Details

analyze4.0ms (0.1%)

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)

sample827.0ms (27.9%)

Results

748.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.2%)

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%)

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

32.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.6b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	31.6b	(sqrt.f64 (.f64 2 (.f64 x x)))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite8.0ms (0.3%)

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)))

simplify74.0ms (2.5%)

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

prune102.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	9	48

Error

0.1b

Counts

48 → 9

Alt Table

Status	Error	Program
	31.1b	(*.f64 (sqrt.f64 2) x)
✓	32.6b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.0b	(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)))))
	52.1b	(sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 6)))
▶	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)))
	41.9b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	2.8b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))

Compiler

Compiled 618 to 365 computations (40.9% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.2b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series17.0ms (0.6%)

Counts

3 → 24

Calls

3 calls:

9.0ms	(sqrt.f64 (hypot.f64 x x))
5.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
3.0ms	(hypot.f64 x x)

rewrite12.0ms (0.4%)

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)

simplify81.0ms (2.7%)

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

prune57.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	102	11	113

Error

0.0b

Counts

113 → 11

Alt Table

Status	Error	Program
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	31.1b	(*.f64 (sqrt.f64 2) x)
	1.4b	(.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))))
	52.1b	(sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 6)))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	23.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
▶	0.2b	(hypot.f64 x x)

Compiler

Compiled 1616 to 422 computations (73.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(hypot.f64 x x)

prune10.0ms (0.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

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

Error

0.0b

Counts

15 → 11

Alt Table

Status	Error	Program
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	31.1b	(*.f64 (sqrt.f64 2) x)
	1.4b	(.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))))
	52.1b	(sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 6)))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	23.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
▶	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓	0.2b	(hypot.f64 x x)

Compiler

Compiled 293 to 136 computations (53.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
✓	0.4b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series903.0ms (30.4%)

Counts

4 → 48

Calls

4 calls:

317.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
312.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
271.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
34×	`pow1_binary64`
27×	`pow1/3_binary64`
26×	`sqrt-pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 127

Calls

4 calls:

12.0ms	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
10.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
2.0ms	(cbrt.f64 (hypot.f64 x x))

simplify168.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
383×	`exp-prod_binary64`
363×	`exp-sum_binary64`
338×	`fma-neg_binary64`
331×	`sqr-pow_binary64`

Counts

175 → 185

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	171	2842
1	358	2516
2	824	2304
3	1408	1940
4	2751	1553
5	4541	1553
6	4106	1553
7	4795	1553
8	5128	1553

prune124.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	4	4	8
Picked	1	0	1
Done	0	2	2
Total	224	10	234

Error

Counts

234 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	31.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.2b	(.f64 (.f64 (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.4b	(.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))))
	1.3b	(*.f64 (fabs.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓	0.2b	(hypot.f64 x x)
	1.0b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))))
	23.7b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	31.1b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 5613 to 1234 computations (78% saved)

regimes401.0ms (13.5%)

Accuracy

Total 0.1b remaining (83.2%)

Threshold costs 0.1b (83.2%)

Counts

117 → 1

Compiler

Compiled 9767 to 4607 computations (52.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end107.0ms (3.6%)

Compiler: Compiled 172 to 75 computations (56.4% saved)

Details

analyze4.0ms (0.1%)

sample827.0ms (27.9%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify74.0ms (2.5%)

prune102.0ms (3.4%)

localize4.0ms (0.1%)

series17.0ms (0.6%)

rewrite12.0ms (0.4%)

simplify81.0ms (2.7%)

prune57.0ms (1.9%)

localize2.0ms (0.1%)

prune10.0ms (0.3%)

localize12.0ms (0.4%)

series903.0ms (30.4%)

rewrite36.0ms (1.2%)

simplify168.0ms (5.7%)

prune124.0ms (4.2%)

regimes401.0ms (13.5%)

simplify2.0ms (0.1%)

end107.0ms (3.6%)

Profiling