Details

analyze11.0ms (0.1%)

Algorithm

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)

sample43.0ms (0.5%)

Algorithm

1×

intervals

Results

30.0ms

256×

body

128

valid

Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify170.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5240	106

prune12.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

32.4b

Counts

2 → 2

Compiler

Compiled 315 to 160 computations (49.2% saved)

localize53.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 x x) 1737369620307813/2251799813685248)
0.3b	(*.f64 763919671262763/18014398509481984 (pow.f64 x 4))
16.0b	(.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)))))
31.8b	(/.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))))

rewrite1.1s (14.2%)

Algorithm

1×	rewrite-expression-head

Error

32.4b

Rules

35×	`add-sqr-sqrt_binary64_2146`
25×	`associate-r_binary64_2064`
24×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
21×	`add-exp-log_binary64_2162`
19×	`times-frac_binary64_2130`
18×	`add-cbrt-cube_binary64_2160`
11×	`pow1_binary64_2185`
8×	`prod-exp_binary64_2173`
7×	`associate-l_binary64_2065`
6×	`cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092`
4×	`add-log-exp_binary64_2163` `associate-/r/_binary64_2070` `pow-prod-down_binary64_2195` `unpow-prod-down_binary64_2203`
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` `sqr-pow_binary64_2096`
1×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-*r/_binary64_2066` `pow-to-exp_binary64_2193` `pow-exp_binary64_2192`

Counts

4 → 109

Calls

4 calls:

37.0ms	(/.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))))
30.0ms	(.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 763919671262763/18014398509481984 (pow.f64 x 4))

Compiler

Compiled 11687 to 9121 computations (22% saved)

series581.0ms (7.2%)

Error

Counts

4 → 26

Calls

4 calls:

222.0ms	(.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)))))
200.0ms	(/.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))))
51.0ms	(*.f64 763919671262763/18014398509481984 (pow.f64 x 4))
44.0ms	(.f64 (.f64 x x) 1737369620307813/2251799813685248)

Compiler

Compiled 1922 to 1584 computations (17.6% saved)

simplify180.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4917	8970
1	4917	8970

prune1.0s (13.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	134	3	137

Error

Counts

137 → 3

Compiler

Compiled 11498 to 8958 computations (22.1% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
0.2b	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite219.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

57×	`times-frac_binary64_2130`
43×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
24×	`unpow-prod-down_binary64_2203`
19×	`associate-/r*_binary64_2068`
12×	`add-exp-log_binary64_2162` `cube-prod_binary64_2152`
8×	`sqr-pow_binary64_2096`
6×	`div-exp_binary64_2175` `add-cbrt-cube_binary64_2160` `associate-/l*_binary64_2069`
4×	`unpow3_binary64_2190` `cube-mult_binary64_2154`
2×	`pow1_binary64_2185` `pow-to-exp_binary64_2193` `pow-exp_binary64_2192` `add-log-exp_binary64_2163` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`

Counts

2 → 110

Calls

2 calls:

14.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))
9.0ms	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))

Compiler

Compiled 2527 to 2021 computations (20% saved)

series82.0ms (1%)

Error

Counts

2 → 6

Calls

2 calls:

40.0ms	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
35.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

Compiler

Compiled 270 to 229 computations (15.2% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4949	1518
1	4949	1518

prune169.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	116	3	119

Error

Counts

119 → 3

Compiler

Compiled 2401 to 1878 computations (21.8% saved)

localize5.0ms (0.1%)

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))

rewrite83.0ms (1%)

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))
5.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))

Compiler

Compiled 594 to 447 computations (24.7% saved)

series148.0ms (1.8%)

Error

Counts

2 → 9

Calls

2 calls:

102.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
37.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 148 to 122 computations (17.6% saved)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5192	542

prune59.0ms (0.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

55 → 3

Compiler

Compiled 563 to 405 computations (28.1% saved)

regimes363.0ms (4.5%)

Accuracy

Total 0.1b remaining (95.4%)

Threshold costs 0.1b (95.4%)

Compiler

Compiled 4184 to 2994 computations (28.4% saved)

bsearch147.0ms (1.8%)

Steps

Iters	Range		Point
9	0.9019020842306558	859126.096984438	384.2356469505801
10	-2698.9092652138343	-6.773264825150337e-08	-141.96569955564678

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	104	172
1	104	172

end0.0ms (0%)

sample3.3s (41.7%)

Algorithm

1×

intervals

Results

1.3s

8000×

body

128

valid

Compiler

Compiled 2207 to 1592 computations (27.9% saved)

Details

analyze11.0ms (0.1%)

sample43.0ms (0.5%)

simplify170.0ms (2.1%)

prune12.0ms (0.1%)

localize53.0ms (0.7%)

rewrite1.1s (14.2%)

series581.0ms (7.2%)

simplify180.0ms (2.2%)

prune1.0s (13.1%)

localize13.0ms (0.2%)

rewrite219.0ms (2.7%)

series82.0ms (1%)

simplify92.0ms (1.1%)

prune169.0ms (2.1%)

localize5.0ms (0.1%)

rewrite83.0ms (1%)

series148.0ms (1.8%)

simplify60.0ms (0.8%)

prune59.0ms (0.7%)

regimes363.0ms (4.5%)

bsearch147.0ms (1.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (41.7%)

Profiling