Details

analyze8.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample818.0ms (45.4%)

Results

790.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	11	9
3	11	9

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	26.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`pow-prod-down_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 35

Calls

2 calls:

4.0ms	(.f64 2 (.f64 x x))
3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify77.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

597×	`distribute-rgt-out_binary64`
429×	`fma-def_binary64`
339×	`*-commutative_binary64`
318×	`times-frac_binary64`
249×	`fma-neg_binary64`

Counts

59 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	514
1	97	472
2	229	461
3	599	461
4	904	401
5	1456	401
6	3025	401
7	4826	401
8	4904	401

prune26.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	6	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Error

0.0b

Counts

48 → 7

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (.f64 2 (.f64 x x)))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓	27.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	2.7b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	32.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 588 to 343 computations (41.7% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series16.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

9.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
3.0ms	(hypot.f64 x x)

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

7.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))
0.0ms	(hypot.f64 x x)

simplify82.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
308×	`sqr-pow_binary64`
263×	`associate-+l+_binary64`
259×	`associate-/l*_binary64`

Counts

102 → 83

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	61	802
1	85	752
2	199	739
3	402	701
4	728	701
5	1353	701
6	2551	685
7	4580	685
8	5171	685

prune53.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	105	6	111

Error

0.0b

Counts

111 → 6

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (.f64 2 (.f64 x x)))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))
	32.2b	(*.f64 (sqrt.f64 2) x)
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 1502 to 374 computations (75.1% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)

prune6.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	4	6	10

Error

0.0b

Counts

10 → 6

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (.f64 2 (.f64 x x)))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 179 to 88 computations (50.8% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/2)
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))

series267.0ms (14.8%)

Counts

2 → 24

Calls

2 calls:

262.0ms	(pow.f64 (hypot.f64 x x) 1/2)
5.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
8×	`unpow-prod-down_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))
1.0ms	(pow.f64 (hypot.f64 x x) 1/2)

simplify91.0ms (5%)

Algorithm

1×	egg-herbie

Rules

737×	`fma-def_binary64`
354×	`*-commutative_binary64`
327×	`exp-prod_binary64`
306×	`associate-/l*_binary64`
295×	`associate-l_binary64`

Counts

84 → 93

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	849
1	145	769
2	379	735
3	1171	679
4	2175	675
5	4349	675
6	4979	675
7	4808	675

prune54.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	118	6	124

Error

0.0b

Counts

124 → 6

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (.f64 2 (.f64 x x)))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 1767 to 644 computations (63.6% saved)

regimes172.0ms (9.6%)

Accuracy

Total 0.1b remaining (71.5%)

Threshold costs 0.1b (71.5%)

Counts

51 → 1

Compiler

Compiled 3219 to 1620 computations (49.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	7	4
2	6	4

end67.0ms (3.7%)

Compiler: Compiled 79 to 42 computations (46.8% saved)

Details

analyze8.0ms (0.4%)

sample818.0ms (45.4%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite9.0ms (0.5%)

simplify77.0ms (4.3%)

prune26.0ms (1.5%)

localize4.0ms (0.2%)

series16.0ms (0.9%)

rewrite12.0ms (0.7%)

simplify82.0ms (4.5%)

prune53.0ms (2.9%)

localize2.0ms (0.1%)

prune6.0ms (0.3%)

localize7.0ms (0.4%)

series267.0ms (14.8%)

rewrite10.0ms (0.5%)

simplify91.0ms (5%)

prune54.0ms (3%)

regimes172.0ms (9.6%)

simplify3.0ms (0.1%)

end67.0ms (3.7%)

Profiling