Details

analyze240.0ms (5.9%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.2s (28.3%)

Results

946.0ms	8256×	body	128	valid
174.0ms	1561×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
10×	`fma-def_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	35	10
3	41	10
4	39	10

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 66 to 47 computations (28.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	0.3b	(*.f64 y (sqrt.f64 z))

series24.0ms (0.6%)

Counts

2 → 16

Calls

2 calls:

14.0ms	(*.f64 y (sqrt.f64 z))
10.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms	(*.f64 y (sqrt.f64 z))
2.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

simplify109.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-neg_binary64`
773×	`fma-def_binary64`
544×	`distribute-rgt-in_binary64`
537×	`unsub-neg_binary64`
453×	`distribute-lft-in_binary64`

Counts

56 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	469
1	148	454
2	387	452
3	951	452
4	2044	452
5	3250	452
6	4140	452
7	4878	452
8	4998	452
9	4834	452

prune43.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	47	7	54

Error

0.0b

Counts

54 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (cbrt.f64 (sqrt.f64 z)))))
	0.7b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (sqrt.f64 z)))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))
	32.9b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)) (sqrt.f64 z))))))

Compiler

Compiled 1055 to 547 computations (48.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
✓	0.1b	(sqrt.f64 (sqrt.f64 z))
✓	0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

series233.0ms (5.7%)

Counts

4 → 65

Calls

4 calls:

192.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
20.0ms	(sqrt.f64 (sqrt.f64 z))
12.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
9.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
5.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
2.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
1.0ms	(sqrt.f64 (sqrt.f64 z))

simplify154.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
518×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
278×	`unsub-neg_binary64`
230×	`fma-neg_binary64`

Counts

156 → 116

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	103	1305
1	232	1272
2	689	1265
3	1315	1265
4	2693	1265
5	4269	1265
6	4492	1265
7	4845	1247
8	4996	1247
9	4819	1247

prune122.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Error

Counts

145 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (fabs.f64 (cbrt.f64 (sqrt.f64 z)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 z))))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))
	32.9b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)) (sqrt.f64 z))))))

Compiler

Compiled 2968 to 1249 computations (57.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2))
✓	0.3b	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
✓	0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)

series672.0ms (16.5%)

Counts

4 → 48

Calls

4 calls:

324.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)
318.0ms	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2))
19.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
10.0ms	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`sqrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
21×	`unpow-prod-down_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 122

Calls

4 calls:

8.0ms	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
8.0ms	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2))
3.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)
2.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))

simplify105.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

780×	`associate-/l*_binary64`
402×	`sqr-pow_binary64`
323×	`*-commutative_binary64`
287×	`associate-+l+_binary64`
226×	`fma-def_binary64`

Counts

170 → 151

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	136	2134
1	262	2041
2	763	2041
3	1063	1875
4	1870	1781
5	3547	1669
6	5075	1669

prune150.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	152	6	158

Error

Counts

158 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (fabs.f64 (cbrt.f64 (sqrt.f64 z)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 z))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))

Compiler

Compiled 3721 to 1959 computations (47.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (sqrt.f64 z))
	0.1b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(*.f64 y (pow.f64 z 3/8))
✓	0.3b	(.f64 (.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

series364.0ms (8.9%)

Counts

2 → 36

Calls

2 calls:

350.0ms	(*.f64 y (pow.f64 z 3/8))
14.0ms	(.f64 (.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`associate-r_binary64`
18×	`sqrt-prod_binary64`
17×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`prod-exp_binary64`

Counts

2 → 57

Calls

2 calls:

7.0ms	(.f64 (.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
4.0ms	(*.f64 y (pow.f64 z 3/8))

simplify101.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
355×	`*-commutative_binary64`
308×	`sqr-pow_binary64`
162×	`associate-l_binary64`

Counts

93 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1164
1	229	1098
2	705	1086
3	1000	1086
4	1590	1086
5	3108	1086
6	4563	1086
7	4913	1086

prune124.0ms (3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	118	6	124

Error

Counts

124 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (fabs.f64 (cbrt.f64 (sqrt.f64 z)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 z))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))

Compiler

Compiled 2650 to 1554 computations (41.4% saved)

regimes269.0ms (6.6%)

Accuracy

Total 0.1b remaining (82.5%)

Threshold costs 0.1b (82.5%)

Counts

34 → 1

Compiler

Compiled 4924 to 3499 computations (28.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	14	10
2	12	10

end85.0ms (2.1%)

Compiler: Compiled 132 to 92 computations (30.3% saved)

Details

analyze240.0ms (5.9%)

sample1.2s (28.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series24.0ms (0.6%)

rewrite7.0ms (0.2%)

simplify109.0ms (2.7%)

prune43.0ms (1.1%)

localize10.0ms (0.2%)

series233.0ms (5.7%)

rewrite22.0ms (0.5%)

simplify154.0ms (3.8%)

prune122.0ms (3%)

localize13.0ms (0.3%)

series672.0ms (16.5%)

rewrite27.0ms (0.7%)

simplify105.0ms (2.6%)

prune150.0ms (3.7%)

localize12.0ms (0.3%)

series364.0ms (8.9%)

rewrite16.0ms (0.4%)

simplify101.0ms (2.5%)

prune124.0ms (3%)

regimes269.0ms (6.6%)

simplify2.0ms (0%)

end85.0ms (2.1%)

Profiling