Details

analyze4.0ms (0.2%)

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
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample697.0ms (35%)

Results

684.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 22 to 18 computations (18.2% saved)

preprocess29.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

271×	`fma-def_binary64`
256×	`fma-neg_binary64`
75×	`cancel-sign-sub-inv_binary64`
54×	`sub-neg_binary64`
30×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	65	11
3	147	11
4	291	9
5	486	9
6	718	9
7	1049	9
8	1166	9
9	1185	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 8 computations (20% saved)

simplify18.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
256×	`fma-neg_binary64`
75×	`cancel-sign-sub-inv_binary64`
54×	`sub-neg_binary64`
30×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	65	11
3	147	11
4	291	9
5	486	9
6	718	9
7	1049	9
8	1166	9
9	1185	9

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x -3/25 -253/1000)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)	x	-inf
1.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)	x	inf
1.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)	x	0
1.0ms	(fma.f64 x -3/25 -253/1000)	x	-inf
1.0ms	(fma.f64 x -3/25 -253/1000)	x	inf

rewrite42.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
263×	`unpow-prod-down_binary64`
236×	`log-prod_binary64`
160×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	136	14
2	1424	14

Stop Event

1×	node limit

Counts

2 → 66

simplify36.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-l_binary64`
391×	`fma-def_binary64`
312×	`distribute-rgt-neg-in_binary64`
301×	`unswap-sqr_binary64`
271×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	222
1	51	204
2	112	156
3	239	144
4	834	144
5	2839	144
6	4254	144

Stop Event

1×	node limit

Counts

90 → 80

prune72.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Error

0.0b

Counts

81 → 6

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (pow.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) 3) 1)
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	55.1b	(fma.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) 2) 1)
	8.3b	(fma.f64 x (/.f64 (+.f64 (.f64 -27/15625 (pow.f64 x 3)) -16194277/1000000000) (+.f64 (pow.f64 (.f64 x -3/25) 2) (-.f64 64009/1000000 (.f64 (.f64 x -3/25) -253/1000)))) 1)
	0.7b	(fma.f64 x (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 2) 3) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 1172 to 945 computations (19.4% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
✓	0.0b	(*.f64 253/1000 x)
✓	0.2b	(*.f64 3/25 (pow.f64 x 2))

series7.0ms (0.3%)

Counts

3 → 3

Calls

9 calls:

1.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))	x	-inf
1.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))	x	inf
1.0ms	(*.f64 3/25 (pow.f64 x 2))	x	0
1.0ms	(*.f64 3/25 (pow.f64 x 2))	x	inf
1.0ms	(*.f64 3/25 (pow.f64 x 2))	x	-inf

rewrite49.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

852×	`log1p-expm1-u_binary64`
852×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`add-cbrt-cube_binary64`
88×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	196	22
2	2348	22

Stop Event

1×	node limit

Counts

3 → 65

simplify56.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

626×	`sqr-pow_binary64`
513×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
280×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	26	18
3	51	18
4	124	18
5	367	18
6	1384	18
7	2272	18
8	2436	18
9	2650	18
10	2870	18
11	3171	18
12	3571	18
13	4057	18
14	4618	18

Stop Event

1×	node limit

Counts

68 → 68

prune88.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
	11.5b	(-.f64 1 (+.f64 (sqrt.f64 (.f64 (pow.f64 x 4) 9/625)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x)))
	11.6b	(-.f64 1 (fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 9/625)) (cbrt.f64 (.f64 3/25 (.f64 x x))) (.f64 x 253/1000)))
	8.3b	(fma.f64 x (/.f64 (+.f64 (.f64 -27/15625 (pow.f64 x 3)) -16194277/1000000000) (+.f64 (pow.f64 (.f64 x -3/25) 2) (-.f64 64009/1000000 (.f64 (.f64 x -3/25) -253/1000)))) 1)
	0.7b	(fma.f64 x (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 2) 3) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 1292 to 949 computations (26.5% saved)

localize47.0ms (2.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))
✓	0.0b	(*.f64 x (sqrt.f64 3/25))
	0.0b	(*.f64 253/1000 x)
✓	0.3b	(pow.f64 (*.f64 x (sqrt.f64 3/25)) 2)

series16.0ms (0.8%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))	x	-inf
2.0ms	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))	x	inf
2.0ms	(pow.f64 (*.f64 x (sqrt.f64 3/25)) 2)	x	-inf
2.0ms	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))	x	0
2.0ms	(pow.f64 (*.f64 x (sqrt.f64 3/25)) 2)	x	0

rewrite49.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

433×	`log-prod_binary64`
313×	`fma-def_binary64`
249×	`pow2_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	218	24
2	2596	24

Stop Event

1×	node limit

Counts

3 → 112

simplify80.0ms (4%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-l_binary64`
649×	`fma-def_binary64`
468×	`associate-r_binary64`
290×	`distribute-lft-in_binary64`
290×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	388
1	25	273
2	47	264
3	124	246
4	460	246
5	2306	246
6	2663	246
7	2991	246
8	3416	246
9	4039	246

Stop Event

1×	node limit

Counts

148 → 118

prune194.0ms (9.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	131	6	137

Error

0.0b

Counts

137 → 6

Alt Table

Status	Error	Program
	11.5b	(-.f64 1 (+.f64 (sqrt.f64 (.f64 (pow.f64 x 4) 9/625)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (.f64 x (.f64 (sqrt.f64 3/25) (.f64 x (sqrt.f64 3/25)))) (.f64 253/1000 x)))
	8.3b	(fma.f64 x (/.f64 (+.f64 (.f64 -27/15625 (pow.f64 x 3)) -16194277/1000000000) (+.f64 (pow.f64 (.f64 x -3/25) 2) (-.f64 64009/1000000 (.f64 (.f64 x -3/25) -253/1000)))) 1)
	32.1b	(-.f64 1 (fma.f64 (sqrt.f64 (.f64 x (sqrt.f64 3/25))) (.f64 (sqrt.f64 (.f64 x (sqrt.f64 3/25))) (.f64 x (sqrt.f64 3/25))) (*.f64 x 253/1000)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 2350 to 1781 computations (24.2% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (sqrt.f64 3/25))
	0.0b	(*.f64 253/1000 x)
✓	0.1b	(.f64 x (.f64 (sqrt.f64 3/25) (*.f64 x (sqrt.f64 3/25))))
✓	0.3b	(.f64 (sqrt.f64 3/25) (.f64 x (sqrt.f64 3/25)))

series16.0ms (0.8%)

Counts

2 → 24

Calls

6 calls:

3.0ms	(.f64 x (.f64 (sqrt.f64 3/25) (*.f64 x (sqrt.f64 3/25))))	x	inf
3.0ms	(.f64 (sqrt.f64 3/25) (.f64 x (sqrt.f64 3/25)))	x	-inf
2.0ms	(.f64 x (.f64 (sqrt.f64 3/25) (*.f64 x (sqrt.f64 3/25))))	x	-inf
2.0ms	(.f64 x (.f64 (sqrt.f64 3/25) (*.f64 x (sqrt.f64 3/25))))	x	0
2.0ms	(.f64 (sqrt.f64 3/25) (.f64 x (sqrt.f64 3/25)))	x	0

rewrite40.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
500×	`unpow-prod-down_binary64`
331×	`log-prod_binary64`
162×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	25
1	142	11
2	1593	11

Stop Event

1×	node limit

Counts

2 → 34

simplify67.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-l_binary64`
538×	`sqr-pow_binary64`
508×	`associate-r_binary64`
475×	`*-commutative_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	252
1	19	132
2	41	132
3	105	132
4	435	132
5	2432	132
6	2541	132
7	2736	132
8	2932	132
9	3161	132
10	3466	132
11	4107	132
12	4582	132

Stop Event

1×	node limit

Counts

58 → 38

prune82.0ms (4.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	74	6	80

Error

0.0b

Counts

80 → 6

Alt Table

Status	Error	Program
	11.5b	(-.f64 1 (+.f64 (sqrt.f64 (.f64 (pow.f64 x 4) 9/625)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 x (.f64 (sqrt.f64 3/25) (.f64 x (sqrt.f64 3/25)))) (.f64 253/1000 x)))
	8.3b	(fma.f64 x (/.f64 (+.f64 (.f64 -27/15625 (pow.f64 x 3)) -16194277/1000000000) (+.f64 (pow.f64 (.f64 x -3/25) 2) (-.f64 64009/1000000 (.f64 (.f64 x -3/25) -253/1000)))) 1)
	32.1b	(-.f64 1 (fma.f64 (sqrt.f64 (.f64 x (sqrt.f64 3/25))) (.f64 (sqrt.f64 (.f64 x (sqrt.f64 3/25))) (.f64 x (sqrt.f64 3/25))) (*.f64 x 253/1000)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 1323 to 1050 computations (20.6% saved)

regimes178.0ms (9%)

Accuracy

Total 0.1b remaining (90.1%)

Threshold costs 0.1b (90.1%)

Counts

55 → 1

Compiler

Compiled 2443 to 1962 computations (19.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	14
2	18	14
3	20	14
4	21	14

Stop Event

1×

saturated

end94.0ms (4.7%)

Stop Event

1×

fuel

Compiler

Compiled 119 to 96 computations (19.3% saved)

Details

analyze4.0ms (0.2%)

sample697.0ms (35%)

preprocess29.0ms (1.4%)

simplify18.0ms (0.9%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite42.0ms (2.1%)

simplify36.0ms (1.8%)

prune72.0ms (3.6%)

localize6.0ms (0.3%)

series7.0ms (0.3%)

rewrite49.0ms (2.5%)

simplify56.0ms (2.8%)

prune88.0ms (4.4%)

localize47.0ms (2.4%)

series16.0ms (0.8%)

rewrite49.0ms (2.5%)

simplify80.0ms (4%)

prune194.0ms (9.7%)

localize9.0ms (0.5%)

series16.0ms (0.8%)

rewrite40.0ms (2%)

simplify67.0ms (3.3%)

prune82.0ms (4.1%)

regimes178.0ms (9%)

simplify2.0ms (0.1%)

end94.0ms (4.7%)

Profiling