Details

analyze955.0ms (13.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample2.4s (34.2%)

Results

1.5s	8256×	body	128	valid
655.0ms	3145×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

prune5.0ms (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

6.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.0b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	5.7b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series36.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

30.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
5.0ms	(-.f64 t (*.f64 z z))

rewrite117.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

524×	`prod-diff_binary64`
397×	`fma-udef_binary64`
355×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`

Counts

2 → 121

Calls

2 calls:

112.0ms	(-.f64 t (*.f64 z z))
112.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	232	24
2	2678	24
3	4790	24
4	4815	24
5	4945	24
0	0	0
1	0	0

simplify221.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-neg-in_binary64`
686×	`fma-def_binary64`
678×	`cube-prod_binary64`
600×	`fma-neg_binary64`
547×	`sqr-pow_binary64`

Counts

193 → 141

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	29	1087
1	85	941
2	200	869
3	491	869
4	1080	869
5	1887	869
6	2612	869
7	3173	869
8	3184	869
9	3382	869
10	3546	869
11	3731	749
12	3361	749
13	3932	749
14	4622	749
15	4884	749

prune132.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	7	142

Error

5.6b

Counts

142 → 7

Alt Table

Status	Error	Program
	35.6b	(.f64 4 (.f64 y t))
	25.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	25.5b	(fma.f64 y (.f64 4 (/.f64 1 (/.f64 (fma.f64 z z t) (-.f64 (.f64 t t) (pow.f64 z 4))))) (*.f64 x x))
▶	6.0b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	40.0b	(pow.f64 x 2)
✓	6.0b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	38.4b	(fma.f64 y (.f64 4 (fma.f64 (+.f64 (sqrt.f64 t) z) (-.f64 (sqrt.f64 t) z) (fma.f64 z (neg.f64 z) (.f64 z z)))) (*.f64 x x))

Compiler

Compiled 2969 to 1219 computations (58.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
✓	0.0b	(.f64 4 (.f64 y (pow.f64 z 2)))
✓	0.0b	(.f64 4 (.f64 y t))
✓	10.3b	(*.f64 y (pow.f64 z 2))

series59.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
10.0ms	(*.f64 y (pow.f64 z 2))
9.0ms	(.f64 4 (.f64 y (pow.f64 z 2)))
7.0ms	(.f64 4 (.f64 y t))

rewrite83.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

327×	`fma-neg_binary64`
280×	`expm1-udef_binary64`
280×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
156×	`log1p-expm1-u_binary64`

Counts

4 → 99

Calls

4 calls:

80.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
80.0ms	(.f64 4 (.f64 y (pow.f64 z 2)))
80.0ms	(.f64 4 (.f64 y t))
80.0ms	(*.f64 y (pow.f64 z 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	331	45
2	3961	45
3	5049	45
0	0	0
1	0	0

simplify133.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1837×	`fma-def_binary64`
773×	`fma-neg_binary64`
332×	`cancel-sign-sub-inv_binary64`
317×	`distribute-rgt-neg-in_binary64`
288×	`unsub-neg_binary64`

Counts

111 → 112

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	112
1	77	110
2	183	110
3	435	110
4	969	110
5	1648	110
6	2554	110
7	3373	110
8	3384	110
9	3577	110
10	3741	110
11	3916	110
12	4972	110
13	4854	110

prune112.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	112	7	119

Error

2.5b

Counts

119 → 7

Alt Table

Status	Error	Program
	40.0b	(pow.f64 x 2)
	6.3b	(fma.f64 (.f64 y 4) t (fma.f64 x x (.f64 (.f64 y (.f64 z z)) -4)))
	35.6b	(.f64 4 (.f64 y t))
	25.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	25.5b	(fma.f64 y (.f64 4 (/.f64 1 (/.f64 (fma.f64 z z t) (-.f64 (.f64 t t) (pow.f64 z 4))))) (*.f64 x x))
	29.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (.f64 z (sqrt.f64 y)) 2)))
▶	6.2b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (cbrt.f64 (.f64 y (*.f64 z z))) 3)))

Compiler

Compiled 2778 to 1409 computations (49.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 4 (.f64 y t))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)
✓	10.3b	(.f64 y (.f64 z z))
✓	25.3b	(cbrt.f64 (.f64 y (.f64 z z)))

series881.0ms (12.8%)

Counts

3 → 72

Calls

3 calls:

456.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)
418.0ms	(cbrt.f64 (.f64 y (.f64 z z)))
7.0ms	(.f64 y (.f64 z z))

rewrite81.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
330×	`log-prod_binary64`
169×	`pow2_binary64`
117×	`expm1-udef_binary64`

Counts

3 → 87

Calls

3 calls:

80.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)
80.0ms	(.f64 y (.f64 z z))
80.0ms	(cbrt.f64 (.f64 y (.f64 z z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	148	23
2	1570	23
3	4958	23
4	4890	23
0	0	0
1	0	0

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

698×	`unswap-sqr_binary64`
316×	`unsub-neg_binary64`
281×	`fma-neg_binary64`
273×	`exp-sum_binary64`
247×	`fma-def_binary64`

Counts

159 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	780
1	130	780
2	237	744
3	708	604
4	2555	604
5	5004	604

prune121.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	102	6	108

Error

0.0b

Counts

108 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (.f64 (cbrt.f64 (*.f64 y z)) (cbrt.f64 z)) 3)))
	25.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	6.3b	(fma.f64 (.f64 y 4) t (fma.f64 x x (.f64 (.f64 y (.f64 z z)) -4)))
▶	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 z (*.f64 y z))))
	29.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 z (sqrt.f64 y)) 2)) 3)))
	29.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (.f64 z (sqrt.f64 y)) 2)))

Compiler

Compiled 2707 to 1580 computations (41.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 z (*.f64 y z))))
✓	0.0b	(.f64 4 (.f64 z (*.f64 y z)))
	0.0b	(.f64 4 (.f64 y t))
✓	0.2b	(.f64 z (.f64 y z))

series58.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

39.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 z (*.f64 y z))))
10.0ms	(.f64 z (.f64 y z))
9.0ms	(.f64 4 (.f64 z (*.f64 y z)))

rewrite114.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

462×	`fma-neg_binary64`
288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`

Counts

3 → 85

Calls

3 calls:

112.0ms	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 z (*.f64 y z))))
112.0ms	(.f64 4 (.f64 z (*.f64 y z)))
112.0ms	(.f64 z (.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	331	38
2	4085	38
3	4984	38
4	5337	38
0	0	0
1	0	0

simplify213.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

708×	`distribute-rgt-neg-in_binary64`
678×	`cube-prod_binary64`
657×	`fma-def_binary64`
600×	`fma-neg_binary64`
547×	`sqr-pow_binary64`

Counts

181 → 103

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	27	1348
1	81	1202
2	192	1130
3	465	1130
4	1047	1130
5	1855	1130
6	2608	1130
7	3162	1130
8	3174	1130
9	3372	1130
10	3536	1130
11	3721	1052
12	3351	1052
13	3922	1052
14	4612	1052
15	4874	1052

prune123.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	114	8	122

Error

Counts

122 → 8

Alt Table

Status	Error	Program
	19.4b	(pow.f64 (sqrt.f64 (fma.f64 4 (.f64 y t) (fma.f64 x x (.f64 (.f64 z (.f64 z y)) -4)))) 2)
	0.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (pow.f64 (cbrt.f64 (.f64 (.f64 z (*.f64 z y)) 4)) 3))
	6.3b	(fma.f64 (.f64 y 4) t (fma.f64 x x (.f64 (.f64 y (.f64 z z)) -4)))
	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (.f64 (cbrt.f64 (*.f64 y z)) (cbrt.f64 z)) 3)))
	25.4b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	0.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (cbrt.f64 (.f64 z (*.f64 z y))) 3)))
✓	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 z (*.f64 y z))))
	29.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (pow.f64 (.f64 z (sqrt.f64 y)) 2)))

Compiler

Compiled 2791 to 1359 computations (51.3% saved)

regimes789.0ms (11.4%)

Accuracy

Total 0.1b remaining (76.8%)

Threshold costs 0.1b (76.8%)

Counts

72 → 1

Compiler

Compiled 16027 to 10660 computations (33.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	17	21
2	17	21

end145.0ms (2.1%)

Compiler: Compiled 218 to 152 computations (30.3% saved)

Details

analyze955.0ms (13.8%)

sample2.4s (34.2%)

simplify64.0ms (0.9%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series36.0ms (0.5%)

rewrite117.0ms (1.7%)

simplify221.0ms (3.2%)

prune132.0ms (1.9%)

localize10.0ms (0.1%)

series59.0ms (0.8%)

rewrite83.0ms (1.2%)

simplify133.0ms (1.9%)

prune112.0ms (1.6%)

localize14.0ms (0.2%)

series881.0ms (12.8%)

rewrite81.0ms (1.2%)

simplify57.0ms (0.8%)

prune121.0ms (1.8%)

localize12.0ms (0.2%)

series58.0ms (0.8%)

rewrite114.0ms (1.7%)

simplify213.0ms (3.1%)

prune123.0ms (1.8%)

regimes789.0ms (11.4%)

simplify3.0ms (0%)

end145.0ms (2.1%)

Profiling