Details

analyze237.0ms (5%)

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 (25.2%)

Results

1.0s	8256×	body	128	valid
167.0ms	1518×	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

prune5.0ms (0.1%)

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 (0.1%)

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))

series23.0ms (0.5%)

Counts

2 → 16

Calls

2 calls:

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

rewrite8.0ms (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:

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

simplify106.0ms (2.2%)

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

prune47.0ms (1%)

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
	33.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (sqrt.f64 z)))))
	33.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.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)))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))

Compiler

Compiled 1047 to 547 computations (47.8% saved)

localize9.0ms (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))
✓	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

series274.0ms (5.7%)

Counts

4 → 65

Calls

4 calls:

232.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
18.0ms	(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)))

rewrite21.0ms (0.4%)

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

simplify152.0ms (3.2%)

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

prune119.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	137	8	145

Error

0.0b

Counts

145 → 8

Alt Table

Status	Error	Program
	33.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	33.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.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))))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.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)))))
✓	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))

Compiler

Compiled 3014 to 1273 computations (57.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2))
✓	0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)
✓	0.4b	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

series669.0ms (14%)

Counts

4 → 48

Calls

4 calls:

427.0ms	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2))
210.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)
21.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
11.0ms	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

rewrite26.0ms (0.5%)

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×	`*-un-lft-identity_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))))
6.0ms	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2))
4.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)
2.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))

simplify152.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

170 → 150

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

prune233.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	150	8	158

Error

Counts

158 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	33.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))))))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (cbrt.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)))))
✓	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))

Compiler

Compiled 3819 to 2018 computations (47.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (sqrt.f64 z))
	0.2b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(*.f64 y (pow.f64 z 3/8))
✓	0.4b	(.f64 (.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

series378.0ms (7.9%)

Counts

2 → 36

Calls

2 calls:

359.0ms	(*.f64 y (pow.f64 z 3/8))
19.0ms	(.f64 (.f64 y (pow.f64 z 3/8)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

rewrite16.0ms (0.3%)

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))))
6.0ms	(*.f64 y (pow.f64 z 3/8))

simplify101.0ms (2.1%)

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

prune143.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	3	2	5
Picked	1	0	1
Done	1	1	2
Total	121	5	126

Error

Counts

126 → 5

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)))))
✓	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 (pow.f64 z 3/8)) (fabs.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))) (sqrt.f64 (cbrt.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)))))
	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 3/8)) (sqrt.f64 (pow.f64 z 1/4)))))

Compiler

Compiled 2637 to 1549 computations (41.3% saved)

regimes722.0ms (15.1%)

Accuracy

Total 0.1b remaining (69.3%)

Threshold costs 0.1b (69.3%)

Counts

93 → 1

Compiler

Compiled 14211 to 10820 computations (23.9% saved)

simplify2.0ms (0%)

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

end92.0ms (1.9%)

Compiler: Compiled 121 to 89 computations (26.4% saved)

Details

analyze237.0ms (5%)

sample1.2s (25.2%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series23.0ms (0.5%)

rewrite8.0ms (0.2%)

simplify106.0ms (2.2%)

prune47.0ms (1%)

localize9.0ms (0.2%)

series274.0ms (5.7%)

rewrite21.0ms (0.4%)

simplify152.0ms (3.2%)

prune119.0ms (2.5%)

localize14.0ms (0.3%)

series669.0ms (14%)

rewrite26.0ms (0.5%)

simplify152.0ms (3.2%)

prune233.0ms (4.9%)

localize13.0ms (0.3%)

series378.0ms (7.9%)

rewrite16.0ms (0.3%)

simplify101.0ms (2.1%)

prune143.0ms (3%)

regimes722.0ms (15.1%)

simplify2.0ms (0%)

end92.0ms (1.9%)

Profiling