Details

analyze1.5s (34.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.1s (24.9%)

Results

929.0ms	8256×	body	128	valid
3.0ms	4×	body	8192	exit

Compiler

Compiled 23 to 20 computations (13% saved)

simplify141.0ms (3.2%)

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%)

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

31.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.0b	(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))
✓	30.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series6.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

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

rewrite8.0ms (0.2%)

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)))

simplify89.0ms (2%)

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

prune37.0ms (0.8%)

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

0.1b

Counts

67 → 8

Alt Table

Status	Error	Program
✓	31.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	45.7b	(sqrt.f64 (log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2)))))
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.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)))
	2.5b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)
	31.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2)))

Compiler

Compiled 815 to 595 computations (27% saved)

localize4.0ms (0.1%)

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))
✓	0.4b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series17.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

10.0ms	(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 (0.3%)

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:

5.0ms	(*.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)

simplify85.0ms (1.9%)

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

prune46.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	105	7	112

Error

0.0b

Counts

112 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	30.4b	(*.f64 (sqrt.f64 2) x)
	45.7b	(sqrt.f64 (log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2)))))
▶	0.1b	(hypot.f64 x x)
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	22.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 1508 to 380 computations (74.8% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

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

prune8.0ms (0.2%)

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

0.0b

Counts

11 → 7

Alt Table

Status	Error	Program
▶	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	30.4b	(*.f64 (sqrt.f64 2) x)
	45.7b	(sqrt.f64 (log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2)))))
✓	0.1b	(hypot.f64 x x)
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	22.2b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))

Compiler

Compiled 185 to 94 computations (49.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.4b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series787.0ms (17.7%)

Counts

4 → 36

Calls

4 calls:

543.0ms	(cbrt.f64 (hypot.f64 x x))
228.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
11.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
4.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
19×	`sqrt-prod_binary64`
18×	`cbrt-prod_binary64`
16×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
6.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
1.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify115.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

415×	`fma-def_binary64`
380×	`fma-neg_binary64`
331×	`unswap-sqr_binary64`
288×	`sqr-pow_binary64`
251×	`*-commutative_binary64`

Counts

132 → 136

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	2082
1	206	1889
2	505	1828
3	791	1342
4	1145	1310
5	2308	1310
6	4584	1310
7	4875	1310

prune100.0ms (2.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	153	10	163

Error

Counts

163 → 10

Alt Table

Status	Error	Program
	45.7b	(sqrt.f64 (log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2)))))
	1.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))))
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	30.4b	(*.f64 (sqrt.f64 2) x)
	42.9b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (hypot.f64 x x) (.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))))
✓	0.1b	(hypot.f64 x x)
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	0.9b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/2))
	1.0b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 3129 to 712 computations (77.2% saved)

regimes188.0ms (4.2%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Counts

37 → 1

Compiler

Compiled 2314 to 1130 computations (51.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end106.0ms (2.4%)

Compiler: Compiled 155 to 75 computations (51.6% saved)

Details

analyze1.5s (34.9%)

sample1.1s (24.9%)

simplify141.0ms (3.2%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite8.0ms (0.2%)

simplify89.0ms (2%)

prune37.0ms (0.8%)

localize4.0ms (0.1%)

series17.0ms (0.4%)

rewrite12.0ms (0.3%)

simplify85.0ms (1.9%)

prune46.0ms (1%)

localize2.0ms (0%)

prune8.0ms (0.2%)

localize7.0ms (0.2%)

series787.0ms (17.7%)

rewrite23.0ms (0.5%)

simplify115.0ms (2.6%)

prune100.0ms (2.2%)

regimes188.0ms (4.2%)

simplify2.0ms (0%)

end106.0ms (2.4%)

Profiling