Details

analyze4.0ms (0.3%)

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 6 computations (25% saved)

sample29.0ms (1.9%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify6.0ms (0.4%)

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 (0.1%)

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

29.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize37.0ms (2.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	28.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite10.0ms (0.6%)

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:

5.0ms	(.f64 2 (.f64 x x))
3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

simplify74.0ms (4.7%)

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

prune28.0ms (1.8%)

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
	29.7b	(*.f64 (sqrt.f64 2) x)
✓	29.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
	30.1b	(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)))))
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.5b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	42.6b	(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)))))
	2.7b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	33.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 632 to 371 computations (41.3% saved)

localize4.0ms (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)))

series18.0ms (1.1%)

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)))
3.0ms	(hypot.f64 x x)

rewrite11.0ms (0.7%)

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)

simplify84.0ms (5.3%)

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

prune63.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	9	104
Fresh	5	1	6
Picked	1	0	1
Done	1	0	1
Total	102	10	112

Error

0.0b

Counts

112 → 10

Alt Table

Status	Error	Program
	21.3b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	42.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (.f64 (*.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))))
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	29.7b	(*.f64 (sqrt.f64 2) x)
	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))
	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))))
▶	0.1b	(hypot.f64 x x)
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))
	1.5b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 1704 to 428 computations (74.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune11.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	4	10	14

Error

0.0b

Counts

14 → 10

Alt Table

Status	Error	Program
	21.3b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	42.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (.f64 (*.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))))
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	29.7b	(*.f64 (sqrt.f64 2) x)
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))
	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))))
✓	0.1b	(hypot.f64 x x)
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))
	1.5b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 381 to 142 computations (62.7% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/2)
	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (hypot.f64 x x) 1/2))

series221.0ms (14.1%)

Counts

2 → 24

Calls

2 calls:

217.0ms	(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))

rewrite10.0ms (0.6%)

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:

5.0ms	(*.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)

simplify90.0ms (5.8%)

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

prune71.0ms (4.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	119	9	128

Error

0.0b

Counts

128 → 9

Alt Table

Status	Error	Program
	21.3b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3)))
	29.7b	(*.f64 (sqrt.f64 2) x)
	0.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 1/4)))
✓	0.1b	(hypot.f64 x x)
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))
	1.5b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (fabs.f64 (cbrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 1/2))
	0.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 1 (sqrt.f64 (hypot.f64 x x))))
	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 1846 to 666 computations (63.9% saved)

regimes260.0ms (16.5%)

Accuracy

Total 0.1b remaining (77.2%)

Threshold costs 0.1b (77.2%)

Counts

75 → 1

Compiler

Compiled 4847 to 2435 computations (49.8% saved)

simplify3.0ms (0.2%)

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)

sample524.0ms (33.3%)

Algorithm

1×

intervals

Results

259.0ms

8000×

body

128

valid

Compiler

Compiled 163 to 69 computations (57.7% saved)

Details

analyze4.0ms (0.3%)

sample29.0ms (1.9%)

simplify6.0ms (0.4%)

prune1.0ms (0.1%)

localize37.0ms (2.3%)

series5.0ms (0.3%)

rewrite10.0ms (0.6%)

simplify74.0ms (4.7%)

prune28.0ms (1.8%)

localize4.0ms (0.2%)

series18.0ms (1.1%)

rewrite11.0ms (0.7%)

simplify84.0ms (5.3%)

prune63.0ms (4%)

localize2.0ms (0.1%)

prune11.0ms (0.7%)

localize7.0ms (0.4%)

series221.0ms (14.1%)

rewrite10.0ms (0.6%)

simplify90.0ms (5.8%)

prune71.0ms (4.5%)

regimes260.0ms (16.5%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample524.0ms (33.3%)

Profiling