Details

analyze289.0ms (11.3%)

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)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify276.0ms (10.7%)

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

32.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	30.9b	(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)))
3.0ms	(*.f64 2 (pow.f64 x 2))

rewrite21.0ms (0.8%)

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:

17.0ms	(*.f64 2 (pow.f64 x 2))
2.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify96.0ms (3.7%)

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

prune68.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Error

0.1b

Counts

67 → 7

Alt Table

Status	Error	Program
✓	32.0b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	53.0b	(sqrt.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 (pow.f64 x 2))) (*.f64 2 (pow.f64 x 2)))))
	2.7b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	31.3b	(*.f64 (sqrt.f64 2) x)
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 811 to 595 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)))

series27.0ms (1%)

Counts

3 → 24

Calls

3 calls:

12.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
11.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(hypot.f64 x x)

rewrite58.0ms (2.3%)

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:

52.0ms	(*.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)

simplify93.0ms (3.6%)

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

prune87.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	2	5
Picked	0	1	1
Done	1	0	1
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
▶	0.1b	(hypot.f64 x x)
	41.6b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1518 to 364 computations (76% 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 (5 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
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)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	41.6b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 195 to 78 computations (60% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.5b	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
✓	0.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series506.0ms (19.7%)

Counts

4 → 36

Calls

4 calls:

250.0ms	(cbrt.f64 (hypot.f64 x x))
241.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
10.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
4.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`

Counts

4 → 89

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
6.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
2.0ms	(cbrt.f64 (hypot.f64 x x))
1.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify121.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

459×	`unswap-sqr_binary64`
433×	`fma-def_binary64`
360×	`fma-neg_binary64`
325×	`*-commutative_binary64`
311×	`sqr-pow_binary64`

Counts

125 → 138

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	2157
1	208	1998
2	536	1829
3	923	1329
4	1177	1298
5	2456	1298
6	4266	1298
7	4938	1298

prune48.0ms (1.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	138	7	145

Error

0.0b

Counts

145 → 7

Alt Table

Status	Error	Program
	41.5b	(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) (sqrt.f64 (hypot.f64 x x)))))
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 2748 to 540 computations (80.3% saved)

regimes174.0ms (6.8%)

Accuracy

Total 0.1b remaining (76.8%)

Threshold costs 0.1b (76.8%)

Counts

38 → 1

Compiler

Compiled 2399 to 1373 computations (42.8% 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

end0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

sample630.0ms (24.5%)

Algorithm

1×

intervals

Results

362.0ms

8000×

body

128

valid

Compiler

Compiled 91 to 46 computations (49.5% saved)

Details

analyze289.0ms (11.3%)

sample19.0ms (0.8%)

simplify276.0ms (10.7%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series6.0ms (0.2%)

rewrite21.0ms (0.8%)

simplify96.0ms (3.7%)

prune68.0ms (2.6%)

localize4.0ms (0.2%)

series27.0ms (1%)

rewrite58.0ms (2.3%)

simplify93.0ms (3.6%)

prune87.0ms (3.4%)

localize2.0ms (0.1%)

prune7.0ms (0.3%)

localize9.0ms (0.4%)

series506.0ms (19.7%)

rewrite20.0ms (0.8%)

simplify121.0ms (4.7%)

prune48.0ms (1.9%)

regimes174.0ms (6.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample630.0ms (24.5%)

Profiling