Details

analyze361.0ms (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample72.0ms (1.1%)

Algorithm

1×

intervals

Results

32.0ms	75×	body	1024	valid
13.0ms	38×	body	2048	valid
9.0ms	31×	body	512	valid
5.0ms	84×	body	128	valid
4.0ms	28×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune5.0ms (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

Error

51.2b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
0.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1783`
8×	`add-log-exp_binary64_1822`
7×	`add-sqr-sqrt_binary64_1805`
6×	`add-cube-cbrt_binary64_1818` `pow1_binary64_1844`
5×	`add-exp-log_binary64_1821`
4×	`add-cbrt-cube_binary64_1819` `log-prod_binary64_1869` `flip-+_binary64_1757` `flip3-+_binary64_1786`
3×	`sqrt-prod_binary64_1799`
2×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800` `sum-log_binary64_1874` `log-div_binary64_1870`
1×	`log-pow_binary64_1872` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rem-log-exp_binary64_1824`

Counts

4 → 53

Calls

4 calls:

16.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
12.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(+.f64 (*.f64 x x) 1)

series163.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
51.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
32.0ms	(+.f64 (*.f64 x x) 1)
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4855	1001
1	4855	1001

prune118.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Error

Counts

66 → 5

Compiler

Compiled 1017 to 668 computations (34.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.0b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1805`
15×	`associate-l_binary64_1724`
13×	`add-exp-log_binary64_1821`
10×	`add-cube-cbrt_binary64_1818` `-un-lft-identity_binary64_1783` `associate-r*_binary64_1723`
8×	`unpow-prod-down_binary64_1862` `add-log-exp_binary64_1822`
7×	`add-cbrt-cube_binary64_1819` `unswap-sqr_binary64_1751`
6×	`prod-exp_binary64_1832`
4×	`sqr-pow_binary64_1755` `cube-prod_binary64_1811`
3×	`pow1_binary64_1844`
2×	`cbrt-unprod_binary64_1816` `diff-log_binary64_1875` `*-commutative_binary64_1714` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`flip3--_binary64_1787` `cube-mult_binary64_1813` `unpow3_binary64_1849` `cancel-sign-sub-inv_binary64_1749` `sum-log_binary64_1874` `associate--l+_binary64_1720` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

3 → 70

Calls

3 calls:

6.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
5.0ms	(*.f64 3/40 (pow.f64 x 5))

series131.0ms (2%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
48.0ms	(*.f64 3/40 (pow.f64 x 5))
23.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5018	1015

prune150.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	79	5	84

Error

Counts

84 → 5

Compiler

Compiled 1483 to 1149 computations (22.5% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2))
0.2b	(/.f64 3/32 (pow.f64 x 4))
0.4b	(/.f64 1/4 (*.f64 x x))
6.6b	(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x)))

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64_1783`
37×	`add-sqr-sqrt_binary64_1805`
27×	`times-frac_binary64_1789`
25×	`add-cube-cbrt_binary64_1818`
17×	`distribute-lft-out--_binary64_1735`
14×	`add-exp-log_binary64_1821`
13×	`cancel-sign-sub-inv_binary64_1749` `unpow-prod-down_binary64_1862` `add-log-exp_binary64_1822` `pow1_binary64_1844`
11×	`add-cbrt-cube_binary64_1819`
9×	`log-pow_binary64_1872`
8×	`distribute-lft-out_binary64_1734` `associate-/r*_binary64_1727`
6×	`associate-/l*_binary64_1728` `diff-log_binary64_1875`
5×	`difference-of-squares_binary64_1752` `sqr-pow_binary64_1755` `div-exp_binary64_1834` `associate--r+_binary64_1719`
4×	`frac-sub_binary64_1792`
3×	`flip3--_binary64_1787` `associate-+r+_binary64_1715` `log-prod_binary64_1869` `flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `sum-log_binary64_1874` `flip3-+_binary64_1786` `flip--_binary64_1758`
2×	`div-inv_binary64_1780` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `sub-neg_binary64_1776`
1×	`+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate--r-_binary64_1722` `associate--l+_binary64_1720` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 126

Calls

4 calls:

49.0ms	(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x)))
8.0ms	(+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2))
5.0ms	(/.f64 3/32 (pow.f64 x 4))
4.0ms	(/.f64 1/4 (*.f64 x x))

series216.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2))
49.0ms	(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x)))
35.0ms	(/.f64 3/32 (pow.f64 x 4))
17.0ms	(/.f64 1/4 (*.f64 x x))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4966	2840
1	4966	2840

prune265.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	138	5	143

Error

Counts

143 → 5

Compiler

Compiled 3346 to 2301 computations (31.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.2b	(/.f64 1/8 (pow.f64 x 3))
9.0b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite141.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64_1789`
97×	`*-un-lft-identity_binary64_1783`
87×	`add-sqr-sqrt_binary64_1805`
80×	`cancel-sign-sub-inv_binary64_1749`
74×	`add-cube-cbrt_binary64_1818`
42×	`associate-+r+_binary64_1715`
31×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
18×	`add-log-exp_binary64_1822`
12×	`associate-/r*_binary64_1727`
11×	`sqr-pow_binary64_1755`
10×	`add-exp-log_binary64_1821` `cube-mult_binary64_1813` `unpow3_binary64_1849`
9×	`distribute-lft-out_binary64_1734`
6×	`add-cbrt-cube_binary64_1819` `log-prod_binary64_1869` `distribute-lft-out--_binary64_1735`
5×	`difference-of-squares_binary64_1752` `sum-log_binary64_1874` `pow1_binary64_1844`
4×	`diff-log_binary64_1875`
3×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `div-inv_binary64_1780` `div-exp_binary64_1834` `flip3-+_binary64_1786`
2×	`frac-sub_binary64_1792` `associate--l+_binary64_1720` `sub-neg_binary64_1776` `log-div_binary64_1870`
1×	`flip3--_binary64_1787` `log-pow_binary64_1872` `+-commutative_binary64_1713` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `rem-log-exp_binary64_1824` `associate-+r-_binary64_1717`

Counts

4 → 203

Calls

4 calls:

41.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
31.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
26.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))

series156.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
34.0ms	(/.f64 1/8 (pow.f64 x 3))
23.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
19.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4897	3393
1	4897	3393

prune385.0ms (5.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	215	5	220

Error

Counts

220 → 5

Compiler

Compiled 4392 to 3145 computations (28.4% saved)

regimes215.0ms (3.3%)

Accuracy

Total 0.2b remaining (95.4%)

Threshold costs 0.2b (95.4%)

Compiler

Compiled 1165 to 887 computations (23.9% saved)

bsearch47.0ms (0.7%)

Steps

Iters	Range		Point
6	0.7761437014994341	4.458122573049154	1.0126904852337015
10	-38395.577244555956	-6.566193378159182e-06	-1.071505362580263

Compiler

Compiled 1 to 1 computations (0% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	277	81
1	277	81

end0.0ms (0%)

sample3.4s (52%)

Algorithm

1×

intervals

Results

1.3s	2445×	body	1024	valid
559.0ms	1202×	body	2048	valid
357.0ms	1238×	body	512	valid
156.0ms	2433×	body	128	valid
104.0ms	645×	body	256	valid
23.0ms	37×	body	4096	valid

Compiler

Compiled 403 to 310 computations (23.1% saved)

Details

analyze361.0ms (5.6%)

sample72.0ms (1.1%)

simplify120.0ms (1.8%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

rewrite45.0ms (0.7%)

series163.0ms (2.5%)

simplify73.0ms (1.1%)

prune118.0ms (1.8%)

localize10.0ms (0.2%)

rewrite23.0ms (0.4%)

series131.0ms (2%)

simplify83.0ms (1.3%)

prune150.0ms (2.3%)

localize27.0ms (0.4%)

rewrite77.0ms (1.2%)

series216.0ms (3.3%)

simplify83.0ms (1.3%)

prune265.0ms (4.1%)

localize18.0ms (0.3%)

rewrite141.0ms (2.2%)

series156.0ms (2.4%)

simplify119.0ms (1.8%)

prune385.0ms (5.9%)

regimes215.0ms (3.3%)

bsearch47.0ms (0.7%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.4s (52%)

Profiling