Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample517.0ms (21.7%)

Results

483.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
7×	`associate-r_binary64`
7×	`associate-l_binary64`
5×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	24	8
3	47	8
4	43	8
5	45	8
6	43	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

3.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.3b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.3b	(*.f64 x (fma.f64 y y 1))

series9.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 x (fma.f64 y y 1))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

3.0ms

(*.f64 x (fma.f64 y y 1))

simplify80.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

746×	`unswap-sqr_binary64`
561×	`distribute-rgt-in_binary64`
550×	`fma-def_binary64`
534×	`distribute-lft-in_binary64`
336×	`distribute-rgt-out_binary64`

Counts

46 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	447
1	81	404
2	264	404
3	597	404
4	1918	404
5	2078	404
6	2869	404
7	4919	404
8	4929	404

prune31.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Error

1.4b

Counts

41 → 4

Alt Table

Status	Error	Program
	3.3b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
▶	3.3b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	32.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 y y 1)))
	30.2b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))

Compiler

Compiled 521 to 303 computations (41.8% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 y)
✓	0.0b	(*.f64 x (hypot.f64 1 y))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
✓	13.0b	(sqrt.f64 (fma.f64 y y 1))

series49.0ms (2.1%)

Counts

4 → 72

Calls

4 calls:

30.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
14.0ms	(*.f64 x (hypot.f64 1 y))
3.0ms	(sqrt.f64 (fma.f64 y y 1))
3.0ms	(hypot.f64 1 y)

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`associate-r_binary64`

Counts

4 → 68

Calls

4 calls:

4.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
3.0ms	(sqrt.f64 (fma.f64 y y 1))
3.0ms	(*.f64 x (hypot.f64 1 y))
0.0ms	(hypot.f64 1 y)

simplify96.0ms (4%)

Algorithm

1×	egg-herbie

Rules

897×	`fma-neg_binary64`
400×	`times-frac_binary64`
387×	`fma-def_binary64`
312×	`cancel-sign-sub-inv_binary64`
293×	`associate-*l/_binary64`

Counts

140 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1769
1	362	1393
2	1008	1363
3	2521	1354
4	4802	1354
5	5209	1354

prune103.0ms (4.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	134	6	140

Error

0.0b

Counts

140 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
	0.3b	(.f64 (.f64 x (hypot.f64 1 y)) (.f64 (.f64 (cbrt.f64 (hypot.f64 1 y)) (cbrt.f64 (hypot.f64 1 y))) (cbrt.f64 (hypot.f64 1 y))))
	44.2b	(.f64 (.f64 x (hypot.f64 1 y)) (neg.f64 y))
	3.3b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	3.3b	(.f64 (.f64 (hypot.f64 1 y) x) (sqrt.f64 (fma.f64 y y 1)))
	3.3b	(.f64 (.f64 (*.f64 x (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (fma.f64 y y 1)))

Compiler

Compiled 2399 to 1619 computations (32.5% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (hypot.f64 1 y))
✓	0.0b	(sqrt.f64 (hypot.f64 1 y))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
✓	0.2b	(*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))

series30.0ms (1.3%)

Counts

3 → 40

Calls

3 calls:

22.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
6.0ms	(sqrt.f64 (hypot.f64 1 y))
3.0ms	(*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`

Counts

3 → 92

Calls

3 calls:

8.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
5.0ms	(*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))
1.0ms	(sqrt.f64 (hypot.f64 1 y))

simplify113.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-neg_binary64`
569×	`fma-def_binary64`
278×	`*-commutative_binary64`
263×	`sub-neg_binary64`
250×	`unswap-sqr_binary64`

Counts

132 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	132	1451
1	297	1257
2	875	1194
3	1747	1162
4	3655	1130
5	4493	1130
6	4890	1130

prune413.0ms (17.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	212	5	217

Error

Counts

217 → 5

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
	0.2b	(.f64 (.f64 (.f64 x (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (hypot.f64 1 y))) (.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
	0.3b	(.f64 (.f64 x (hypot.f64 1 y)) (.f64 (.f64 (cbrt.f64 (hypot.f64 1 y)) (cbrt.f64 (hypot.f64 1 y))) (cbrt.f64 (hypot.f64 1 y))))
▶	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (hypot.f64 1 y))
	3.3b	(+.f64 (*.f64 (pow.f64 y 2) x) x)

Compiler

Compiled 4311 to 3215 computations (25.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 y)
	0.0b	(*.f64 x (hypot.f64 1 y))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (hypot.f64 1 y))

series39.0ms (1.6%)

Counts

1 → 24

Calls

1 calls:

39.0ms

(*.f64 (*.f64 x (hypot.f64 1 y)) (hypot.f64 1 y))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x (hypot.f64 1 y)) (hypot.f64 1 y))

simplify130.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

474×	`times-frac_binary64`
452×	`associate-/r/_binary64`
443×	`associate-/l/_binary64`
354×	`associate-/l*_binary64`
346×	`associate-l_binary64`

Counts

44 → 35

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	43	560
1	105	476
2	310	461
3	520	461
4	642	428
5	868	428
6	1511	428
7	3570	423
8	4915	423
9	4940	423

prune127.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	1	3
Picked	0	1	1
Done	1	0	1
Total	92	4	96

Error

Counts

96 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (hypot.f64 1 y))
	3.3b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	0.1b	(.f64 (.f64 (*.f64 x (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (hypot.f64 1 y))) (hypot.f64 1 y))
	0.3b	(.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (cbrt.f64 (hypot.f64 1 y)) (cbrt.f64 (hypot.f64 1 y)))) (cbrt.f64 (hypot.f64 1 y)))

Compiler

Compiled 1380 to 941 computations (31.8% saved)

regimes433.0ms (18.2%)

Accuracy

Total 0.1b remaining (74.9%)

Threshold costs 0.1b (74.9%)

Counts

52 → 1

Compiler

Compiled 3934 to 2792 computations (29% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	11	13
2	10	13

end128.0ms (5.4%)

Compiler: Compiled 81 to 60 computations (25.9% saved)

Details

analyze1.0ms (0.1%)

sample517.0ms (21.7%)

simplify10.0ms (0.4%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series9.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify80.0ms (3.4%)

prune31.0ms (1.3%)

localize7.0ms (0.3%)

series49.0ms (2.1%)

rewrite13.0ms (0.6%)

simplify96.0ms (4%)

prune103.0ms (4.3%)

localize6.0ms (0.3%)

series30.0ms (1.3%)

rewrite23.0ms (1%)

simplify113.0ms (4.7%)

prune413.0ms (17.3%)

localize8.0ms (0.3%)

series39.0ms (1.6%)

rewrite6.0ms (0.2%)

simplify130.0ms (5.5%)

prune127.0ms (5.3%)

regimes433.0ms (18.2%)

simplify2.0ms (0.1%)

end128.0ms (5.4%)

Profiling