Details

analyze1.5s (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	74.7%	25.3%	8
0%	74.7%	25.3%	9
0%	65.4%	34.6%	10
0%	51.4%	48.6%	11
0%	51.4%	48.6%	12
0%	51.4%	48.6%	13
0%	51.4%	48.6%	14

Compiler

Compiled 30 to 21 computations (30% saved)

sample4.6s (18.9%)

Symmetry

(sort z t a)

Results

2.3s	11135×	body	128	invalid
2.2s	8251×	body	128	valid
1.0ms	4×	body	256	valid
1.0ms	1×	body	1024	valid

Compiler

Compiled 89 to 62 computations (30.3% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2664×	`associate-+l+_binary64`
1041×	`associate-+r+_binary64`
923×	`+-commutative_binary64`
750×	`fma-def_binary64`
5×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	41	26
2	109	26
3	376	26
4	1118	26
5	1592	26
6	1698	26
7	1698	26
8	1698	26
9	1698	26
10	2706	26
11	2958	26
12	2958	26
13	2910	26
14	2910	26
15	2540	26
16	2524	26

prune4.0ms (0%)

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 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

Compiler

Compiled 99 to 61 computations (38.4% saved)

localize175.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
✓	0.1b	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
✓	0.1b	(fma.f64 x (log.f64 y) z)

series1.6s (6.5%)

Counts

3 → 216

Calls

3 calls:

833.0ms

(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))

656.0ms

(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

94.0ms

(fma.f64 x (log.f64 y) z)

rewrite72.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

360×	`log1p-udef_binary64`
199×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
185×	`add-log-exp_binary64`

Counts

3 → 66

Calls

3 calls:

70.0ms

(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

70.0ms

(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))

70.0ms

(fma.f64 x (log.f64 y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	55
1	383	55
2	4868	55
3	5415	55
0	0	0
1	0	0

simplify151.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

801×	`sub-neg_binary64`
774×	`associate--l+_binary64`
618×	`fma-neg_binary64`
576×	`+-commutative_binary64`
426×	`fma-def_binary64`

Counts

282 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	4881
1	372	4881
2	1183	4401
3	3310	4381
4	4648	4381
5	5091	4381

prune108.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

0.1b

Counts

118 → 4

Alt Table

Status	Error	Program
	1.3b	(*.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) 2))
▶	0.1b	(-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 y i) (+.f64 (.f64 (log.f64 y) x) (+.f64 z (.f64 (log.f64 c) b)))))) (.f64 1/2 (log.f64 c)))
	1.2b	(fma.f64 y i (pow.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) 3))
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

Compiler

Compiled 2952 to 1105 computations (62.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (log.f64 y) x) (+.f64 z (.f64 (log.f64 c) b)))
✓	0.0b	(+.f64 (.f64 y i) (+.f64 (.f64 (log.f64 y) x) (+.f64 z (*.f64 (log.f64 c) b))))
✓	0.3b	(*.f64 (log.f64 y) x)
✓	0.3b	(*.f64 (log.f64 c) b)

series1.5s (6.2%)

Counts

4 → 136

Calls

4 calls:

584.0ms	(+.f64 (.f64 (log.f64 y) x) (+.f64 z (.f64 (log.f64 c) b)))
505.0ms	(+.f64 (.f64 y i) (+.f64 (.f64 (log.f64 y) x) (+.f64 z (*.f64 (log.f64 c) b))))
226.0ms	(*.f64 (log.f64 c) b)
193.0ms	(*.f64 (log.f64 y) x)

rewrite84.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

304×	`expm1-udef_binary64`
304×	`log1p-udef_binary64`
167×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`

Counts

4 → 106

Calls

4 calls:

76.0ms	(+.f64 (.f64 (log.f64 y) x) (+.f64 z (.f64 (log.f64 c) b)))
76.0ms	(+.f64 (.f64 y i) (+.f64 (.f64 (log.f64 y) x) (+.f64 z (*.f64 (log.f64 c) b))))
76.0ms	(*.f64 (log.f64 y) x)
76.0ms	(*.f64 (log.f64 c) b)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	323	42
2	4363	42
3	5279	42
0	0	0
1	0	0

simplify236.0ms (1%)

Algorithm

1×	egg-herbie

Rules

781×	`unsub-neg_binary64`
765×	`sub-neg_binary64`
675×	`fma-def_binary64`
464×	`distribute-neg-in_binary64`
407×	`+-commutative_binary64`

Counts

242 → 143

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	71	1814
1	189	1718
2	367	1718
3	940	1718
4	2684	1718
5	3479	1718
6	4013	1718
7	4195	1718
8	4360	1718
9	4265	1718
10	4267	1718
11	5002	1718

prune140.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	144	3	147

Error

0.1b

Counts

147 → 3

Alt Table

Status	Error	Program
▶	0.9b	(-.f64 (+.f64 a (+.f64 t (.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)))) (.f64 1/2 (log.f64 c)))
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	0.9b	(-.f64 (+.f64 a (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 3))) (*.f64 1/2 (log.f64 c)))

Compiler

Compiled 4384 to 1515 computations (65.4% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (log.f64 c) b z)
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)
✓	0.6b	(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z))))

series4.0s (16.7%)

Counts

4 → 252

Calls

4 calls:

1.8s	(pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)
1.4s	(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z))))
775.0ms	(*.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2))
93.0ms	(fma.f64 (log.f64 c) b z)

rewrite76.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

633×	`log-prod_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
238×	`log-pow_binary64`
192×	`prod-diff_binary64`

Counts

4 → 120

Calls

4 calls:

72.0ms	(fma.f64 (log.f64 c) b z)
72.0ms	(*.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2))
72.0ms	(pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)
72.0ms	(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	65
1	292	65
2	3138	65
3	5584	65
0	0	0
1	0	0

simplify457.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
421×	`times-frac_binary64`
104×	`sqr-pow_binary64`
80×	`sub-neg_binary64`
46×	`unpow1/3_binary64`

Counts

372 → 394

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3091	38600
1	5124	38600

prune1.7s (7.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	572	2	574
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	573	4	577

Error

0.0b

Counts

577 → 4

Alt Table

Status	Error	Program
	1.1b	(-.f64 (+.f64 a (+.f64 t (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z))))) 3) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)))) (.f64 1/2 (log.f64 c)))
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
▶	0.9b	(-.f64 (+.f64 a (+.f64 t (.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2))))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)))) (*.f64 1/2 (log.f64 c)))
	0.9b	(-.f64 (+.f64 a (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 3))) (*.f64 1/2 (log.f64 c)))

Compiler

Compiled 88172 to 46204 computations (47.6% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2)
✓	0.6b	(cbrt.f64 (fma.f64 (log.f64 c) b z))
✓	0.6b	(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (*.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2)))))
	0.6b	(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z))))

series2.6s (10.6%)

Counts

3 → 144

Calls

3 calls:

1.8s

(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (*.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2)))))

433.0ms

(pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2)

363.0ms

(cbrt.f64 (fma.f64 (log.f64 c) b z))

rewrite62.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
260×	`prod-diff_binary64`
252×	`log-pow_binary64`
159×	`fma-def_binary64`

Counts

3 → 65

Calls

3 calls:

60.0ms

(pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2)

60.0ms

(cbrt.f64 (fma.f64 (log.f64 c) b z))

60.0ms

(cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (*.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	308	40
2	3295	40
3	4940	40
0	0	0
1	0	0

simplify244.0ms (1%)

Algorithm

1×	egg-herbie

Rules

449×	`associate-r_binary64`
368×	`fma-def_binary64`
256×	`associate-*r/_binary64`
248×	`associate-/l*_binary64`
222×	`associate-/r*_binary64`

Counts

209 → 263

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1778	21294
1	5226	21294

prune1.3s (5.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	469	1	470
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	469	5	474

Error

0.0b

Counts

474 → 5

Alt Table

Status	Error	Program
	41.9b	(-.f64 (+.f64 a (+.f64 t (.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (.f64 (pow.f64 (.f64 (log.f64 c) b) 1/3) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2))))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)))) (.f64 1/2 (log.f64 c)))
	1.1b	(-.f64 (+.f64 a (+.f64 t (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z))))) 3) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)))) (.f64 1/2 (log.f64 c)))
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
✓	0.9b	(-.f64 (+.f64 a (+.f64 t (.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 c) b z)) 2))))) (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 2)))) (*.f64 1/2 (log.f64 c)))
	0.9b	(-.f64 (+.f64 a (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 y i (fma.f64 (log.f64 y) x (fma.f64 (log.f64 c) b z)))) 3))) (*.f64 1/2 (log.f64 c)))

Compiler

Compiled 69388 to 35682 computations (48.6% saved)

regimes2.9s (12.1%)

Accuracy

Total 0.0b remaining (30.9%)

Threshold costs 0.0b (30.9%)

Counts

130 → 1

Compiler

Compiled 59424 to 35312 computations (40.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	31
1	31	31
2	38	31
3	42	31
4	45	31
5	46	31
6	45	31

end596.0ms (2.5%)

Compiler: Compiled 335 to 196 computations (41.5% saved)

Details

analyze1.5s (6%)

sample4.6s (18.9%)

simplify78.0ms (0.3%)

prune4.0ms (0%)

localize175.0ms (0.7%)

series1.6s (6.5%)

rewrite72.0ms (0.3%)

simplify151.0ms (0.6%)

prune108.0ms (0.4%)

localize19.0ms (0.1%)

series1.5s (6.2%)

rewrite84.0ms (0.3%)

simplify236.0ms (1%)

prune140.0ms (0.6%)

localize26.0ms (0.1%)

series4.0s (16.7%)

rewrite76.0ms (0.3%)

simplify457.0ms (1.9%)

prune1.7s (7.1%)

localize43.0ms (0.2%)

series2.6s (10.6%)

rewrite62.0ms (0.3%)

simplify244.0ms (1%)

prune1.3s (5.4%)

regimes2.9s (12.1%)

simplify3.0ms (0%)

end596.0ms (2.5%)

Profiling