Details

analyze316.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample31.0ms (0%)

Algorithm

1×

intervals

Results

11.0ms	76×	body	1024	valid
4.0ms	46×	body	512	valid
2.0ms	93×	body	128	valid
2.0ms	12×	body	2048	valid
1.0ms	29×	body	256	valid

Compiler

Compiled 18 to 16 computations (11.1% saved)

simplify92.0ms (0%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

prune3.0ms (0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1	3	4
Fresh	0	4	4
Picked	0	0	0
Done	0	0	0
Total	1	7	8

Error

40.1b

Counts

8 → 4

Compiler

Compiled 10 to 8 computations (20% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

5.9b	(-.f64 (exp.f64 x) 1)
0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.9b	(-.f64 (exp.f64 x) 1)

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1805`
30×	`*-un-lft-identity_binary64_1783`
21×	`times-frac_binary64_1789`
15×	`add-cube-cbrt_binary64_1818`
10×	`difference-of-squares_binary64_1752`
7×	`associate-/r*_binary64_1727`
5×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
4×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `add-exp-log_binary64_1821` `cancel-sign-sub-inv_binary64_1749`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`div-inv_binary64_1780` `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

2 → 63

Calls

4 calls:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.0ms	(-.f64 (exp.f64 x) 1)

series64.0ms (0%)

Counts

2 → 12

Calls

2 calls:

44.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
19.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 111 computations (20.7% saved)

simplify67.0ms (0%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5105	1195

prune282.0ms (0.1%)

Pruning

43 alts after pruning (42 fresh and 1 done)

	Pruned	Kept	Total
New	36	39	75
Fresh	0	3	3
Picked	0	0	0
Done	0	1	1
Total	36	43	79

Error

0.0b

Counts

79 → 43

Compiler

Compiled 1241 to 740 computations (40.4% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
0.0b	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
0.0b	(+.f64 1/6 (*.f64 1/24 x))
0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
0.0b	(+.f64 1/6 (*.f64 1/24 x))
0.0b	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
0.2b	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
0.3b	(*.f64 1/24 x)

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1805`
13×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
9×	`add-cube-cbrt_binary64_1818` `-un-lft-identity_binary64_1783` `associate-r*_binary64_1723`
7×	`associate-l_binary64_1724`
6×	`add-log-exp_binary64_1822`
5×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
4×	`associate-*r/_binary64_1725`
3×	`flip-+_binary64_1757` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751`
2×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
1×	`+-commutative_binary64_1713` `sum-log_binary64_1874`

Counts

4 → 74

Calls

8 calls:

7.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
6.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
4.0ms	(*.f64 1/24 x)
3.0ms	(+.f64 1/6 (*.f64 1/24 x))
0.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))

series141.0ms (0%)

Counts

4 → 20

Calls

4 calls:

52.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
42.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
30.0ms	(+.f64 1/6 (*.f64 1/24 x))
17.0ms	(*.f64 1/24 x)

Compiler

Compiled 550 to 411 computations (25.3% saved)

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4986	1168
1	4986	1168

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (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 6 expressions with local error:

5.9b	(-.f64 (exp.f64 x) 1)
0.7b	(*.f64 (exp.f64 x) (/.f64 1 (-.f64 (exp.f64 x) 1)))
0.0b	(/.f64 1 (-.f64 (exp.f64 x) 1))
0.0b	(/.f64 1 (-.f64 (exp.f64 x) 1))
0.7b	(*.f64 (exp.f64 x) (/.f64 1 (-.f64 (exp.f64 x) 1)))
5.9b	(-.f64 (exp.f64 x) 1)

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_1805`
53×	`*-un-lft-identity_binary64_1783`
44×	`times-frac_binary64_1789`
28×	`add-cube-cbrt_binary64_1818`
27×	`associate-r_binary64_1723`
16×	`difference-of-squares_binary64_1752`
12×	`add-exp-log_binary64_1821`
10×	`add-cbrt-cube_binary64_1819`
8×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
7×	`associate-/r*_binary64_1727`
6×	`pow1_binary64_1844`
5×	`add-log-exp_binary64_1822`
4×	`associate-/r/_binary64_1729` `prod-exp_binary64_1832` `div-exp_binary64_1834`
3×	`flip3--_binary64_1787` `associate-/l_binary64_1728` `cancel-sign-sub-inv_binary64_1749` `associate-l*_binary64_1724` `unswap-sqr_binary64_1751` `flip--_binary64_1758`
2×	`cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `rec-exp_binary64_1833`
1×	`associate-r/_binary64_1725` `un-div-inv_binary64_1781` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `sub-neg_binary64_1776`

Counts

3 → 117

Calls

6 calls:

18.0ms	(*.f64 (exp.f64 x) (/.f64 1 (-.f64 (exp.f64 x) 1)))
7.0ms	(/.f64 1 (-.f64 (exp.f64 x) 1))
4.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 1 (-.f64 (exp.f64 x) 1))
0.0ms	(*.f64 (exp.f64 x) (/.f64 1 (-.f64 (exp.f64 x) 1)))

series100.0ms (0%)

Counts

3 → 18

Calls

3 calls:

46.0ms	(*.f64 (exp.f64 x) (/.f64 1 (-.f64 (exp.f64 x) 1)))
37.0ms	(/.f64 1 (-.f64 (exp.f64 x) 1))
18.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 236 to 192 computations (18.6% saved)

simplify129.0ms (0%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4869	1831
1	4869	1831

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.7b	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
0.6b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(pow.f64 (exp.f64 x) 2)
0.6b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.7b	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
5.9b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite79.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_1789`
238×	`*-un-lft-identity_binary64_1783`
156×	`add-sqr-sqrt_binary64_1805`
112×	`add-cube-cbrt_binary64_1818`
88×	`difference-of-sqr--1_binary64_1754`
63×	`distribute-lft-out_binary64_1734`
42×	`associate-/r*_binary64_1727`
25×	`unpow-prod-down_binary64_1862`
23×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
11×	`add-cbrt-cube_binary64_1819` `associate-/r/_binary64_1729` `associate-/l*_binary64_1728`
9×	`add-exp-log_binary64_1821`
7×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
6×	`div-inv_binary64_1780` `add-log-exp_binary64_1822`
5×	`pow1_binary64_1844`
4×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `pow-pow_binary64_1855`
3×	`pow-unpow_binary64_1860` `exp-prod_binary64_1835`
2×	`associate-/l/_binary64_1730` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`+-commutative_binary64_1713` `sum-log_binary64_1874` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 267

Calls

8 calls:

19.0ms	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
12.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.0ms	(pow.f64 (exp.f64 x) 2)
0.0ms	(+.f64 (exp.f64 x) 1)

series213.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

94.0ms	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
61.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
34.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
23.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 462 to 353 computations (23.6% saved)

simplify108.0ms (0%)

Algorithm

1×	egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5433	8094

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(*.f64 (exp.f64 x) (exp.f64 x))
0.0b	(+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1)))
0.0b	(+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 3)
0.8b	(.f64 (/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 1)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))))
0.8b	(/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 1))
5.9b	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

rewrite86.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

160×	`add-sqr-sqrt_binary64_1805`
99×	`*-un-lft-identity_binary64_1783`
97×	`times-frac_binary64_1789`
64×	`difference-of-squares_binary64_1752`
54×	`associate-l_binary64_1724`
51×	`add-cube-cbrt_binary64_1818`
32×	`difference-of-sqr-1_binary64_1753`
27×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
25×	`sqr-pow_binary64_1755`
16×	`associate-/r*_binary64_1727`
12×	`add-cbrt-cube_binary64_1819`
9×	`add-exp-log_binary64_1821`
8×	`distribute-lft-out--_binary64_1735`
7×	`pow1_binary64_1844`
6×	`add-log-exp_binary64_1822`
4×	`associate-/r/_binary64_1729` `pow-pow_binary64_1855`
3×	`flip3--_binary64_1787` `associate-/l_binary64_1728` `pow-unpow_binary64_1860` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758` `exp-prod_binary64_1835` `associate-r*_binary64_1723`
2×	`associate-*r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `frac-times_binary64_1793` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751`
1×	`rem-cube-cbrt_binary64_1806` `distribute-lft-in_binary64_1732` `cube-mult_binary64_1813` `unpow3_binary64_1849` `associate-l/_binary64_1726` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 213

Calls

8 calls:

32.0ms	(.f64 (/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 1)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))))
15.0ms	(/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 1))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
4.0ms	(pow.f64 (exp.f64 x) 3)
0.0ms	(+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))

series297.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

130.0ms	(.f64 (/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 1)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))))
79.0ms	(/.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 1))
51.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
36.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 728 to 518 computations (28.8% saved)

simplify111.0ms (0%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4971	5596
1	4971	5596

prune13.2s (3.9%)

Pruning

301 alts after pruning (295 fresh and 6 done)

	Pruned	Kept	Total
New	492	265	757
Fresh	7	30	37
Picked	0	0	0
Done	0	6	6
Total	499	301	800

Error

0.0b

Counts

800 → 301

Compiler

Compiled 18909 to 12035 computations (36.4% saved)

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 x 1/12)
0.0b	(+.f64 (*.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2))
0.0b	(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2)))
0.0b	(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2)))
0.0b	(+.f64 (*.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2))
0.3b	(*.f64 x 1/12)

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1805`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
7×	`add-cbrt-cube_binary64_1819` `pow1_binary64_1844`
6×	`add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`associate-+r+_binary64_1715`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`associate-r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `-commutative_binary64_1714` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`
1×	`+-commutative_binary64_1713` `distribute-lft-in_binary64_1732` `diff-log_binary64_1875` `distribute-rgt-in_binary64_1733` `sub-neg_binary64_1776` `associate-+r-_binary64_1717`

Counts

3 → 57

Calls

6 calls:

14.0ms	(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2)))
11.0ms	(+.f64 (*.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2))
4.0ms	(*.f64 x 1/12)
0.0ms	(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2)))
0.0ms	(+.f64 (*.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2))

series146.0ms (0%)

Counts

3 → 22

Calls

3 calls:

74.0ms	(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2)))
49.0ms	(+.f64 (*.f64 x 1/12) (-.f64 (/.f64 1 x) 1/2))
22.0ms	(*.f64 x 1/12)

Compiler

Compiled 316 to 251 computations (20.6% saved)

simplify75.0ms (0%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5037	1093

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(+.f64 (/.f64 1 x) 1/2)
0.1b	(+.f64 (/.f64 1 x) 1/2)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_1783`
3×	`add-log-exp_binary64_1822`
2×	`distribute-lft-out_binary64_1734`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `flip-+_binary64_1757` `div-inv_binary64_1780` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

7.0ms	(+.f64 (/.f64 1 x) 1/2)
0.0ms	(+.f64 (/.f64 1 x) 1/2)

series15.0ms (0%)

Counts

1 → 6

Calls

1 calls:

15.0ms

(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 35 to 37 computations (-5.7% saved)

simplify89.0ms (0%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4874	165
1	4874	165

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (/.f64 (exp.f64 x) (.f64 x 3)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1))))
0.0b	(*.f64 (exp.f64 x) (exp.f64 x))
0.0b	(+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1)))
0.0b	(+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))
0.0b	(+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1)))
0.0b	(*.f64 (exp.f64 x) (exp.f64 x))
0.2b	(.f64 (/.f64 (exp.f64 x) (.f64 x 3)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1))))
0.2b	(/.f64 (exp.f64 x) (*.f64 x 3))

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1805`
20×	`add-cbrt-cube_binary64_1819`
19×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
18×	`exp-prod_binary64_1835`
14×	`add-exp-log_binary64_1821`
13×	`pow1_binary64_1844`
10×	`associate-l_binary64_1724`
9×	`add-log-exp_binary64_1822`
6×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `times-frac_binary64_1789` `associate-r_binary64_1723`
5×	`pow-prod-down_binary64_1854`
4×	`pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
3×	`associate-/l*_binary64_1728` `swap-sqr_binary64_1750` `flip-+_binary64_1757` `sum-log_binary64_1874` `flip3-+_binary64_1786`
2×	`associate-r/_binary64_1725` `div-inv_binary64_1780` `-commutative_binary64_1714` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
1×	`associate-+r+_binary64_1715` `+-commutative_binary64_1713` `distribute-lft-in_binary64_1732` `pow-plus_binary64_1846` `associate-/r_binary64_1727` `associate-l/_binary64_1726` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `clear-num_binary64_1782` `pow2_binary64_1864`

Counts

4 → 101

Calls

8 calls:

19.0ms	(.f64 (/.f64 (exp.f64 x) (.f64 x 3)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1))))
16.0ms	(+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1)))
7.0ms	(*.f64 (exp.f64 x) (exp.f64 x))
5.0ms	(/.f64 (exp.f64 x) (*.f64 x 3))
0.0ms	(+.f64 (.f64 1 1) (.f64 (exp.f64 x) 1))

series173.0ms (0.1%)

Counts

4 → 14

Calls

4 calls:

89.0ms	(.f64 (/.f64 (exp.f64 x) (.f64 x 3)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1))))
32.0ms	(/.f64 (exp.f64 x) (*.f64 x 3))
27.0ms	(+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 1 1) (*.f64 (exp.f64 x) 1)))
25.0ms	(*.f64 (exp.f64 x) (exp.f64 x))

Compiler

Compiled 449 to 334 computations (25.6% saved)

simplify101.0ms (0%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4942	1781
1	4942	1781

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))
0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(exp.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
0.7b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
5.9b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite76.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`*-un-lft-identity_binary64_1783`
109×	`add-sqr-sqrt_binary64_1805`
80×	`times-frac_binary64_1789`
51×	`distribute-lft-out_binary64_1734`
49×	`exp-prod_binary64_1835`
48×	`difference-of-squares_binary64_1752`
37×	`add-cube-cbrt_binary64_1818`
15×	`unpow-prod-down_binary64_1862`
13×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
12×	`distribute-lft-out--_binary64_1735`
8×	`associate-/r*_binary64_1727`
7×	`add-log-exp_binary64_1822`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`associate-/l*_binary64_1728` `pow1_binary64_1844`
4×	`associate-/r/_binary64_1729` `pow-pow_binary64_1855`
3×	`flip3--_binary64_1787` `pow-unpow_binary64_1860` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758`
2×	`associate-/l/_binary64_1730` `div-inv_binary64_1780`
1×	`rem-exp-log_binary64_1823` `flip-+_binary64_1757` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 163

Calls

8 calls:

21.0ms	(exp.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
21.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(pow.f64 (exp.f64 x) 2)
0.0ms	(+.f64 (exp.f64 x) 1)

series312.0ms (0.1%)

Counts

4 → 21

Calls

4 calls:

132.0ms	(exp.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
109.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
46.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
25.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 600 to 471 computations (21.5% saved)

simplify119.0ms (0%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5022	5360

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 (exp.f64 x) 1)
0.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))) (/.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (+.f64 (exp.f64 x) -1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))))
1.3b	(/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
1.3b	(/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))
5.9b	(+.f64 (exp.f64 x) -1)

rewrite1.5s (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

2211×	`times-frac_binary64_1789`
1467×	`*-un-lft-identity_binary64_1783`
1349×	`add-sqr-sqrt_binary64_1805`
789×	`add-cube-cbrt_binary64_1818`
575×	`sqrt-prod_binary64_1799`
456×	`unpow-prod-down_binary64_1862`
399×	`cbrt-prod_binary64_1814`
379×	`associate-l_binary64_1724`
339×	`distribute-lft-out_binary64_1734`
251×	`associate-r_binary64_1723`
112×	`unswap-sqr_binary64_1751`
103×	`add-exp-log_binary64_1821`
90×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
63×	`associate-/r/_binary64_1729`
60×	`sqrt-div_binary64_1800`
58×	`div-exp_binary64_1834`
43×	`difference-of-sqr--1_binary64_1754`
41×	`add-cbrt-cube_binary64_1819` `associate-/r*_binary64_1727`
33×	`div-inv_binary64_1780`
32×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
22×	`cbrt-undiv_binary64_1817`
21×	`prod-exp_binary64_1832`
15×	`associate-/l*_binary64_1728`
9×	`cbrt-unprod_binary64_1816` `pow1_binary64_1844`
8×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
6×	`add-log-exp_binary64_1822`
2×	`associate-/l/_binary64_1730` `pow-div_binary64_1858` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `pow1/2_binary64_1863` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `sum-log_binary64_1874` `frac-times_binary64_1793` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854`

Counts

4 → 1000

Calls

8 calls:

1.2s	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))) (/.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (+.f64 (exp.f64 x) -1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))))
32.0ms	(/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
11.0ms	(/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))
5.0ms	(+.f64 (exp.f64 x) -1)
0.0ms	(+.f64 (exp.f64 x) 1)

series305.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

172.0ms	(/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
55.0ms	(/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))
51.0ms	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))) (/.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (+.f64 (exp.f64 x) -1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))))
27.0ms	(+.f64 (exp.f64 x) -1)

Compiler

Compiled 944 to 705 computations (25.3% saved)

simplify490.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1024 → 1024

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4981	51136
1	4981	51136

prune1.0min (18.4%)

Pruning

733 alts after pruning (723 fresh and 10 done)

	Pruned	Kept	Total
New	944	477	1421
Fresh	44	246	290
Picked	0	0	0
Done	1	10	11
Total	989	733	1722

Error

0.0b

Counts

1722 → 733

Compiler

Compiled 56838 to 35870 computations (36.9% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(+.f64 (.f64 (.f64 x 1/12) (exp.f64 x)) (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))
0.3b	(*.f64 x 1/12)
0.0b	(.f64 (.f64 x 1/12) (exp.f64 x))
0.0b	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
0.0b	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
0.0b	(.f64 (.f64 x 1/12) (exp.f64 x))
0.3b	(*.f64 x 1/12)
0.6b	(+.f64 (.f64 (.f64 x 1/12) (exp.f64 x)) (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1805`
13×	`add-cbrt-cube_binary64_1819` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
12×	`associate-l_binary64_1724`
10×	`add-exp-log_binary64_1821`
9×	`add-cube-cbrt_binary64_1818` `associate-r_binary64_1723`
6×	`add-log-exp_binary64_1822`
5×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
3×	`difference-of-squares_binary64_1752` `*-commutative_binary64_1714`
2×	`distribute-lft-out--_binary64_1735` `associate-*l/_binary64_1726` `times-frac_binary64_1789` `unswap-sqr_binary64_1751`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `distribute-rgt-out_binary64_1736` `flip-+_binary64_1757` `div-inv_binary64_1780` `sum-log_binary64_1874` `flip3-+_binary64_1786` `flip--_binary64_1758`

Counts

4 → 73

Calls

8 calls:

12.0ms	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
9.0ms	(+.f64 (.f64 (.f64 x 1/12) (exp.f64 x)) (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))
9.0ms	(.f64 (.f64 x 1/12) (exp.f64 x))
4.0ms	(*.f64 x 1/12)
0.0ms	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))

series180.0ms (0.1%)

Counts

4 → 27

Calls

4 calls:

84.0ms	(+.f64 (.f64 (.f64 x 1/12) (exp.f64 x)) (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))
39.0ms	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
38.0ms	(.f64 (.f64 x 1/12) (exp.f64 x))
18.0ms	(*.f64 x 1/12)

Compiler

Compiled 514 to 384 computations (25.3% saved)

simplify79.0ms (0%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4937	1287
1	4937	1287

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(+.f64 (/.f64 1 x) 1/2)
0.1b	(+.f64 (/.f64 1 x) 1/2)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_1783`
3×	`add-log-exp_binary64_1822`
2×	`distribute-lft-out_binary64_1734`
1×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `flip-+_binary64_1757` `div-inv_binary64_1780` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow1_binary64_1844`

Counts

1 → 13

Calls

2 calls:

7.0ms	(+.f64 (/.f64 1 x) 1/2)
0.0ms	(+.f64 (/.f64 1 x) 1/2)

series17.0ms (0%)

Counts

1 → 6

Calls

1 calls:

17.0ms

(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 53 to 55 computations (-3.8% saved)

simplify90.0ms (0%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4874	165
1	4874	165

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(pow.f64 (exp.f64 x) 2)
0.7b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
5.9b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`*-un-lft-identity_binary64_1783`
68×	`add-sqr-sqrt_binary64_1805`
40×	`times-frac_binary64_1789`
28×	`difference-of-squares_binary64_1752`
27×	`distribute-lft-out_binary64_1734`
26×	`add-cube-cbrt_binary64_1818`
13×	`unpow-prod-down_binary64_1862`
9×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
8×	`associate-/r*_binary64_1727` `pow-pow_binary64_1855`
7×	`distribute-lft-out--_binary64_1735`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow-unpow_binary64_1860` `exp-prod_binary64_1835` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`associate-/l*_binary64_1728`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`flip-+_binary64_1757` `div-inv_binary64_1780` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

4 → 130

Calls

8 calls:

19.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(pow.f64 (exp.f64 x) 2)
3.0ms	(pow.f64 (exp.f64 x) 2)
0.0ms	(+.f64 (exp.f64 x) 1)

series206.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

110.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
42.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
28.0ms	(pow.f64 (exp.f64 x) 2)
25.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 656 to 519 computations (20.9% saved)

simplify107.0ms (0%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4968	3973
1	4968	3973

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))
0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(log.f64 (exp.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x)))))))
0.0b	(exp.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x))))))
0.6b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x)))))
0.7b	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x)))))
5.9b	(-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x))))

rewrite390.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1376×	`*-un-lft-identity_binary64_1783`
1328×	`times-frac_binary64_1789`
1225×	`add-sqr-sqrt_binary64_1805`
540×	`difference-of-squares_binary64_1752`
514×	`distribute-lft-out_binary64_1734`
381×	`sqrt-prod_binary64_1799`
370×	`exp-prod_binary64_1835`
361×	`add-cube-cbrt_binary64_1818`
216×	`unpow-prod-down_binary64_1862`
108×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
64×	`associate-/r/_binary64_1729`
54×	`distribute-lft-out--_binary64_1735`
32×	`div-inv_binary64_1780`
31×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786`
18×	`associate-/r*_binary64_1727`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
7×	`add-log-exp_binary64_1822`
6×	`cancel-sign-sub-inv_binary64_1749`
4×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `pow1_binary64_1844`
3×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `flip--_binary64_1758`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`rem-exp-log_binary64_1823` `diff-log_binary64_1875` `sub-neg_binary64_1776`

Counts

4 → 872

Calls

8 calls:

79.0ms	(exp.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x))))))
39.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x)))))
19.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x)))))
11.0ms	(-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x))))
0.0ms	(log.f64 (exp.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x)))))))

series514.0ms (0.2%)

Counts

4 → 21

Calls

4 calls:

190.0ms	(exp.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x))))))
180.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x))))) (-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x)))))
98.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 x) (sqrt.f64 (exp.f64 (neg.f64 x)))))
46.0ms	(-.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 2) (sqrt.f64 (exp.f64 (neg.f64 x))))

Compiler

Compiled 764 to 547 computations (28.4% saved)

simplify474.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

893 → 893

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4947	51534
1	4947	51534

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 (exp.f64 x) 1)
0.8b	(/.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (+.f64 (exp.f64 x) -1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
1.3b	(/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))
1.4b	(/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x))) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
5.9b	(+.f64 (exp.f64 x) -1)

rewrite313.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1415×	`times-frac_binary64_1789`
1138×	`*-un-lft-identity_binary64_1783`
662×	`add-sqr-sqrt_binary64_1805`
612×	`add-cube-cbrt_binary64_1818`
441×	`cbrt-prod_binary64_1814`
400×	`sqrt-prod_binary64_1799`
315×	`unpow-prod-down_binary64_1862`
263×	`distribute-lft-out_binary64_1734`
82×	`associate-/r*_binary64_1727`
50×	`difference-of-sqr--1_binary64_1754`
48×	`associate-/r/_binary64_1729`
46×	`sqrt-div_binary64_1800`
35×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
25×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786`
24×	`associate-/l*_binary64_1728` `add-exp-log_binary64_1821`
14×	`add-cbrt-cube_binary64_1819`
13×	`div-exp_binary64_1834`
7×	`cbrt-undiv_binary64_1817` `pow1_binary64_1844`
6×	`add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`associate-/l/_binary64_1730` `pow-div_binary64_1858` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`+-commutative_binary64_1713` `pow1/2_binary64_1863` `sum-log_binary64_1874` `sqrt-pow1_binary64_1801`

Counts

4 → 921

Calls

8 calls:

28.0ms	(/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x))) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
22.0ms	(/.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (+.f64 (exp.f64 x) -1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
11.0ms	(/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))
10.0ms	(+.f64 (exp.f64 x) -1)
0.0ms	(+.f64 (exp.f64 x) 1)

series440.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

186.0ms	(/.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (+.f64 (exp.f64 x) -1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
170.0ms	(/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x))) 2) (/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1))))
49.0ms	(/.f64 (+.f64 (exp.f64 x) 1) (sqrt.f64 (+.f64 (exp.f64 x) 1)))
36.0ms	(+.f64 (exp.f64 x) -1)

Compiler

Compiled 1762 to 1272 computations (27.8% saved)

simplify402.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

945 → 945

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5762	41009

prune2.5min (44.5%)

Pruning

1133 alts after pruning (1119 fresh and 14 done)

	Pruned	Kept	Total
New	1643	468	2111
Fresh	67	651	718
Picked	0	0	0
Done	1	14	15
Total	1711	1133	2844

Error

Counts

2844 → 1133

Compiler

Compiled 45879 to 23134 computations (49.6% saved)

simplify2.5s (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	6957	140768

regimes22.0s (6.6%)

Compiler: Compiled 300664 to 193782 computations (35.5% saved)

bsearch0.0ms (0%)

regimes1.4s (0.4%)

Compiler: Compiled 13052 to 10193 computations (21.9% saved)

bsearch9.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

regimes1.5s (0.4%)

Compiler: Compiled 12555 to 9828 computations (21.7% saved)

bsearch0.0ms (0%)

regimes475.0ms (0.1%)

Compiler: Compiled 4543 to 3686 computations (18.9% saved)

bsearch0.0ms (0%)

regimes63.0ms (0%)

Compiler: Compiled 230 to 210 computations (8.7% saved)

bsearch16.0ms (0%)

Steps

Iters	Range		Point
9	-0.006878606696061898	-4.104631650491468e-11	-7.720461622783971e-06

Compiler

Compiled 1 to 1 computations (0% saved)

regimes33.0ms (0%)

Compiler: Compiled 141 to 134 computations (5% saved)

bsearch0.0ms (0%)

regimes38.0ms (0%)

Compiler: Compiled 107 to 104 computations (2.8% saved)

bsearch12.0ms (0%)

Steps

Iters	Range		Point
7	-455.97378299735567	-1.999530549370125	-354.81276147133286

Compiler

Compiled 1 to 1 computations (0% saved)

regimes28.0ms (0%)

Compiler: Compiled 52 to 56 computations (-7.7% saved)

bsearch11.0ms (0%)

Steps

Iters	Range		Point
7	-455.97378299735567	-1.999530549370125	-2.05985498186887

Compiler

Compiled 1 to 1 computations (0% saved)

regimes15.0ms (0%)

Compiler: Compiled 9 to 13 computations (-44.4% saved)

bsearch10.0ms (0%)

Steps

Iters	Range		Point
7	-455.97378299735567	-1.999530549370125	-354.81276147133286

Compiler

Compiled 1 to 1 computations (0% saved)

regimes16.0ms (0%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch55.0ms (0%)

Steps

Iters	Range		Point
9	-5.316121818640865e-304	3.716692992538301e-307	5.758332088306613e-309

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0%)

Accuracy

Total 0.9b remaining (99.8%)

Threshold costs 0.9b (99.8%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch12.0ms (0%)

Compiler: Compiled 128 to 107 computations (16.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	73	190
1	73	190

end0.0ms (0%)

sample1.2min (22%)

Algorithm

1×

intervals

Results

377.0ms	2601×	body	1024	valid
107.0ms	1355×	body	512	valid
76.0ms	3076×	body	128	valid
44.0ms	267×	body	2048	valid
35.0ms	701×	body	256	valid

Compiler

Compiled 82094 to 52831 computations (35.6% saved)

Pareto

0.9759565732846899