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)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	129×	body	128	valid
8.0ms	67×	body	1024	valid
3.0ms	36×	body	512	valid
2.0ms	10×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify230.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune2.0ms (0%)

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: 31.4b

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))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite68.0ms (1.3%)

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:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series128.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

74.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
29.0ms	(/.f64 x (+.f64 x 1))
25.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5940	2299

prune165.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

Compiler

Compiled 2567 to 1831 computations (28.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.1b	(/.f64 -1 (*.f64 x x))
0.3b	(/.f64 3 (pow.f64 x 3))
4.8b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite95.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1768` `*-un-lft-identity_binary64_1762`
39×	`add-sqr-sqrt_binary64_1783`
35×	`add-cube-cbrt_binary64_1794`
14×	`add-exp-log_binary64_1797`
13×	`associate-/r*_binary64_1708`
12×	`cube-prod_binary64_1787` `unpow-prod-down_binary64_1838`
11×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795`
9×	`unpow3_binary64_1825`
6×	`distribute-lft-out_binary64_1715` `associate-/l*_binary64_1709`
5×	`div-exp_binary64_1810`
4×	`cube-mult_binary64_1789` `distribute-rgt-out_binary64_1717` `sqr-pow_binary64_1734` `div-inv_binary64_1759` `pow1_binary64_1820`
3×	`cbrt-undiv_binary64_1793` `frac-sub_binary64_1771`
2×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `distribute-lft-out--_binary64_1716` `difference-of-squares_binary64_1731` `frac-add_binary64_1770` `sum-log_binary64_1850`
1×	`flip3--_binary64_1766` `prod-exp_binary64_1808` `associate--r+_binary64_1700` `+-commutative_binary64_1694` `distribute-rgt1-in_binary64_1720` `pow-exp_binary64_1827` `cbrt-unprod_binary64_1792` `flip--_binary64_1737` `sub-neg_binary64_1755` `pow-to-exp_binary64_1828`

Counts

4 → 128

Calls

4 calls:

43.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
30.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))

series220.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
44.0ms	(/.f64 3 (pow.f64 x 3))
35.0ms	(/.f64 -1 (*.f64 x x))
35.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5229	2228

prune158.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	139	5	144

Merged error: 0.0b

Counts

144 → 5

Compiler

Compiled 2981 to 2065 computations (30.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 -1 (*.f64 x x))
0.2b	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
0.2b	(/.f64 1 (pow.f64 x 3))
4.8b	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

rewrite72.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1768` `*-un-lft-identity_binary64_1762`
39×	`add-sqr-sqrt_binary64_1783`
37×	`add-cube-cbrt_binary64_1794`
20×	`add-exp-log_binary64_1797`
16×	`associate-r_binary64_1704`
13×	`associate-/r*_binary64_1708` `add-cbrt-cube_binary64_1795`
12×	`cube-prod_binary64_1787` `unpow-prod-down_binary64_1838`
10×	`unpow3_binary64_1825`
8×	`div-exp_binary64_1810`
7×	`div-inv_binary64_1759` `distribute-lft-out_binary64_1715`
6×	`add-log-exp_binary64_1798` `associate-r/_binary64_1706` `associate-/l_binary64_1709` `pow1_binary64_1820`
5×	`distribute-rgt-out_binary64_1717`
4×	`cube-mult_binary64_1789` `sqr-pow_binary64_1734`
3×	`pow-exp_binary64_1827` `cbrt-undiv_binary64_1793` `frac-sub_binary64_1771` `pow-to-exp_binary64_1828` `1-exp_binary64_1803` `rec-exp_binary64_1809` `associate-l_binary64_1705`
2×	`frac-2neg_binary64_1773` `prod-exp_binary64_1808` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `associate--r+_binary64_1700` `cbrt-unprod_binary64_1792` `distribute-rgt-in_binary64_1714` `frac-add_binary64_1770` `distribute-lft-in_binary64_1713`
1×	`flip3--_binary64_1766` `diff-log_binary64_1851` `inv-pow_binary64_1844` `pow-prod-down_binary64_1830` `unswap-sqr_binary64_1730` `distribute-rgt1-in_binary64_1720` `pow-flip_binary64_1833` `flip--_binary64_1737` `sub-neg_binary64_1755` `*-commutative_binary64_1695`

Counts

4 → 146

Calls

4 calls:

38.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
8.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))
6.0ms	(/.f64 1 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))

series197.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
52.0ms	(/.f64 1 (pow.f64 x 3))
33.0ms	(/.f64 -1 (*.f64 x x))
29.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5120	2078

prune182.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	158	5	163

Merged error: 0.0b

Counts

163 → 5

Compiler

Compiled 3451 to 2438 computations (29.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1)))
0.0b	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
0.0b	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
2.5b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))

rewrite244.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

296×	`*-un-lft-identity_binary64_1762`
168×	`times-frac_binary64_1768`
162×	`add-sqr-sqrt_binary64_1783`
112×	`cube-prod_binary64_1787` `unpow-prod-down_binary64_1838`
61×	`distribute-lft-out--_binary64_1716`
52×	`difference-of-squares_binary64_1731` `distribute-lft-out_binary64_1715`
46×	`add-cube-cbrt_binary64_1794`
14×	`sqr-pow_binary64_1734`
10×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
8×	`associate-/r/_binary64_1710` `difference-of-sqr-1_binary64_1732` `add-log-exp_binary64_1798`
6×	`pow-unpow_binary64_1836` `pow1_binary64_1820`
4×	`rem-cube-cbrt_binary64_1784` `cube-div_binary64_1788` `div-inv_binary64_1759` `pow-exp_binary64_1827`
3×	`flip3--_binary64_1766` `flip3-+_binary64_1765` `flip-+_binary64_1736` `flip--_binary64_1737` `frac-add_binary64_1770`
2×	`cube-mult_binary64_1789` `unpow3_binary64_1825` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `pow-pow_binary64_1831` `pow-to-exp_binary64_1828`
1×	`diff-log_binary64_1851` `frac-times_binary64_1772` `associate-l/_binary64_1707` `+-commutative_binary64_1694` `associate-r/_binary64_1706` `frac-sub_binary64_1771` `sub-neg_binary64_1755` `difference-cubes_binary64_1764` `sum-log_binary64_1850`

Counts

4 → 244

Calls

4 calls:

145.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
23.0ms	(+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1)))
13.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
8.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

series305.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
100.0ms	(+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1)))
37.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
33.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

simplify120.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4939	7254
1	4939	7254

prune1.0s (20%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	256	5	261

Merged error: 0.0b

Counts

261 → 5

Compiler

Compiled 14366 to 10553 computations (26.5% saved)

regimes176.0ms (3.4%)

Compiler: Compiled 1704 to 1307 computations (23.3% saved)

bsearch49.0ms (1%)

Steps

Iters	Range		Point
9	2082.790261631103	31785431694.52961	10060.368876720395
10	-57867379.025228694	-8.453621939525379e-09	-10407.262752958486

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	83	106
1	83	106

end0.0ms (0%)

sample1.4s (28%)

Algorithm

1×

intervals

Results

248.0ms	1969×	body	1024	valid
147.0ms	4278×	body	128	valid
97.0ms	1018×	body	512	valid
38.0ms	227×	body	2048	valid
32.0ms	508×	body	256	valid

Compiler

Compiled 888 to 680 computations (23.4% saved)

Details

analyze5.0ms (0.1%)

sample28.0ms (0.5%)

simplify230.0ms (4.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite68.0ms (1.3%)

series128.0ms (2.5%)

simplify76.0ms (1.5%)

prune165.0ms (3.2%)

localize9.0ms (0.2%)

rewrite95.0ms (1.8%)

series220.0ms (4.3%)

simplify51.0ms (1%)

prune158.0ms (3.1%)

localize11.0ms (0.2%)

rewrite72.0ms (1.4%)

series197.0ms (3.8%)

simplify50.0ms (1%)

prune182.0ms (3.5%)

localize17.0ms (0.3%)

rewrite244.0ms (4.7%)

series305.0ms (5.9%)

simplify120.0ms (2.3%)

prune1.0s (20%)

regimes176.0ms (3.4%)

bsearch49.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (28%)

Profiling