Details

analyze5.0ms (0.2%)

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 7 computations (12.5% saved)

sample1.0s (40.9%)

Results

863.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify140.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

prune2.0ms (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

27.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
2.0ms	(*.f64 2 (pow.f64 x 2))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(*.f64 2 (pow.f64 x 2))
2.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify248.0ms (9.8%)

Algorithm

1×	egg-herbie

Rules

823×	`unswap-sqr_binary64`
448×	`hypot-def_binary64`
432×	`*-commutative_binary64`
402×	`sqr-pow_binary64`
358×	`times-frac_binary64`

Counts

53 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	490
1	110	449
2	247	437
3	826	431
4	1358	371
5	3482	371
6	4011	371
7	4935	371
8	4869	371

prune171.0ms (6.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	8	67

Error

0.0b

Counts

67 → 8

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 2 (pow.f64 x 2)))))
	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)))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	32.2b	(*.f64 (sqrt.f64 2) x)
	27.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

Compiler

Compiled 841 to 617 computations (26.6% 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)))

series17.0ms (0.7%)

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)))
4.0ms	(hypot.f64 x x)

rewrite12.0ms (0.5%)

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)

simplify83.0ms (3.3%)

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

prune55.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	105	7	112

Error

Counts

112 → 7

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 2 (pow.f64 x 2)))))
	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))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) 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)
	27.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 1528 to 402 computations (73.7% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune7.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	4	7	11

Error

Counts

11 → 7

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 2 (pow.f64 x 2)))))
	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))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) 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)
	27.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 205 to 116 computations (43.4% saved)

localize7.0ms (0.3%)

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))

series224.0ms (8.8%)

Counts

2 → 24

Calls

2 calls:

220.0ms	(pow.f64 (hypot.f64 x x) 1/2)
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))

rewrite11.0ms (0.4%)

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:

6.0ms	(*.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)

simplify88.0ms (3.5%)

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

prune52.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	118	7	125

Error

Counts

125 → 7

Alt Table

Status	Error	Program
	27.4b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 2 (pow.f64 x 2)))))
	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))))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) 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)
	27.5b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 1780 to 658 computations (63% saved)

regimes275.0ms (10.9%)

Accuracy

Total 0.1b remaining (73.8%)

Threshold costs 0.1b (73.8%)

Counts

52 → 1

Compiler

Compiled 3283 to 1777 computations (45.9% saved)

simplify2.0ms (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

end77.0ms (3.1%)

Compiler: Compiled 92 to 56 computations (39.1% saved)

Details

analyze5.0ms (0.2%)

sample1.0s (40.9%)

simplify140.0ms (5.5%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify248.0ms (9.8%)

prune171.0ms (6.7%)

localize4.0ms (0.2%)

series17.0ms (0.7%)

rewrite12.0ms (0.5%)

simplify83.0ms (3.3%)

prune55.0ms (2.2%)

localize2.0ms (0.1%)

prune7.0ms (0.3%)

localize7.0ms (0.3%)

series224.0ms (8.8%)

rewrite11.0ms (0.4%)

simplify88.0ms (3.5%)

prune52.0ms (2.1%)

regimes275.0ms (10.9%)

simplify2.0ms (0.1%)

end77.0ms (3.1%)

Profiling