Details

analyze151.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify344.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5044	25

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
0.2b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1783`
11×	`add-log-exp_binary64_1798`
10×	`*-un-lft-identity_binary64_1762` `add-exp-log_binary64_1797` `pow1_binary64_1820`
9×	`add-cbrt-cube_binary64_1795`
7×	`add-cube-cbrt_binary64_1794`
3×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `pow-unpow_binary64_1836` `associate-l_binary64_1705` `unpow-prod-down_binary64_1838`
2×	`diff-log_binary64_1851` `difference-of-squares_binary64_1731` `sum-log_binary64_1850`
1×	`flip3--_binary64_1766` `difference-of-sqr-1_binary64_1732` `sqr-pow_binary64_1734` `flip3-+_binary64_1765` `unpow2_binary64_1824` `flip-+_binary64_1736` `unswap-sqr_binary64_1730` `+-commutative_binary64_1694` `pow-exp_binary64_1827` `distribute-lft-out--_binary64_1716` `flip--_binary64_1737` `pow-pow_binary64_1831` `sub-neg_binary64_1755` `-commutative_binary64_1695` `pow-to-exp_binary64_1828` `associate--l+_binary64_1701` `associate-r*_binary64_1704`

Counts

4 → 65

Calls

4 calls:

23.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
17.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
12.0ms	(.f64 4 (.f64 b b))
11.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series526.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
161.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
111.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
75.0ms	(.f64 4 (.f64 b b))

simplify166.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4990	1617
1	4990	1617

prune159.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	3	78

Merged error: 0b

Counts

78 → 3

Compiler

Compiled 1894 to 904 computations (52.3% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
0.0b	(-.f64 (+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
0.0b	(.f64 4 (.f64 b b))
1.9b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite129.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
23×	`add-log-exp_binary64_1798`
18×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
10×	`add-sqr-sqrt_binary64_1783`
9×	`sum-log_binary64_1850`
8×	`*-un-lft-identity_binary64_1762`
5×	`add-cube-cbrt_binary64_1794`
4×	`diff-log_binary64_1851` `associate-l_binary64_1705`
2×	`difference-of-squares_binary64_1731` `-commutative_binary64_1695` `associate-r*_binary64_1704`
1×	`flip3--_binary64_1766` `difference-of-sqr-1_binary64_1732` `flip3-+_binary64_1765` `flip-+_binary64_1736` `unswap-sqr_binary64_1730` `+-commutative_binary64_1694` `distribute-lft-out--_binary64_1716` `flip--_binary64_1737` `sub-neg_binary64_1755` `associate--l+_binary64_1701` `associate-+r+_binary64_1696`

Counts

4 → 79

Calls

4 calls:

45.0ms	(-.f64 (+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
33.0ms	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
18.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
13.0ms	(.f64 4 (.f64 b b))

series505.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(-.f64 (+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
141.0ms	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
102.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
74.0ms	(.f64 4 (.f64 b b))

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5228	1994

prune239.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Merged error: 0b

Counts

94 → 3

Compiler

Compiled 2774 to 1816 computations (34.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))
19.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
19.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
19.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

rewrite104.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`cbrt-prod_binary64_1790`
52×	`add-sqr-sqrt_binary64_1783`
31×	`unpow-prod-down_binary64_1838`
25×	`unswap-sqr_binary64_1730`
22×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
17×	`sqr-pow_binary64_1734` `unpow2_binary64_1824`
11×	`swap-sqr_binary64_1729` `pow1_binary64_1820` `associate-l_binary64_1705` `associate-r_binary64_1704`
9×	`pow1/3_binary64_1841`
6×	`add-exp-log_binary64_1797`
4×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795`
2×	`pow-sqr_binary64_1735` `pow-prod-down_binary64_1830` `pow-prod-up_binary64_1829`
1×	`prod-exp_binary64_1808` `pow-plus_binary64_1822` `cbrt-unprod_binary64_1792` `*-commutative_binary64_1695` `pow2_binary64_1840`

Counts

4 → 124

Calls

4 calls:

35.0ms	(.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))
11.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
11.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
10.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

series1.2s (15%)

Counts

4 → 12

Calls

4 calls:

323.0ms	(.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))
288.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
283.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
259.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

simplify187.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4914	3517
1	4914	3517

prune404.0ms (5.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	136	3	139

Merged error: 0b

Counts

139 → 3

Compiler

Compiled 6130 to 2359 computations (61.5% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (*.f64 16 (pow.f64 b 4)))
0.2b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
38.3b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))

rewrite92.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
9×	`times-frac_binary64_1768`
8×	`add-exp-log_binary64_1797`
6×	`add-log-exp_binary64_1798` `pow-unpow_binary64_1836` `add-cbrt-cube_binary64_1795` `pow1_binary64_1820` `unpow-prod-down_binary64_1838`
3×	`flip3--_binary64_1766` `associate-/r_binary64_1708` `flip--_binary64_1737` `associate-/l_binary64_1709`
2×	`associate-/r/_binary64_1710` `sqr-pow_binary64_1734` `associate-/l/_binary64_1711` `pow-exp_binary64_1827` `pow-pow_binary64_1831` `pow-to-exp_binary64_1828`
1×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `div-sub_binary64_1767` `unpow2_binary64_1824` `clear-num_binary64_1761` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `sub-neg_binary64_1755`

Counts

4 → 78

Calls

4 calls:

34.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))
17.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (*.f64 16 (pow.f64 b 4)))
11.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
11.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)

series1.6s (20.2%)

Counts

4 → 12

Calls

4 calls:

592.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (*.f64 16 (pow.f64 b 4)))
568.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))
306.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
88.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify129.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4965	2937
1	4965	2937

prune241.0ms (3.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	90	3	93

Merged error: 0b

Counts

93 → 3

Compiler

Compiled 3760 to 1808 computations (51.9% saved)

regimes106.0ms (1.4%)

Compiler: Compiled 487 to 307 computations (37% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	37
1	35	37

end0.0ms (0%)

sample1.2s (15.5%)

Algorithm

1×

intervals

Results

683.0ms	8000×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 141 to 94 computations (33.3% saved)

Details

analyze151.0ms (2%)

sample30.0ms (0.4%)

simplify344.0ms (4.5%)

prune5.0ms (0.1%)

localize19.0ms (0.3%)

rewrite74.0ms (1%)

series526.0ms (6.8%)

simplify166.0ms (2.2%)

prune159.0ms (2.1%)

localize30.0ms (0.4%)

rewrite129.0ms (1.7%)

series505.0ms (6.6%)

simplify89.0ms (1.2%)

prune239.0ms (3.1%)

localize26.0ms (0.3%)

rewrite104.0ms (1.4%)

series1.2s (15%)

simplify187.0ms (2.4%)

prune404.0ms (5.3%)

localize30.0ms (0.4%)

rewrite92.0ms (1.2%)

series1.6s (20.2%)

simplify129.0ms (1.7%)

prune241.0ms (3.1%)

regimes106.0ms (1.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (15.5%)

Profiling