Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample995.0ms (28.8%)

Results

960.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify9.0ms (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

prune3.0ms (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

26.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

series14.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
4.0ms	(.f64 2 (.f64 x x))

rewrite15.0ms (0.4%)

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:

7.0ms	(.f64 2 (.f64 x x))
5.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify143.0ms (4.1%)

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

prune51.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Error

0.1b

Counts

48 → 8

Alt Table

Status	Error	Program
	3.0b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.9b	(*.f64 (sqrt.f64 2) x)
✓	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))
	27.3b	(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)))))
▶	0.5b	(*.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)))
	36.9b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 x x))) (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (.f64 2 (.f64 x x)))))

Compiler

Compiled 632 to 371 computations (41.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series30.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

12.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
12.0ms	(sqrt.f64 (hypot.f64 x x))
6.0ms	(hypot.f64 x x)

rewrite17.0ms (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:

8.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))
1.0ms	(hypot.f64 x x)

simplify159.0ms (4.6%)

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

prune135.0ms (3.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	9	104
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	101	11	112

Error

0.0b

Counts

112 → 11

Alt Table

Status	Error	Program
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	0.1b	(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)))))
	2.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (expm1.f64 (log1p.f64 (sqrt.f64 (hypot.f64 x x)))))
	0.6b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	36.9b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	30.9b	(*.f64 (sqrt.f64 2) x)
	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(.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))))
	1.9b	(.f64 (.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))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (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)))))

Compiler

Compiled 1726 to 426 computations (75.3% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune20.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	4	11	15

Error

0.0b

Counts

15 → 11

Alt Table

Status	Error	Program
	36.9b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(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)))))
	2.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (expm1.f64 (log1p.f64 (sqrt.f64 (hypot.f64 x x)))))
	30.9b	(*.f64 (sqrt.f64 2) x)
	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
▶	0.6b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.3b	(.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))))
	1.9b	(.f64 (.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))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (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)))))

Compiler

Compiled 367 to 136 computations (62.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

series864.0ms (25.1%)

Counts

3 → 36

Calls

3 calls:

554.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

299.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

11.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

rewrite47.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`sqrt-pow1_binary64`
51×	`pow1_binary64`
47×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
36×	`pow-prod-up_binary64`

Counts

3 → 121

Calls

3 calls:

14.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

10.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

2.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify143.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
340×	`unswap-sqr_binary64`
272×	`exp-sum_binary64`
265×	`distribute-rgt-in_binary64`
219×	`fma-neg_binary64`

Counts

157 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1915
1	224	1702
2	445	1614
3	843	1530
4	2021	1476
5	4741	1476
6	4949	1476

prune115.0ms (3.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	193	11	204

Error

0.0b

Counts

204 → 11

Alt Table

Status	Error	Program
	36.9b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(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)))))
	2.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (expm1.f64 (log1p.f64 (sqrt.f64 (hypot.f64 x x)))))
	30.9b	(*.f64 (sqrt.f64 2) x)
	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.6b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.3b	(.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))))
	1.9b	(.f64 (.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))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (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)))))

Compiler

Compiled 3939 to 941 computations (76.1% saved)

regimes461.0ms (13.4%)

Accuracy

Total 0.1b remaining (82.8%)

Threshold costs 0.1b (82.8%)

Counts

74 → 1

Compiler

Compiled 4387 to 2368 computations (46% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end195.0ms (5.7%)

Compiler: Compiled 173 to 66 computations (61.8% saved)

Details

analyze2.0ms (0.1%)

sample995.0ms (28.8%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series14.0ms (0.4%)

rewrite15.0ms (0.4%)

simplify143.0ms (4.1%)

prune51.0ms (1.5%)

localize7.0ms (0.2%)

series30.0ms (0.9%)

rewrite17.0ms (0.5%)

simplify159.0ms (4.6%)

prune135.0ms (3.9%)

localize3.0ms (0.1%)

prune20.0ms (0.6%)

localize11.0ms (0.3%)

series864.0ms (25.1%)

rewrite47.0ms (1.4%)

simplify143.0ms (4.1%)

prune115.0ms (3.3%)

regimes461.0ms (13.4%)

simplify3.0ms (0.1%)

end195.0ms (5.7%)

Profiling