
1	4977	2894

prune485.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	159	3	162

Error

Counts

162 → 3

Compiler

Compiled 5075 to 3767 computations (25.8% saved)

regimes417.0ms (4.6%)

Accuracy

Total 0.3b remaining (99.7%)

Threshold costs 0.3b (99.7%)

Compiler

Compiled 5774 to 4254 computations (26.3% saved)

bsearch120.0ms (1.3%)

Steps

Iters	Range		Point
10	1.1504938872689576e-05	4573304.562979324	1.1805393633449974
9	-388.23628625783846	-8.99985194152174e-05	-1.18621719126689

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	67
1	71	67

end0.0ms (0%)

sample3.3s (36.2%)

Algorithm

1×

intervals

Results

980.0ms

8000×

body

128

valid

Compiler

Compiled 2932 to 2166 computations (26.1% saved)

Details

analyze159.0ms (1.8%)

sample48.0ms (0.5%)

simplify63.0ms (0.7%)

prune8.0ms (0.1%)

localize44.0ms (0.5%)

rewrite981.0ms (10.9%)

series457.0ms (5.1%)

simplify144.0ms (1.6%)

prune836.0ms (9.3%)

localize4.0ms (0%)

rewrite48.0ms (0.5%)

series100.0ms (1.1%)

simplify52.0ms (0.6%)

prune38.0ms (0.4%)

localize13.0ms (0.1%)

rewrite418.0ms (4.6%)

series226.0ms (2.5%)

simplify69.0ms (0.8%)

prune328.0ms (3.6%)

localize15.0ms (0.2%)

rewrite406.0ms (4.5%)

series186.0ms (2.1%)

simplify82.0ms (0.9%)

prune485.0ms (5.4%)

regimes417.0ms (4.6%)

bsearch120.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (36.2%)

Profiling