Details

analyze123.0ms (1.6%)

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%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample24.0ms (0.3%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify154.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5029	46

prune3.0ms (0%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
14×	`add-cbrt-cube_binary64_1819`
10×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
8×	`add-cube-cbrt_binary64_1818`
7×	`associate-r_binary64_1723`
6×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
4×	`associate-*r/_binary64_1725` `distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
3×	`pow-unpow_binary64_1860` `unpow-prod-down_binary64_1862`
2×	`associate-+r+_binary64_1715` `flip-+_binary64_1757` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `sqr-pow_binary64_1755` `distribute-lft-out_binary64_1734` `unpow2_binary64_1848` `sum-log_binary64_1874` `pow-pow_binary64_1855` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 80

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series639.0ms (8.5%)

Counts

4 → 43

Calls

4 calls:

348.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
202.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
67.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
22.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2019 to 1634 computations (19.1% saved)

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5866	2515

prune203.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	4	124

Merged error: 0.0b

Counts

124 → 4

Compiler

Compiled 4554 to 2508 computations (44.9% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.6b	(.f64 (.f64 b b) (*.f64 a a))

rewrite62.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_1844`
32×	`associate-*r/_binary64_1725`
26×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
20×	`frac-add_binary64_1791` `pow-prod-down_binary64_1854`
14×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `flip3-+_binary64_1786`
13×	`add-log-exp_binary64_1822`
8×	`add-sqr-sqrt_binary64_1805` `-un-lft-identity_binary64_1783` `associate-r*_binary64_1723`
6×	`add-cube-cbrt_binary64_1818` `sum-log_binary64_1874`
5×	`flip3--_binary64_1787` `flip--_binary64_1758`
4×	`distribute-lft-in_binary64_1732` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `distribute-rgt-in_binary64_1733`
3×	`associate-l_binary64_1724` `*-commutative_binary64_1714` `unswap-sqr_binary64_1751`
2×	`associate-+r+_binary64_1715` `cancel-sign-sub-inv_binary64_1749` `pow-sqr_binary64_1756` `sub-neg_binary64_1776` `pow2_binary64_1864`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `associate-+l+_binary64_1716`

Counts

4 → 106

Calls

4 calls:

17.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
11.0ms	(.f64 (.f64 b b) (*.f64 a a))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series529.0ms (7.1%)

Counts

4 → 31

Calls

4 calls:

345.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
86.0ms	(.f64 (.f64 b b) (*.f64 a a))
69.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
28.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 1779 to 1428 computations (19.7% saved)

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4982	5352
1	4982	5352

prune346.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	137	4	141

Merged error: 0.0b

Counts

141 → 4

Compiler

Compiled 7294 to 4293 computations (41.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
8.1b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
8.1b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64_1844`
14×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
12×	`add-sqr-sqrt_binary64_1805`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-prod_binary64_1799` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
4×	`associate-*r/_binary64_1725` `distribute-lft-in_binary64_1732` `cancel-sign-sub-inv_binary64_1749` `sqrt-div_binary64_1800` `distribute-rgt-in_binary64_1733` `sub-neg_binary64_1776` `add-log-exp_binary64_1822`
2×	`flip3--_binary64_1787` `flip-+_binary64_1757` `pow1/2_binary64_1863` `associate-l_binary64_1724` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758`

Counts

4 → 80

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))

series673.0ms (9%)

Counts

4 → 46

Calls

4 calls:

270.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
260.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
72.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
70.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

Compiler

Compiled 4796 to 3476 computations (27.5% saved)

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5149	3506

prune362.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	126	4	130

Merged error: 0.0b

Counts

130 → 4

Compiler

Compiled 8519 to 4598 computations (46% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
8.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
8.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
8.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `cbrt-prod_binary64_1814` `pow1_binary64_1844`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`cbrt-div_binary64_1815`
4×	`add-log-exp_binary64_1822`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1/3_binary64_1865` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
2×	`associate-*r/_binary64_1725` `distribute-lft-in_binary64_1732` `cancel-sign-sub-inv_binary64_1749` `distribute-rgt-in_binary64_1733` `sub-neg_binary64_1776`
1×	`flip3--_binary64_1787` `associate-l_binary64_1724` `*-commutative_binary64_1714` `unswap-sqr_binary64_1751` `flip--_binary64_1758`

Counts

4 → 64

Calls

4 calls:

9.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))

series1.8s (23.9%)

Counts

4 → 45

Calls

4 calls:

578.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
570.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
557.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))) (.f64 (.f64 a a) (+.f64 1 a))))))
86.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

Compiler

Compiled 8315 to 5877 computations (29.3% saved)

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4940	4713
1	4940	4713

prune519.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Merged error: 0.0b

Counts

113 → 4

Compiler

Compiled 11161 to 6014 computations (46.1% saved)

regimes285.0ms (3.8%)

Compiler: Compiled 5009 to 3190 computations (36.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	58
1	79	58

end0.0ms (0%)

sample1.2s (16.5%)

Algorithm

1×

intervals

Results

527.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 908 to 583 computations (35.8% saved)

Details

analyze123.0ms (1.6%)

sample24.0ms (0.3%)

simplify154.0ms (2.1%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite39.0ms (0.5%)

series639.0ms (8.5%)

simplify54.0ms (0.7%)

prune203.0ms (2.7%)

localize21.0ms (0.3%)

rewrite62.0ms (0.8%)

series529.0ms (7.1%)

simplify99.0ms (1.3%)

prune346.0ms (4.6%)

localize24.0ms (0.3%)

rewrite45.0ms (0.6%)

series673.0ms (9%)

simplify84.0ms (1.1%)

prune362.0ms (4.8%)

localize25.0ms (0.3%)

rewrite46.0ms (0.6%)

series1.8s (23.9%)

simplify87.0ms (1.2%)

prune519.0ms (6.9%)

regimes285.0ms (3.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (16.5%)

Profiling