Details

analyze311.0ms (5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.0s (16.9%)

Symmetry

(sort x y)

Results

913.0ms	8256×	body	128	valid
47.0ms	449×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-neg_binary64`
527×	`rules-6_binary64`
422×	`rules-4_binary64`
308×	`rules-1_binary64`
303×	`rules-5-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	25	14
2	69	14
3	218	14
4	649	14
5	3714	14
6	4641	14
7	5082	14

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.4b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	4.5b	(*.f64 y (fma.f64 z z 1))

series88.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

80.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
8.0ms	(*.f64 y (fma.f64 z z 1))

rewrite64.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

825×	`log1p-expm1-u_binary64`
825×	`expm1-log1p-u_binary64`
242×	`prod-diff_binary64`
94×	`egg-rr`
87×	`add-sqr-sqrt_binary64`

Counts

2 → 94

Calls

2 calls:

62.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
62.0ms	(*.f64 y (fma.f64 z z 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	201	22
2	2469	22
3	5921	22
0	0	0
1	0	0

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Rules

837×	`rules-14-rev_binary64`
661×	`fma-def_binary64`
427×	`rules-6_binary64`
262×	`rules-15-rev_binary64`
253×	`rules-1_binary64`

Counts

154 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	993
1	156	903
2	640	804
3	3841	791
4	6288	791

prune132.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Error

4.8b

Counts

121 → 9

Alt Table

Status	Error	Program
	7.1b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
	24.5b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))) 3))
	6.7b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (cbrt.f64 (fma.f64 z z 1)) (.f64 y (pow.f64 (cbrt.f64 (fma.f64 z z 1)) 2)) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
	6.6b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	33.0b	(/.f64 (-.f64 (/.f64 1 (.f64 z z)) (/.f64 1 (pow.f64 z 4))) (.f64 y x))
	38.1b	(cbrt.f64 (/.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
	7.5b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
▶	6.5b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))

Compiler

Compiled 2610 to 1745 computations (33.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (sqrt.f64 (fma.f64 z z 1)))
✓	0.1b	(fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y)))
✓	3.4b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
✓	17.0b	(sqrt.f64 (fma.f64 z z 1))

series137.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

97.0ms	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
23.0ms	(fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y)))
13.0ms	(*.f64 y (sqrt.f64 (fma.f64 z z 1)))
2.0ms	(sqrt.f64 (fma.f64 z z 1))

rewrite93.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

872×	`fma-neg_binary64`
489×	`prod-diff_binary64`
209×	`egg-rr`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`

Counts

4 → 209

Calls

4 calls:

89.0ms	(*.f64 y (sqrt.f64 (fma.f64 z z 1)))
89.0ms	(fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y)))
89.0ms	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
89.0ms	(sqrt.f64 (fma.f64 z z 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	83
1	362	39
2	3166	39
3	5250	39
0	0	0
1	0	0

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

414×	`rules-15-rev_binary64`
366×	`rules-20_binary64`
357×	`fma-neg_binary64`
339×	`rules-12-rev_binary64`
326×	`rules-11_binary64`

Counts

305 → 281

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1517
1	365	1352
2	1504	1340
3	5261	1340

prune436.0ms (7.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	339	1	340
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	340	9	349

Error

4.8b

Counts

349 → 9

Alt Table

Status	Error	Program
	7.1b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
	24.5b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))) 3))
	6.7b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (cbrt.f64 (fma.f64 z z 1)) (.f64 y (pow.f64 (cbrt.f64 (fma.f64 z z 1)) 2)) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
▶	6.6b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	33.0b	(/.f64 (-.f64 (/.f64 1 (.f64 z z)) (/.f64 1 (pow.f64 z 4))) (.f64 y x))
	38.1b	(cbrt.f64 (/.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	31.9b	(/.f64 1 (.f64 (.f64 z z) (*.f64 y x)))
✓	6.5b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))

Compiler

Compiled 11070 to 7642 computations (31% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
✓	3.4b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	4.5b	(*.f64 y (fma.f64 z z 1))

series102.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

71.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
30.0ms	(/.f64 1 (*.f64 y (fma.f64 z z 1)))

rewrite94.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

801×	`fma-neg_binary64`
448×	`fma-def_binary64`
284×	`prod-diff_binary64`
199×	`egg-rr`
173×	`expm1-udef_binary64`

Counts

2 → 199

Calls

2 calls:

88.0ms	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
88.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	226	25
2	2806	25
3	5105	25
0	0	0
1	0	0

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

949×	`fma-def_binary64`
524×	`rules-6_binary64`
380×	`rules-15-rev_binary64`
305×	`rules-5-rev_binary64`
293×	`rules-4-rev_binary64`

Counts

259 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1218
1	223	1146
2	938	996
3	4320	990
4	4789	990
5	5124	990

prune336.0ms (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	303	3	306
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	307	8	315

Error

4.8b

Counts

315 → 8

Alt Table

Status	Error	Program
	7.1b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
▶	6.5b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	31.9b	(/.f64 1 (.f64 (.f64 z z) (*.f64 y x)))
✓	6.5b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
	7.1b	(/.f64 (/.f64 (/.f64 1 x) (fma.f64 z z 1)) y)
	6.7b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (cbrt.f64 (fma.f64 z z 1)) (.f64 y (pow.f64 (cbrt.f64 (fma.f64 z z 1)) 2)) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
	25.8b	(.f64 (/.f64 1 x) (sqrt.f64 (pow.f64 (.f64 y (fma.f64 z z 1)) -2)))

Compiler

Compiled 7341 to 5101 computations (30.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
✓	3.4b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	4.5b	(*.f64 y (fma.f64 z z 1))

series70.0ms (1.1%)

Counts

1 → 36

Calls

1 calls:

69.0ms

(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)

rewrite56.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

818×	`log1p-expm1-u_binary64`
818×	`expm1-log1p-u_binary64`
217×	`prod-diff_binary64`
87×	`add-sqr-sqrt_binary64`
79×	`add-cbrt-cube_binary64`

Counts

1 → 30

Calls

1 calls:

55.0ms

(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	201	14
2	2457	14
3	5832	14
0	0	0
1	0	0

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

843×	`rules-14-rev_binary64`
614×	`fma-def_binary64`
370×	`rules-6_binary64`
262×	`rules-15-rev_binary64`
240×	`rules-5-rev_binary64`

Counts

66 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	720
1	155	720
2	640	621
3	3799	608
4	6208	608

prune196.0ms (3.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	174	8	182

Error

4.8b

Counts

182 → 8

Alt Table

Status	Error	Program
	7.1b	(/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 z z 1))) 3))
✓	6.5b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	31.9b	(/.f64 1 (.f64 (.f64 z z) (*.f64 y x)))
✓	6.5b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 y (sqrt.f64 (fma.f64 z z 1))) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
	7.1b	(/.f64 (/.f64 (/.f64 1 x) (fma.f64 z z 1)) y)
	6.7b	(/.f64 (/.f64 1 x) (+.f64 (fma.f64 (cbrt.f64 (fma.f64 z z 1)) (.f64 y (pow.f64 (cbrt.f64 (fma.f64 z z 1)) 2)) (neg.f64 (.f64 0 y))) (fma.f64 0 y (*.f64 0 y))))
	25.8b	(.f64 (/.f64 1 x) (sqrt.f64 (pow.f64 (.f64 y (fma.f64 z z 1)) -2)))

Compiler

Compiled 3238 to 2142 computations (33.8% saved)

regimes2.3s (38.1%)

Accuracy

Total 0.2b remaining (3.8%)

Threshold costs 0.2b (3.8%)

Counts

213 → 2

Compiler

Compiled 38153 to 27661 computations (27.5% saved)

bsearch23.0ms (0.4%)

Steps

Iters	Range		Point
7	7.400139832122017e-20	4.5618048914309036e-17	3.958220094131283e-17

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	55
1	22	55
2	21	55

end261.0ms (4.2%)

Compiler: Compiled 312 to 218 computations (30.1% saved)

Details

analyze311.0ms (5%)

sample1.0s (16.9%)

simplify79.0ms (1.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series88.0ms (1.4%)

rewrite64.0ms (1%)

simplify61.0ms (1%)

prune132.0ms (2.1%)

localize13.0ms (0.2%)

series137.0ms (2.2%)

rewrite93.0ms (1.5%)

simplify57.0ms (0.9%)

prune436.0ms (7.1%)

localize7.0ms (0.1%)

series102.0ms (1.6%)

rewrite94.0ms (1.5%)

simplify93.0ms (1.5%)

prune336.0ms (5.5%)

localize6.0ms (0.1%)

series70.0ms (1.1%)

rewrite56.0ms (0.9%)

simplify56.0ms (0.9%)

prune196.0ms (3.2%)

regimes2.3s (38.1%)

bsearch23.0ms (0.4%)

simplify2.0ms (0%)

end261.0ms (4.2%)

Profiling