Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.5s (38.5%)

Results

1.5s	8256×	body	128	valid
1.0ms	3×	body	128	invalid

Compiler

Compiled 142 to 66 computations (53.5% saved)

preprocess31.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

642×	`distribute-lft-out_binary64`
588×	`associate-/l*_binary64`
406×	`associate-/r*_binary64`
400×	`*-commutative_binary64`
244×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	251	41
3	1208	37
4	2394	37
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 68 to 31 computations (54.4% saved)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-lft-out_binary64`
588×	`associate-/l*_binary64`
406×	`associate-/r*_binary64`
400×	`*-commutative_binary64`
244×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	251	41
3	1208	37
4	2394	37

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.6b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Status

Error

Program

▶

0.1b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

0.6b

(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))

Compiler

Compiled 278 to 149 computations (46.4% saved)

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	0.1b	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
✓	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series22.0ms (0.6%)

Counts

4 → 36

Calls

9 calls:

5.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))	x	-inf
3.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))	x	inf
2.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))	x	0
2.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))	x	-inf
2.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))	x	inf

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
106×	`add-sqr-sqrt_binary64`
103×	`add-cbrt-cube_binary64`
102×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	245	19
2	2579	19

Stop Event

1×	node limit

Counts

4 → 69

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

776×	`sqr-pow_binary64`
400×	`unswap-sqr_binary64`
357×	`pow-sqr_binary64`
321×	`*-commutative_binary64`
270×	`cube-prod_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	252
1	21	252
2	45	252
3	98	252
4	242	228
5	796	228
6	1635	228
7	1738	228
8	1880	180
9	2074	180
10	2314	180
11	2631	180
12	3034	180
13	3530	180
14	4161	180
15	4971	180

Stop Event

1×	node limit

Counts

105 → 73

prune170.0ms (4.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	3	128

Error

0.0b

Counts

128 → 3

Alt Table

Status	Error	Program
	0.6b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 8426 to 3457 computations (59% saved)

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
	0.1b	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))

prune133.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Error

0.0b

Counts

94 → 3

Alt Table

Status	Error	Program
	0.6b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
▶	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 5429 to 2885 computations (46.9% saved)

localize29.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (cbrt.f64 x))
✓	0.2b	(pow.f64 (*.f64 x (cbrt.f64 x)) 3)
✓	0.6b	(cbrt.f64 x)
	1.0b	(sqrt.f64 (PI.f64))

series50.0ms (1.3%)

Counts

3 → 0

Calls

9 calls:

19.0ms	(pow.f64 (*.f64 x (cbrt.f64 x)) 3)	x	-inf
9.0ms	(cbrt.f64 x)	x	-inf
9.0ms	(*.f64 x (cbrt.f64 x))	x	-inf
3.0ms	(pow.f64 (*.f64 x (cbrt.f64 x)) 3)	x	0
3.0ms	(pow.f64 (*.f64 x (cbrt.f64 x)) 3)	x	inf

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`unpow-prod-down_binary64`
472×	`log1p-expm1-u_binary64`
472×	`expm1-log1p-u_binary64`
255×	`log-prod_binary64`
133×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	125	16
2	1421	16

Stop Event

1×	node limit

Counts

3 → 107

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

107 → 107

prune207.0ms (5.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	130	3	133

Error

0.0b

Counts

133 → 3

Alt Table

Status	Error	Program
▶	0.6b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
✓	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 8926 to 4005 computations (55.1% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/21 (pow.f64 x 6))
✓	0.1b	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
✓	0.2b	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))

series16.0ms (0.4%)

Counts

3 → 24

Calls

9 calls:

3.0ms	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))	x	-inf
3.0ms	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))	x	inf
3.0ms	(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))	x	0
2.0ms	(*.f64 1/21 (pow.f64 x 6))	x	inf
1.0ms	(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))	x	-inf

rewrite49.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
195×	`log-pow_binary64`
138×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	300	28
2	3458	28

Stop Event

1×	node limit

Counts

3 → 81

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

518×	`sqr-pow_binary64`
487×	`associate-l_binary64`
467×	`unswap-sqr_binary64`
440×	`fma-def_binary64`
300×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	291
1	32	291
2	56	291
3	123	267
4	399	267
5	1478	267
6	2937	267
7	3286	267
8	3570	267
9	3854	267
10	4219	267
11	4698	267

Stop Event

1×	node limit

Counts

105 → 86

prune113.0ms (3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	108	4	112

Error

0.0b

Counts

112 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	2.6b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (sqrt.f64 (.f64 (pow.f64 x 12) 1/441))) (fma.f64 2/3 (*.f64 x x) 2))))
✓	0.6b	(fabs.f64 (.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
✓	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 3277 to 2102 computations (35.9% saved)

regimes1.1s (27.8%)

Accuracy

Total 0.2b remaining (89%)

Threshold costs 0.2b (89%)

Counts

123 → 1

Compiler

Compiled 29742 to 20008 computations (32.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`sqr-abs_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	76
1	56	76
2	60	76

Stop Event

1×

saturated

end142.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 270 to 171 computations (36.7% saved)

Details

analyze5.0ms (0.1%)

sample1.5s (38.5%)

preprocess31.0ms (0.8%)

simplify21.0ms (0.5%)

prune5.0ms (0.1%)

localize23.0ms (0.6%)

series22.0ms (0.6%)

rewrite42.0ms (1.1%)

simplify71.0ms (1.9%)

prune170.0ms (4.5%)

localize26.0ms (0.7%)

prune133.0ms (3.5%)

localize29.0ms (0.8%)

series50.0ms (1.3%)

rewrite37.0ms (1%)

simplify7.0ms (0.2%)

prune207.0ms (5.4%)

localize15.0ms (0.4%)

series16.0ms (0.4%)

rewrite49.0ms (1.3%)

simplify66.0ms (1.7%)

prune113.0ms (3%)

regimes1.1s (27.8%)

simplify3.0ms (0.1%)

end142.0ms (3.7%)

Profiling