Details

analyze201.0ms (6.6%)

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
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)

sample41.0ms (1.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
2.0ms	37×	body	128	nan
1.0ms	13×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify7.0ms (0.2%)

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

prune15.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 46 to 33 computations (28.3% 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)))
✓	0.2b	(*.f64 y (sqrt.f64 z))

series22.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

12.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
10.0ms	(*.f64 y (sqrt.f64 z))

rewrite13.0ms (0.4%)

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:

3.0ms	(*.f64 y (sqrt.f64 z))
2.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

simplify113.0ms (3.7%)

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

prune44.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Error

0.0b

Counts

53 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.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)))))
	30.0b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	35.5b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) (cbrt.f64 (.f64 y (sqrt.f64 z)))) (cbrt.f64 (.f64 y (sqrt.f64 z))))))

Compiler

Compiled 1065 to 547 computations (48.6% saved)

localize9.0ms (0.3%)

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))
✓	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

series264.0ms (8.7%)

Counts

4 → 65

Calls

4 calls:

222.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
19.0ms	(sqrt.f64 (sqrt.f64 z))
12.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

rewrite20.0ms (0.7%)

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)))
6.0ms	(*.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))

simplify160.0ms (5.3%)

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

prune111.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	139	6	145

Error

0.0b

Counts

145 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))))
	35.5b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))
	30.0b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 z))))))

Compiler

Compiled 2942 to 1239 computations (57.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))
	0.1b	(sqrt.f64 (sqrt.f64 z))
✓	0.3b	(*.f64 y (pow.f64 z 1/4))
✓	0.3b	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))

series246.0ms (8.1%)

Counts

3 → 41

Calls

3 calls:

215.0ms	(*.f64 y (pow.f64 z 1/4))
16.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))
14.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
16×	`associate-r_binary64`
15×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 70

Calls

3 calls:

6.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))
4.0ms	(*.f64 y (pow.f64 z 1/4))
2.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))

simplify158.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

807×	`unswap-sqr_binary64`
678×	`fma-neg_binary64`
604×	`*-commutative_binary64`
229×	`fma-def_binary64`
218×	`distribute-rgt-neg-in_binary64`

Counts

111 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	122	1392
1	274	1316
2	878	1223
3	1790	923
4	2873	922
5	4984	922
6	5145	922

prune213.0ms (7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	121	7	128

Error

Counts

128 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))))
	35.5b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))
	30.0b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 z))))))

Compiler

Compiled 2679 to 1601 computations (40.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))
	0.3b	(*.f64 y (pow.f64 z 1/4))
✓	0.3b	(.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))

series78.0ms (2.6%)

Counts

2 → 37

Calls

2 calls:

66.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))
12.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
7×	`associate-r_binary64`
7×	`add-cbrt-cube_binary64`
7×	`pow-exp_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))
3.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))

simplify81.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
699×	`fma-neg_binary64`
292×	`*-commutative_binary64`
284×	`cancel-sign-sub-inv_binary64`
262×	`distribute-rgt-neg-in_binary64`

Counts

85 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	774
1	211	687
2	698	670
3	1488	669
4	3547	669
5	4655	669
6	4872	669

prune95.0ms (3.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	100	7	107

Error

Counts

107 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4))))
	35.5b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))))))
	30.0b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 z))))))

Compiler

Compiled 2152 to 1491 computations (30.7% saved)

regimes201.0ms (6.6%)

Accuracy

Total 0.1b remaining (66.3%)

Threshold costs 0.1b (66.3%)

Counts

26 → 1

Compiler

Compiled 3494 to 2406 computations (31.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	17	12
2	15	12

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample885.0ms (29.1%)

Algorithm

1×

intervals

Results

409.0ms	8000×	body	128	valid
66.0ms	1012×	body	128	nan
17.0ms	388×	body	128	invalid

Compiler

Compiled 162 to 118 computations (27.2% saved)

Details

analyze201.0ms (6.6%)

sample41.0ms (1.4%)

simplify7.0ms (0.2%)

prune15.0ms (0.5%)

localize7.0ms (0.2%)

series22.0ms (0.7%)

rewrite13.0ms (0.4%)

simplify113.0ms (3.7%)

prune44.0ms (1.5%)

localize9.0ms (0.3%)

series264.0ms (8.7%)

rewrite20.0ms (0.7%)

simplify160.0ms (5.3%)

prune111.0ms (3.6%)

localize13.0ms (0.4%)

series246.0ms (8.1%)

rewrite15.0ms (0.5%)

simplify158.0ms (5.2%)

prune213.0ms (7%)

localize10.0ms (0.3%)

series78.0ms (2.6%)

rewrite15.0ms (0.5%)

simplify81.0ms (2.7%)

prune95.0ms (3.1%)

regimes201.0ms (6.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample885.0ms (29.1%)

Profiling