Details

analyze10.0ms (0.2%)

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 (0.7%)

Algorithm

1×

intervals

Results

29.0ms

256×

body

128

valid

Compiler

Compiled 347 to 94 computations (72.9% saved)

simplify156.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5240	106

prune11.0ms (0.2%)

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

31.4b

Counts

2 → 2

Compiler

Compiled 315 to 160 computations (49.2% saved)

localize44.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 3782789308857969/36028797018963968 (.f64 x x))
0.1b	(.f64 1737369620307813/2251799813685248 (.f64 x x))
14.5b	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
30.8b	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))

rewrite976.0ms (15.3%)

Algorithm

1×	rewrite-expression-head

Error

31.4b

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` `associate-l_binary64_2065`
19×	`times-frac_binary64_2130`
16×	`pow1_binary64_2185`
8×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
7×	`pow-prod-down_binary64_2195`
5×	`associate-r_binary64_2064`
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-*l/_binary64_2067`

Counts

4 → 103

Calls

4 calls:

90.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))
76.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
6.0ms	(.f64 1737369620307813/2251799813685248 (.f64 x x))
6.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

Compiler

Compiled 26812 to 6290 computations (76.5% saved)

series557.0ms (8.8%)

Error

Counts

4 → 24

Calls

4 calls:

226.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
198.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 3782789308857969/36028797018963968 (.f64 x x))) (.f64 763919671262763/18014398509481984 (.f64 (.f64 x x) (.f64 x x)))) (.f64 8375303961237363/1152921504606846976 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 583843369866023/1152921504606846976 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 825478423409049/4611686018427387904 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1737369620307813/2251799813685248 (.f64 x x))) (.f64 2620859570069187/9007199254740992 (.f64 (.f64 x x) (.f64 x x)))) (.f64 2502400853142105/36028797018963968 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2017691060547333/144115188075855872 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 7681173503746455/9223372036854775808 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 825478423409049/4611686018427387904) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))
45.0ms	(.f64 1737369620307813/2251799813685248 (.f64 x x))
43.0ms	(.f64 3782789308857969/36028797018963968 (.f64 x x))

Compiler

Compiled 3718 to 1347 computations (63.8% saved)

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5674	8742

prune724.0ms (11.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	2	129

Error

Counts

129 → 2

Compiler

Compiled 18274 to 7432 computations (59.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))
0.5b	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))

rewrite170.0ms (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:

5.0ms	(/.f64 1660320414109913/6603827387272392 (pow.f64 x 3))
4.0ms	(/.f64 370645858300289935006419108089/2422807564493828181570755855648 (pow.f64 x 5))

Compiler

Compiled 2527 to 2021 computations (20% saved)

series85.0ms (1.3%)

Error

Counts

2 → 6

Calls

2 calls:

44.0ms	(/.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)

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4949	1518
1	4949	1518

prune141.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	116	2	118

Error

Counts

118 → 2

Compiler

Compiled 2407 to 1883 computations (21.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
0.1b	(*.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5))
0.1b	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))
20.9b	(+.f64 (.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5)) (-.f64 x (.f64 24015124616067039/36028797018963968 (pow.f64 x 3))))

rewrite128.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

23×	`add-sqr-sqrt_binary64_2146`
19×	`associate-r_binary64_2064`
14×	`add-exp-log_binary64_2162`
11×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
8×	`add-cbrt-cube_binary64_2160` `unpow-prod-down_binary64_2203`
7×	`unswap-sqr_binary64_2092`
6×	`prod-exp_binary64_2173` `associate-l_binary64_2065`
4×	`pow1_binary64_2185` `cube-prod_binary64_2152` `sqr-pow_binary64_2096`
2×	`diff-log_binary64_2216` `sum-log_binary64_2215` `sub-neg_binary64_2117` `associate-+r+_binary64_2056` `cancel-sign-sub-inv_binary64_2090` `pow-to-exp_binary64_2193` `pow-exp_binary64_2192` `cbrt-unprod_binary64_2157` `*-commutative_binary64_2055`
1×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-+r-_binary64_2058` `+-commutative_binary64_2054` `unpow3_binary64_2190` `cube-mult_binary64_2154` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

4 → 83

Calls

4 calls:

9.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))
7.0ms	(+.f64 (.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5)) (-.f64 x (.f64 24015124616067039/36028797018963968 (pow.f64 x 3))))
5.0ms	(*.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5))
3.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))

Compiler

Compiled 1696 to 1328 computations (21.7% saved)

series197.0ms (3.1%)

Error

Counts

4 → 17

Calls

4 calls:

61.0ms	(-.f64 x (*.f64 24015124616067039/36028797018963968 (pow.f64 x 3)))
50.0ms	(+.f64 (.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5)) (-.f64 x (.f64 24015124616067039/36028797018963968 (pow.f64 x 3))))
37.0ms	(*.f64 21556931916393198394382988102651/81129638414606681695789005144064 (pow.f64 x 5))
36.0ms	(*.f64 24015124616067039/36028797018963968 (pow.f64 x 3))

Compiler

Compiled 506 to 420 computations (17% saved)

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4953	1222
1	4953	1222

prune105.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	100	2	102

Error

Counts

102 → 2

Compiler

Compiled 1705 to 1318 computations (22.7% saved)

regimes330.0ms (5.2%)

Accuracy

Total 0.0b remaining (87.2%)

Threshold costs 0.0b (87.2%)

Compiler

Compiled 6508 to 1872 computations (71.2% saved)

bsearch225.0ms (3.5%)

Steps

Iters	Range		Point
10	0.00043834338194570705	298743086.62611073	54907335.3391805
9	-7215008719.130454	-2852.081410118134	-1830711657.4542089

Compiler

Compiled 1 to 1 computations (0% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	377	633
1	377	633

end0.0ms (0%)

sample2.1s (33.6%)

Algorithm

1×

intervals

Results

1.1s

8000×

body

128

valid

Compiler

Compiled 3677 to 1062 computations (71.1% saved)

Details

analyze10.0ms (0.2%)

sample43.0ms (0.7%)

simplify156.0ms (2.4%)

prune11.0ms (0.2%)

localize44.0ms (0.7%)

rewrite976.0ms (15.3%)

series557.0ms (8.8%)

simplify160.0ms (2.5%)

prune724.0ms (11.4%)

localize9.0ms (0.1%)

rewrite170.0ms (2.7%)

series85.0ms (1.3%)

simplify82.0ms (1.3%)

prune141.0ms (2.2%)

localize9.0ms (0.1%)

rewrite128.0ms (2%)

series197.0ms (3.1%)

simplify54.0ms (0.8%)

prune105.0ms (1.6%)

regimes330.0ms (5.2%)

bsearch225.0ms (3.5%)

simplify13.0ms (0.2%)

end0.0ms (0%)

sample2.1s (33.6%)

Profiling