Details

analyze248.0ms (6.8%)

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 (32.1%)

Results

967.0ms	8256×	body	128	valid
167.0ms	1520×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% 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

prune3.0ms (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 (0.2%)

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))

series27.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

14.0ms	(*.f64 y (sqrt.f64 z))
13.0ms	(+.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)))

simplify115.0ms (3.2%)

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

prune55.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Error

0.0b

Counts

53 → 8

Alt Table

Status	Error	Program
	31.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (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)))))
	32.9b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	0.7b	(.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))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.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)))))
	0.7b	(.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)))))

Compiler

Compiled 1099 to 573 computations (47.9% 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)))

series376.0ms (10.3%)

Counts

4 → 65

Calls

4 calls:

280.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
58.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
21.0ms	(sqrt.f64 (sqrt.f64 z))
17.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))

rewrite20.0ms (0.6%)

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)))
3.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
1.0ms	(sqrt.f64 (sqrt.f64 z))

simplify161.0ms (4.4%)

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

prune127.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	139	7	146

Error

0.0b

Counts

146 → 7

Alt Table

Status	Error	Program
	32.9b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	0.5b	(.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)))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))))

Compiler

Compiled 2980 to 1265 computations (57.6% saved)

localize14.0ms (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)))

series322.0ms (8.9%)

Counts

3 → 41

Calls

3 calls:

291.0ms	(*.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)))

rewrite16.0ms (0.4%)

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

simplify105.0ms (2.9%)

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

prune129.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Error

0.0b

Counts

129 → 7

Alt Table

Status	Error	Program
	32.9b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	0.5b	(.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)))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))))

Compiler

Compiled 2681 to 1599 computations (40.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
	0.1b	(sqrt.f64 (sqrt.f64 z))
✓	0.2b	(.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
✓	0.5b	(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))

series34.0ms (0.9%)

Counts

3 → 37

Calls

3 calls:

15.0ms	(.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
13.0ms	(+.f64 x (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`sqrt-prod_binary64`
64×	`add-sqr-sqrt_binary64`
32×	`sqrt-pow1_binary64`
31×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 122

Calls

3 calls:

17.0ms	(.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))
8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))
2.0ms	(+.f64 x (.f64 y (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z)))))

simplify132.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
703×	`fma-neg_binary64`
328×	`cancel-sign-sub-inv_binary64`
262×	`*-commutative_binary64`
241×	`unswap-sqr_binary64`

Counts

159 → 135

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	112	1135
1	215	1096
2	637	1082
3	1448	1041
4	3580	1041
5	4418	992
6	4780	986
7	4929	986
8	4887	986

prune162.0ms (4.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	179	7	186

Error

0.0b

Counts

186 → 7

Alt Table

Status	Error	Program
	32.9b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	0.5b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 (sqrt.f64 z))))))
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (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)))))
✓	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))))

Compiler

Compiled 3527 to 1618 computations (54.1% saved)

regimes244.0ms (6.7%)

Accuracy

Total 0.1b remaining (68.6%)

Threshold costs 0.1b (68.6%)

Counts

34 → 1

Compiler

Compiled 4775 to 3071 computations (35.7% saved)

simplify2.0ms (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

end98.0ms (2.7%)

Compiler: Compiled 150 to 108 computations (28% saved)

Details

analyze248.0ms (6.8%)

sample1.2s (32.1%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series27.0ms (0.7%)

rewrite7.0ms (0.2%)

simplify115.0ms (3.2%)

prune55.0ms (1.5%)

localize9.0ms (0.2%)

series376.0ms (10.3%)

rewrite20.0ms (0.6%)

simplify161.0ms (4.4%)

prune127.0ms (3.5%)

localize14.0ms (0.4%)

series322.0ms (8.9%)

rewrite16.0ms (0.4%)

simplify105.0ms (2.9%)

prune129.0ms (3.6%)

localize9.0ms (0.2%)

series34.0ms (0.9%)

rewrite40.0ms (1.1%)

simplify132.0ms (3.6%)

prune162.0ms (4.5%)

regimes244.0ms (6.7%)

simplify2.0ms (0.1%)

end98.0ms (2.7%)

Profiling