Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	37.5%	12.5%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample8.0ms (0%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	19	7
1	19	7

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 5 to 3 computations (40% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
2×	`*-un-lft-identity_binary64_1783`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))

series36.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

35.0ms

(+.f64 x (*.f64 x x))

Compiler

Compiled 37 to 31 computations (16.2% saved)

simplify81.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5054	165

prune52.0ms (0.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	7	12	19
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	7	13	20

Error

Counts

20 → 13

Compiler

Compiled 234 to 111 computations (52.6% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
2×	`*-un-lft-identity_binary64_1783`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

4.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))

series33.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

33.0ms

(+.f64 x (*.f64 x x))

Compiler

Compiled 55 to 49 computations (10.9% saved)

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5054	165

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
2×	`*-un-lft-identity_binary64_1783`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))

series37.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

37.0ms

(+.f64 x (*.f64 x x))

Compiler

Compiled 55 to 49 computations (10.9% saved)

simplify81.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5054	165

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

4.2b	(exp.f64 (log.f64 (+.f64 x (*.f64 x x))))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
4.2b	(exp.f64 (log.f64 (+.f64 x (*.f64 x x))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_1783`
5×	`log-prod_binary64_1869` `exp-sum_binary64_1829`
4×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `exp-prod_binary64_1835` `add-log-exp_binary64_1822`
3×	`pow1_binary64_1844`
2×	`add-cbrt-cube_binary64_1819` `exp-diff_binary64_1831` `add-exp-log_binary64_1821` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `flip3-+_binary64_1786` `log-div_binary64_1870`
1×	`rem-exp-log_binary64_1823` `log-pow_binary64_1872` `+-commutative_binary64_1713` `sum-log_binary64_1874`

Counts

2 → 32

Calls

4 calls:

4.0ms	(exp.f64 (log.f64 (+.f64 x (*.f64 x x))))
3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(exp.f64 (log.f64 (+.f64 x (*.f64 x x))))
0.0ms	(+.f64 x (*.f64 x x))

series188.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

150.0ms	(exp.f64 (log.f64 (+.f64 x (*.f64 x x))))
38.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 168 to 146 computations (13.1% saved)

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4908	397
1	4908	397

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (+.f64 x (*.f64 x x))))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.2b	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (+.f64 x (*.f64 x x))))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64_1799`
25×	`add-sqr-sqrt_binary64_1805`
18×	`pow1_binary64_1844`
17×	`*-un-lft-identity_binary64_1783`
12×	`sqrt-div_binary64_1800`
11×	`add-cube-cbrt_binary64_1818`
10×	`swap-sqr_binary64_1750`
8×	`flip-+_binary64_1757` `pow1/2_binary64_1863` `associate-l_binary64_1724` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `associate-r_binary64_1723`
7×	`add-log-exp_binary64_1822`
6×	`distribute-rgt-out_binary64_1736` `distribute-rgt1-in_binary64_1739`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow-prod-up_binary64_1853`
4×	`frac-times_binary64_1793` `unswap-sqr_binary64_1751`
3×	`pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
2×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `associate-l/_binary64_1726` `sum-log_binary64_1874` `rem-sqrt-square_binary64_1796`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `sqr-abs_binary64_1798` `pow2_binary64_1864`

Counts

3 → 90

Calls

6 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (+.f64 x (*.f64 x x))))
3.0ms	(+.f64 x (*.f64 x x))
3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))
0.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (+.f64 x (*.f64 x x))))

series109.0ms (0.3%)

Counts

3 → 18

Calls

3 calls:

37.0ms	(+.f64 x (*.f64 x x))
37.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (+.f64 x (*.f64 x x))))
34.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 255 to 183 computations (28.2% saved)

simplify103.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4917	1171
1	4917	1171

prune952.0ms (2.3%)

Pruning

68 alts after pruning (63 fresh and 5 done)

	Pruned	Kept	Total
New	134	56	190
Fresh	0	7	7
Picked	0	0	0
Done	1	5	6
Total	135	68	203

Error

Counts

203 → 68

Compiler

Compiled 2302 to 985 computations (57.2% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
2×	`*-un-lft-identity_binary64_1783`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))

series38.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

38.0ms

(+.f64 x (*.f64 x x))

Compiler

Compiled 73 to 67 computations (8.2% saved)

simplify78.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5054	165

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

4.6b	(pow.f64 E.f64 (log.f64 (+.f64 x (*.f64 x x))))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
4.6b	(pow.f64 E.f64 (log.f64 (+.f64 x (*.f64 x x))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_1783`
5×	`unpow-prod-up_binary64_1861` `log-prod_binary64_1869` `add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
4×	`pow-unpow_binary64_1860` `add-log-exp_binary64_1822` `pow1_binary64_1844`
3×	`add-exp-log_binary64_1821` `unpow-prod-down_binary64_1862`
2×	`add-cbrt-cube_binary64_1819` `pow-sub_binary64_1859` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `flip3-+_binary64_1786` `pow-exp_binary64_1851` `log-div_binary64_1870`
1×	`log-pow_binary64_1872` `+-commutative_binary64_1713` `sqr-pow_binary64_1755` `e-exp-1_binary64_1828` `sum-log_binary64_1874` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852`

Counts

2 → 39

Calls

4 calls:

5.0ms	(pow.f64 E.f64 (log.f64 (+.f64 x (*.f64 x x))))
3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))
0.0ms	(pow.f64 E.f64 (log.f64 (+.f64 x (*.f64 x x))))

series231.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

194.0ms	(pow.f64 E.f64 (log.f64 (+.f64 x (*.f64 x x))))
36.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 111 to 93 computations (16.2% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5009	679

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 2)
0.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x (.f64 x x))) 2) (cbrt.f64 (+.f64 x (*.f64 x x))))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x (.f64 x x))) 2) (cbrt.f64 (+.f64 x (*.f64 x x))))
0.5b	(pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 2)
0.6b	(cbrt.f64 (+.f64 x (*.f64 x x)))
0.6b	(cbrt.f64 (+.f64 x (*.f64 x x)))

rewrite31.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64_1814`
30×	`add-sqr-sqrt_binary64_1805`
20×	`unpow-prod-down_binary64_1862`
19×	`*-un-lft-identity_binary64_1783`
14×	`add-cube-cbrt_binary64_1818`
13×	`associate-l_binary64_1724`
10×	`add-exp-log_binary64_1821` `unswap-sqr_binary64_1751`
8×	`associate-r_binary64_1723`
6×	`unpow2_binary64_1848` `cbrt-div_binary64_1815` `pow1_binary64_1844`
5×	`add-cbrt-cube_binary64_1819` `distribute-rgt-out_binary64_1736` `distribute-rgt1-in_binary64_1739`
4×	`sqr-pow_binary64_1755` `add-log-exp_binary64_1822`
3×	`prod-exp_binary64_1832` `pow-unpow_binary64_1860` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1/3_binary64_1865`
2×	`associate-*r/_binary64_1725` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`pow3_binary64_1866` `cbrt-unprod_binary64_1816` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `rem-3cbrt-lft_binary64_1808` `*-commutative_binary64_1714`

Counts

4 → 103

Calls

8 calls:

13.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 x (.f64 x x))) 2) (cbrt.f64 (+.f64 x (*.f64 x x))))
5.0ms	(pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 2)
3.0ms	(cbrt.f64 (+.f64 x (*.f64 x x)))
2.0ms	(cbrt.f64 (+.f64 x (*.f64 x x)))
0.0ms	(+.f64 x (*.f64 x x))

series271.0ms (0.7%)

Counts

4 → 42

Calls

4 calls:

90.0ms	(pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 2)
76.0ms	(cbrt.f64 (+.f64 x (*.f64 x x)))
69.0ms	(cbrt.f64 (+.f64 x (*.f64 x x)))
35.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 x (.f64 x x))) 2) (cbrt.f64 (+.f64 x (*.f64 x x))))

Compiler

Compiled 957 to 789 computations (17.6% saved)

simplify98.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4922	2472
1	4922	2472

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4))))
0.0b	(-.f64 (*.f64 x x) (pow.f64 x 4))
0.0b	(-.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(-.f64 (*.f64 x x) (pow.f64 x 4))
0.1b	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4))))
9.5b	(/.f64 (.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4)))) (sqrt.f64 (-.f64 x (.f64 x x))))
20.2b	(sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)))

rewrite57.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1805`
31×	`sqrt-prod_binary64_1799`
28×	`sqrt-div_binary64_1800`
18×	`*-un-lft-identity_binary64_1783`
15×	`add-cube-cbrt_binary64_1818`
11×	`add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821`
9×	`flip3--_binary64_1787` `flip--_binary64_1758` `associate-r_binary64_1723` `pow1_binary64_1844`
8×	`associate-/l/_binary64_1730` `associate-/r_binary64_1727` `associate-l*_binary64_1724` `times-frac_binary64_1789` `frac-times_binary64_1793`
7×	`cancel-sign-sub-inv_binary64_1749`
6×	`flip-+_binary64_1757` `unpow-prod-down_binary64_1862` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
4×	`associate-r/_binary64_1725` `sqr-pow_binary64_1755` `associate-l/_binary64_1726` `unswap-sqr_binary64_1751`
3×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854`
2×	`associate-/r/_binary64_1729` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `distribute-rgt-out--_binary64_1737`
1×	`associate-/l_binary64_1728` `distribute-rgt-out_binary64_1736` `div-inv_binary64_1780` `sqrt-undiv_binary64_1804` `distribute-rgt1-in_binary64_1739` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 124

Calls

8 calls:

16.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4)))) (sqrt.f64 (-.f64 x (.f64 x x))))
15.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4))))
6.0ms	(sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)))
6.0ms	(-.f64 (*.f64 x x) (pow.f64 x 4))
0.0ms	(+.f64 x (*.f64 x x))

series226.0ms (0.5%)

Counts

4 → 19

Calls

4 calls:

100.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4)))) (sqrt.f64 (-.f64 x (.f64 x x))))
65.0ms	(-.f64 (*.f64 x x) (pow.f64 x 4))
37.0ms	(sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)))
23.0ms	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (sqrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4))))

Compiler

Compiled 527 to 367 computations (30.4% saved)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4975	3353
1	4975	3353

prune4.8s (11.6%)

Pruning

228 alts after pruning (218 fresh and 10 done)

	Pruned	Kept	Total
New	194	164	358
Fresh	4	54	58
Picked	0	0	0
Done	0	10	10
Total	198	228	426

Error

Counts

426 → 228

Compiler

Compiled 10890 to 4995 computations (54.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
2×	`*-un-lft-identity_binary64_1783`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `distribute-rgt1-in_binary64_1739` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))

series36.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

36.0ms

(+.f64 x (*.f64 x x))

Compiler

Compiled 91 to 85 computations (6.6% saved)

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5054	165

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (+.f64 x 1))
0.0b	(*.f64 x (+.f64 x 1))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`associate-r_binary64_1723`
3×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-l_binary64_1724` `pow1_binary64_1844`
2×	`associate-*r/_binary64_1725`
1×	`distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`

Counts

1 → 23

Calls

2 calls:

6.0ms	(*.f64 x (+.f64 x 1))
0.0ms	(*.f64 x (+.f64 x 1))

series39.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

38.0ms

(*.f64 x (+.f64 x 1))

Compiler

Compiled 37 to 31 computations (16.2% saved)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5431	230

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

40.4b	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))
4.2b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))))
0.1b	(pow.f64 (+.f64 x (*.f64 x x)) 3)
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.1b	(pow.f64 (+.f64 x (*.f64 x x)) 3)
4.2b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))))
40.4b	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64_1814`
22×	`*-un-lft-identity_binary64_1783`
19×	`log-prod_binary64_1869` `exp-sum_binary64_1829`
15×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
7×	`distribute-rgt-out_binary64_1736` `distribute-rgt1-in_binary64_1739`
6×	`cube-div_binary64_1812` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `exp-prod_binary64_1835`
4×	`flip-+_binary64_1757` `cbrt-div_binary64_1815` `flip3-+_binary64_1786`
3×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `pow-unpow_binary64_1860` `unpow3_binary64_1849`
2×	`exp-diff_binary64_1831` `log-pow_binary64_1872` `pow1/3_binary64_1865` `log-div_binary64_1870`
1×	`rem-exp-log_binary64_1823` `+-commutative_binary64_1713` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sum-log_binary64_1874` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 103

Calls

8 calls:

7.0ms	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))
4.0ms	(pow.f64 (+.f64 x (*.f64 x x)) 3)
3.0ms	(+.f64 x (*.f64 x x))
0.0ms	(+.f64 x (*.f64 x x))

series247.0ms (0.6%)

Counts

4 → 30

Calls

4 calls:

137.0ms	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))))
41.0ms	(pow.f64 (+.f64 x (*.f64 x x)) 3)
36.0ms	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 3))
34.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 424 to 378 computations (10.8% saved)

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	1576
1	4963	1576

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x (.f64 x x))) 2) (/.f64 (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4))) (cbrt.f64 (-.f64 x (.f64 x x)))))
0.0b	(-.f64 (*.f64 x x) (pow.f64 x 4))
0.0b	(-.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.5b	(/.f64 (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4))) (cbrt.f64 (-.f64 x (.f64 x x))))
0.6b	(cbrt.f64 (-.f64 x (*.f64 x x)))
0.6b	(cbrt.f64 (+.f64 x (*.f64 x x)))
31.0b	(cbrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`cbrt-prod_binary64_1814`
76×	`add-sqr-sqrt_binary64_1805`
72×	`times-frac_binary64_1789`
57×	`*-un-lft-identity_binary64_1783`
45×	`add-cube-cbrt_binary64_1818`
41×	`difference-of-squares_binary64_1752`
11×	`distribute-rgt-out--_binary64_1737`
10×	`sqr-pow_binary64_1755` `cbrt-div_binary64_1815` `unpow-prod-down_binary64_1862`
9×	`associate-/l*_binary64_1728`
8×	`associate-/r*_binary64_1727`
6×	`add-exp-log_binary64_1821`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `flip--_binary64_1758` `add-log-exp_binary64_1822` `pow1_binary64_1844`
3×	`pow1/3_binary64_1865`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729`
1×	`distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `div-inv_binary64_1780` `distribute-rgt1-in_binary64_1739` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782`

Counts

4 → 151

Calls

8 calls:

13.0ms	(/.f64 (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4))) (cbrt.f64 (-.f64 x (.f64 x x))))
6.0ms	(cbrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)))
5.0ms	(cbrt.f64 (+.f64 x (*.f64 x x)))
3.0ms	(cbrt.f64 (-.f64 x (*.f64 x x)))
0.0ms	(+.f64 x (*.f64 x x))

series324.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

88.0ms	(cbrt.f64 (+.f64 x (*.f64 x x)))
87.0ms	(cbrt.f64 (-.f64 x (*.f64 x x)))
79.0ms	(/.f64 (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 x 4))) (cbrt.f64 (-.f64 x (.f64 x x))))
69.0ms	(cbrt.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)))

Compiler

Compiled 1365 to 1069 computations (21.7% saved)

simplify137.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4866	5434
1	4866	5434

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (sqrt.f64 (+.f64 x (.f64 x x))) (/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8))) (sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
0.0b	(-.f64 x (*.f64 x x))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(+.f64 (*.f64 x x) (pow.f64 x 4))
10.5b	(-.f64 (pow.f64 x 4) (pow.f64 x 8))
10.6b	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8)))
20.2b	(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8))) (sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4))))
30.0b	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4)))

rewrite78.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`add-sqr-sqrt_binary64_1805`
158×	`sqrt-prod_binary64_1799`
96×	`times-frac_binary64_1789`
81×	`difference-of-squares_binary64_1752`
74×	`*-un-lft-identity_binary64_1783`
57×	`unpow-prod-down_binary64_1862`
56×	`add-cube-cbrt_binary64_1818`
55×	`sqr-pow_binary64_1755`
16×	`associate-/l*_binary64_1728`
9×	`distribute-lft-out--_binary64_1735`
8×	`sqrt-div_binary64_1800`
7×	`cancel-sign-sub-inv_binary64_1749`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-/r*_binary64_1727` `add-log-exp_binary64_1822` `pow1_binary64_1844`
3×	`flip3--_binary64_1787` `flip--_binary64_1758`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `pow1/2_binary64_1863` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`
1×	`div-inv_binary64_1780` `sqrt-undiv_binary64_1804` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

4 → 203

Calls

8 calls:

22.0ms	(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8))) (sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4))))
8.0ms	(-.f64 (pow.f64 x 4) (pow.f64 x 8))
8.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8)))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4)))
0.0ms	(+.f64 (*.f64 x x) (pow.f64 x 4))

series451.0ms (1.1%)

Counts

4 → 22

Calls

4 calls:

304.0ms	(-.f64 (pow.f64 x 4) (pow.f64 x 8))
52.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8)))
48.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4)))
47.0ms	(/.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 8))) (sqrt.f64 (+.f64 (*.f64 x x) (pow.f64 x 4))))

Compiler

Compiled 999 to 654 computations (34.5% saved)

simplify139.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4933	7566
1	4933	7566

prune14.6s (35.5%)

Pruning

448 alts after pruning (433 fresh and 15 done)

	Pruned	Kept	Total
New	364	229	593
Fresh	9	204	213
Picked	0	0	0
Done	0	15	15
Total	373	448	821

Error

Counts

821 → 448

Compiler

Compiled 11900 to 5456 computations (54.2% saved)

simplify669.0ms (1.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	3272	28120
1	3272	28120

regimes2.8s (6.8%)

Compiler: Compiled 31642 to 19050 computations (39.8% saved)

bsearch0.0ms (0%)

regimes21.0ms (0.1%)

Compiler: Compiled 9 to 11 computations (-22.2% saved)

bsearch19.0ms (0%)

Steps

Iters	Range		Point
8	0.0037070930194020454	57.51658933111033	1.0150417341532645
10	-762080614756.6744	-0.004185610438705886	-0.9979022278705204

Compiler

Compiled 1 to 1 computations (0% saved)

regimes8.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 6 to 9 computations (-50% saved)

bsearch2.0ms (0%)

Compiler: Compiled 21 to 12 computations (42.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	27
1	15	27

end0.0ms (0%)

sample13.1s (31.8%)

Algorithm

1×

intervals

Results

128.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 15878 to 9565 computations (39.8% saved)

Pareto

0.4024549614387391