Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	78×	body	1024	valid
4.0ms	131×	body	128	valid
3.0ms	29×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify240.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune2.0ms (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

Merged error: 30.5b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite73.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_1762`
60×	`times-frac_binary64_1768`
57×	`add-sqr-sqrt_binary64_1783`
25×	`add-cube-cbrt_binary64_1794`
20×	`distribute-lft-out_binary64_1715`
18×	`distribute-lft-out--_binary64_1716`
14×	`difference-of-squares_binary64_1731`
11×	`associate-/r*_binary64_1708`
7×	`associate-/l*_binary64_1709` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
5×	`difference-of-sqr-1_binary64_1732` `add-log-exp_binary64_1798`
4×	`associate-/r/_binary64_1710`
3×	`pow1_binary64_1820`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `flip--_binary64_1737`
1×	`diff-log_binary64_1851` `frac-sub_binary64_1771` `sub-neg_binary64_1755`

Counts

3 → 113

Calls

3 calls:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series123.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

73.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
25.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
25.0ms	(/.f64 x (+.f64 x 1))

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5940	2299

prune175.0ms (4.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	5	123

Merged error: 0b

Counts

123 → 5

Compiler

Compiled 2580 to 1846 computations (28.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.3b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite124.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`*-un-lft-identity_binary64_1762`
80×	`times-frac_binary64_1768`
72×	`add-sqr-sqrt_binary64_1783`
31×	`distribute-lft-out--_binary64_1716`
28×	`distribute-lft-out_binary64_1715` `add-cube-cbrt_binary64_1794`
18×	`difference-of-squares_binary64_1731`
17×	`log-pow_binary64_1848`
16×	`exp-prod_binary64_1811`
11×	`associate-/r*_binary64_1708`
8×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
7×	`associate-/l*_binary64_1709`
6×	`add-log-exp_binary64_1798`
5×	`difference-of-sqr-1_binary64_1732` `pow1_binary64_1820`
4×	`associate-/r/_binary64_1710` `log-prod_binary64_1845`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `flip--_binary64_1737` `sub-neg_binary64_1755`
1×	`diff-log_binary64_1851` `frac-sub_binary64_1771` `exp-diff_binary64_1807` `exp-sum_binary64_1805` `log-div_binary64_1846` `rem-log-exp_binary64_1800`

Counts

4 → 143

Calls

4 calls:

47.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
45.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series226.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
71.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
24.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
23.0ms	(/.f64 x (+.f64 x 1))

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4900	2877
1	4900	2877

prune189.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	155	5	160

Merged error: 0b

Counts

160 → 5

Compiler

Compiled 3492 to 2577 computations (26.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
7.6b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

rewrite59.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_1783`
69×	`*-un-lft-identity_binary64_1762`
56×	`times-frac_binary64_1768`
37×	`add-cube-cbrt_binary64_1794`
27×	`associate-r_binary64_1704`
19×	`add-exp-log_binary64_1797`
14×	`difference-of-squares_binary64_1731`
13×	`add-cbrt-cube_binary64_1795`
11×	`associate-/r*_binary64_1708`
7×	`difference-of-sqr-1_binary64_1732` `distribute-lft-out--_binary64_1716` `pow1_binary64_1820`
6×	`associate-/r/_binary64_1710` `add-log-exp_binary64_1798` `frac-sub_binary64_1771` `associate-/l*_binary64_1709`
5×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `div-exp_binary64_1810` `distribute-lft-out_binary64_1715`
4×	`frac-times_binary64_1772` `prod-exp_binary64_1808` `associate-l/_binary64_1707` `associate-l*_binary64_1705`
3×	`flip3--_binary64_1766` `div-inv_binary64_1759` `unswap-sqr_binary64_1730` `cbrt-undiv_binary64_1793` `flip--_binary64_1737`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `associate-*r/_binary64_1706` `cbrt-unprod_binary64_1792` `un-div-inv_binary64_1760` `1-exp_binary64_1803` `rec-exp_binary64_1809`
1×	`diff-log_binary64_1851` `inv-pow_binary64_1844` `pow-prod-down_binary64_1830` `pow-flip_binary64_1833` `sub-neg_binary64_1755` `*-commutative_binary64_1695`

Counts

4 → 154

Calls

4 calls:

17.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
13.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series150.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
32.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
27.0ms	(/.f64 x (+.f64 x 1))
18.0ms	(/.f64 1 (-.f64 x 1))

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5061	2533

prune185.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	166	5	171

Merged error: 0b

Counts

171 → 5

Compiler

Compiled 3546 to 2579 computations (27.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
0.0b	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
0.0b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
3.2b	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite149.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

390×	`*-un-lft-identity_binary64_1762`
292×	`cbrt-prod_binary64_1790`
252×	`add-sqr-sqrt_binary64_1783`
250×	`times-frac_binary64_1768`
92×	`add-cube-cbrt_binary64_1794`
75×	`swap-sqr_binary64_1729`
72×	`distribute-lft-out_binary64_1715`
68×	`difference-of-squares_binary64_1731`
40×	`difference-of-sqr-1_binary64_1732` `distribute-lft-out--_binary64_1716`
37×	`associate-l_binary64_1705` `associate-r_binary64_1704`
18×	`cbrt-div_binary64_1791`
12×	`associate-/r/_binary64_1710`
11×	`pow1_binary64_1820`
9×	`unswap-sqr_binary64_1730`
8×	`pow1/3_binary64_1841`
7×	`flip3--_binary64_1766` `frac-sub_binary64_1771` `flip--_binary64_1737`
6×	`frac-times_binary64_1772` `div-inv_binary64_1759` `associate-*l/_binary64_1707` `add-log-exp_binary64_1798` `add-exp-log_binary64_1797`
4×	`associate-*r/_binary64_1706` `add-cbrt-cube_binary64_1795`
2×	`pow-sqr_binary64_1735` `pow-prod-down_binary64_1830` `pow-prod-up_binary64_1829`
1×	`diff-log_binary64_1851` `prod-exp_binary64_1808` `pow-plus_binary64_1822` `cbrt-unprod_binary64_1792` `sub-neg_binary64_1755` `*-commutative_binary64_1695` `pow2_binary64_1840`

Counts

4 → 283

Calls

4 calls:

50.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
13.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
9.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))

series281.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
76.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
55.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
51.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify160.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4903	9555
1	4903	9555

prune881.0ms (20.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	295	5	300

Merged error: 0b

Counts

300 → 5

Compiler

Compiled 12243 to 9323 computations (23.9% saved)

regimes42.0ms (1%)

Compiler: Compiled 232 to 184 computations (20.7% saved)

bsearch39.0ms (0.9%)

Steps

Iters	Range		Point
10	6.678391225351904	484360414951.354	12064.14325946773
9	-4590392.709799706	-0.004645704772350229	-10203.564768070848

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	59
1	90	59

end0.0ms (0%)

sample827.0ms (19.6%)

Algorithm

1×

intervals

Results

245.0ms	1994×	body	1024	valid
160.0ms	4341×	body	128	valid
87.0ms	917×	body	512	valid
35.0ms	225×	body	2048	valid
33.0ms	523×	body	256	valid

Compiler

Compiled 155 to 123 computations (20.6% saved)

Details

analyze5.0ms (0.1%)

sample23.0ms (0.6%)

simplify240.0ms (5.7%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

rewrite73.0ms (1.7%)

series123.0ms (2.9%)

simplify76.0ms (1.8%)

prune175.0ms (4.2%)

localize11.0ms (0.3%)

rewrite124.0ms (2.9%)

series226.0ms (5.3%)

simplify81.0ms (1.9%)

prune189.0ms (4.5%)

localize10.0ms (0.2%)

rewrite59.0ms (1.4%)

series150.0ms (3.5%)

simplify71.0ms (1.7%)

prune185.0ms (4.4%)

localize10.0ms (0.2%)

rewrite149.0ms (3.5%)

series281.0ms (6.7%)

simplify160.0ms (3.8%)

prune881.0ms (20.9%)

regimes42.0ms (1%)

bsearch39.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample827.0ms (19.6%)

Profiling