Details

analyze365.0ms (9.2%)

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
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)

sample1.1s (28.1%)

Results

923.0ms	8256×	body	128	valid
154.0ms	1472×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify6.0ms (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

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)

localize6.0ms (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))

series21.0ms (0.5%)

Counts

2 → 16

Calls

2 calls:

11.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
10.0ms	(*.f64 y (sqrt.f64 z))

rewrite9.0ms (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:

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

simplify109.0ms (2.8%)

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

prune53.0ms (1.3%)

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
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.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))))))
	45.0b	(.f64 (/.f64 1 2) (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (sqrt.f64 z)) (.f64 y (sqrt.f64 z))) (.f64 x (.f64 y (sqrt.f64 z)))))))
	0.3b	(.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 (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	30.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))

Compiler

Compiled 1085 to 557 computations (48.7% 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))))
✓	0.2b	(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)))

series298.0ms (7.5%)

Counts

4 → 65

Calls

4 calls:

256.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
19.0ms	(sqrt.f64 (sqrt.f64 z))
11.0ms	(+.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)))

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:

6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
5.0ms	(sqrt.f64 (sqrt.f64 z))
4.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
2.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))

simplify151.0ms (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

prune138.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	137	8	145

Error

Counts

145 → 8

Alt Table

Status	Error	Program
	0.3b	(.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 (.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (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)))))
	45.0b	(.f64 (/.f64 1 2) (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (sqrt.f64 z)) (.f64 y (sqrt.f64 z))) (.f64 x (.f64 y (sqrt.f64 z)))))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	30.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))

Compiler

Compiled 3054 to 1303 computations (57.3% saved)

localize11.0ms (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))) (pow.f64 z 1/4)))
	0.2b	(sqrt.f64 (sqrt.f64 z))
	0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))

series33.0ms (0.8%)

Counts

2 → 37

Calls

2 calls:

20.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4)))
12.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
9×	`prod-exp_binary64`
7×	`associate-r_binary64`
7×	`add-cbrt-cube_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 42

Calls

2 calls:

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

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

747×	`unswap-sqr_binary64`
691×	`fma-neg_binary64`
434×	`*-commutative_binary64`
321×	`cancel-sign-sub-inv_binary64`
285×	`distribute-rgt-neg-in_binary64`

Counts

79 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	87	978
1	219	920
2	734	899
3	1613	622
4	2662	621
5	4850	621
6	5021	621

prune204.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	120	7	127

Error

Counts

127 → 7

Alt Table

Status	Error	Program
	0.3b	(.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 (.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (pow.f64 z 1/8) 3)) (sqrt.f64 (pow.f64 z 1/4)))))
	30.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 2616 to 1476 computations (43.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (sqrt.f64 z))
✓	0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
✓	0.3b	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

series485.0ms (12.3%)

Counts

3 → 52

Calls

3 calls:

245.0ms

(*.f64 (*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

230.0ms

(*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

10.0ms

(*.f64 (*.f64 (*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-prod_binary64`
33×	`associate-r_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`

Counts

3 → 90

Calls

3 calls:

11.0ms

(*.f64 (*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

11.0ms

(*.f64 (*.f64 (*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))

6.0ms

(*.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

simplify129.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

420×	`associate-*r/_binary64`
367×	`unswap-sqr_binary64`
364×	`*-commutative_binary64`
364×	`associate-*l/_binary64`
254×	`associate-l_binary64`

Counts

142 → 110

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	104	1756
1	230	1437
2	748	1437
3	1012	1437
4	1346	1437
5	2036	1437
6	4122	1437
7	4992	1437
8	4915	1437

prune183.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	176	7	183

Error

Counts

183 → 7

Alt Table

Status	Error	Program
	0.3b	(.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 (.f64 y (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (pow.f64 z 1/8) 3)) (sqrt.f64 (pow.f64 z 1/4)))))
	30.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 z)))) (sqrt.f64 (sqrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 4691 to 1649 computations (64.8% saved)

regimes364.0ms (9.2%)

Accuracy

Total 0.1b remaining (78.5%)

Threshold costs 0.1b (78.5%)

Counts

48 → 1

Compiler

Compiled 7512 to 4779 computations (36.4% 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

end113.0ms (2.9%)

Compiler: Compiled 157 to 114 computations (27.4% saved)

Details

analyze365.0ms (9.2%)

sample1.1s (28.1%)

simplify6.0ms (0.2%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

series21.0ms (0.5%)

rewrite9.0ms (0.2%)

simplify109.0ms (2.8%)

prune53.0ms (1.3%)

localize9.0ms (0.2%)

series298.0ms (7.5%)

rewrite22.0ms (0.5%)

simplify151.0ms (3.8%)

prune138.0ms (3.5%)

localize11.0ms (0.3%)

series33.0ms (0.8%)

rewrite10.0ms (0.3%)

simplify76.0ms (1.9%)

prune204.0ms (5.2%)

localize10.0ms (0.3%)

series485.0ms (12.3%)

rewrite35.0ms (0.9%)

simplify129.0ms (3.2%)

prune183.0ms (4.6%)

regimes364.0ms (9.2%)

simplify2.0ms (0%)

end113.0ms (2.9%)

Profiling