Details

analyze116.0ms (3.9%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample777.0ms (26.2%)

Results

727.0ms	8256×	body	128	valid
11.0ms	145×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify7.0ms (0.2%)

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

prune2.0ms (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

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.6b	(*.f64 x (fma.f64 y y 1))

series13.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

13.0ms

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

rewrite3.0ms (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))

simplify82.0ms (2.8%)

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

prune28.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	7	41

Error

3.7b

Counts

41 → 7

Alt Table

Status	Error	Program
	21.5b	x
✓	7.1b	(*.f64 x (fma.f64 y y 1))
▶	7.1b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	7.3b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	8.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	30.6b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))
	8.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (fma.f64 y y 1))) (cbrt.f64 (.f64 x (fma.f64 y y 1)))) (cbrt.f64 (*.f64 x (fma.f64 y y 1))))

Compiler

Compiled 615 to 362 computations (41.1% saved)

localize12.0ms (0.4%)

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)))
✓	6.6b	(sqrt.f64 (fma.f64 y y 1))

series45.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

28.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
13.0ms	(*.f64 x (hypot.f64 1 y))
2.0ms	(sqrt.f64 (fma.f64 y y 1))
2.0ms	(hypot.f64 1 y)

rewrite14.0ms (0.5%)

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:

8.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
2.0ms	(*.f64 x (hypot.f64 1 y))
1.0ms	(sqrt.f64 (fma.f64 y y 1))
0.0ms	(hypot.f64 1 y)

simplify98.0ms (3.3%)

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

prune115.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	135	8	143

Error

0.0b

Counts

143 → 8

Alt Table

Status	Error	Program
	7.3b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	53.0b	(.f64 (.f64 x (hypot.f64 1 y)) (neg.f64 y))
	7.2b	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (sqrt.f64 (fma.f64 y y 1))))
	7.3b	(.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (cbrt.f64 (hypot.f64 1 y)) (cbrt.f64 (hypot.f64 1 y)))) (cbrt.f64 (sqrt.f64 (fma.f64 y y 1))))
▶	0.2b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
✓	7.1b	(*.f64 x (fma.f64 y y 1))
	0.4b	(.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))))
	50.0b	(.f64 (.f64 x (hypot.f64 1 y)) y)

Compiler

Compiled 2471 to 1670 computations (32.4% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.9%)

Counts

3 → 40

Calls

3 calls:

20.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))
4.0ms	(sqrt.f64 (hypot.f64 1 y))
2.0ms	(*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))

rewrite21.0ms (0.7%)

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:

7.0ms	(.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))

simplify103.0ms (3.5%)

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

prune269.0ms (9.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	207	4	211
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	210	9	219

Error

Counts

219 → 9

Alt Table

Status	Error	Program
	7.3b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	53.0b	(.f64 (.f64 x (hypot.f64 1 y)) (neg.f64 y))
	50.0b	(.f64 (.f64 x (hypot.f64 1 y)) y)
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))))
	7.3b	(.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (cbrt.f64 (hypot.f64 1 y)) (cbrt.f64 (hypot.f64 1 y)))) (cbrt.f64 (sqrt.f64 (fma.f64 y y 1))))
✓	7.1b	(*.f64 x (fma.f64 y y 1))
▶	0.2b	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (hypot.f64 1 y)))
	0.4b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 1 y))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 1 y))) 3)))
	0.6b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 1 y))) 4) (cbrt.f64 (hypot.f64 1 y))))

Compiler

Compiled 4520 to 3371 computations (25.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series69.0ms (2.3%)

Counts

2 → 40

Calls

2 calls:

49.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))
21.0ms	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (hypot.f64 1 y)))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-r_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 49

Calls

2 calls:

6.0ms	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (hypot.f64 1 y)))
4.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y)))

simplify117.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
373×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
307×	`*-commutative_binary64`
254×	`sqr-pow_binary64`

Counts

89 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	94	1420
1	245	1156
2	767	1121
3	1266	1110
4	2092	1086
5	4321	1086
6	4705	1086
7	4941	1086
8	4765	1086

prune211.0ms (7.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	176	7	183

Error

Counts

183 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (cbrt.f64 (hypot.f64 1 y)) (sqrt.f64 (cbrt.f64 (hypot.f64 1 y))))) (sqrt.f64 (hypot.f64 1 y)))
	50.0b	(.f64 (.f64 x (hypot.f64 1 y)) y)
	4.3b	(.f64 (pow.f64 (.f64 x (pow.f64 (sqrt.f64 (hypot.f64 1 y)) 3)) 1) (sqrt.f64 (hypot.f64 1 y)))
	7.3b	(.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 (cbrt.f64 (hypot.f64 1 y)) (cbrt.f64 (hypot.f64 1 y)))) (cbrt.f64 (sqrt.f64 (fma.f64 y y 1))))
	0.3b	(.f64 (.f64 (.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (sqrt.f64 (hypot.f64 1 y)))) (sqrt.f64 (sqrt.f64 (hypot.f64 1 y))))
✓	7.1b	(*.f64 x (fma.f64 y y 1))
	53.0b	(.f64 (.f64 x (hypot.f64 1 y)) (neg.f64 y))

Compiler

Compiled 3709 to 2755 computations (25.7% saved)

regimes641.0ms (21.6%)

Accuracy

Total 0.2b remaining (90.8%)

Threshold costs 0.2b (90.8%)

Counts

112 → 1

Compiler

Compiled 10899 to 8272 computations (24.1% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	14	23
2	13	23

end158.0ms (5.3%)

Compiler: Compiled 149 to 113 computations (24.2% saved)

Details

analyze116.0ms (3.9%)

sample777.0ms (26.2%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series13.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify82.0ms (2.8%)

prune28.0ms (0.9%)

localize12.0ms (0.4%)

series45.0ms (1.5%)

rewrite14.0ms (0.5%)

simplify98.0ms (3.3%)

prune115.0ms (3.9%)

localize6.0ms (0.2%)

series27.0ms (0.9%)

rewrite21.0ms (0.7%)

simplify103.0ms (3.5%)

prune269.0ms (9.1%)

localize7.0ms (0.2%)

series69.0ms (2.3%)

rewrite14.0ms (0.5%)

simplify117.0ms (3.9%)

prune211.0ms (7.1%)

regimes641.0ms (21.6%)

simplify5.0ms (0.2%)

end158.0ms (5.3%)

Profiling