Details

analyze1.3s (26.6%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (23.8%)

Results

1.0s	8253×	body	128	valid
90.0ms	743×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

575×	`div-sub_binary64`
522×	`times-frac_binary64`
522×	`fma-neg_binary64`
259×	`fma-def_binary64`
198×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	44	14
3	88	14
4	193	14
5	384	14
6	898	14
7	2363	14

Stop Event

1×	node limit

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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)

Compiler

Compiled 56 to 32 computations (42.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a z))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)

series57.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

39.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)
18.0ms	(/.f64 (-.f64 t z) (-.f64 a z))

rewrite52.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
192×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	226	24
2	3371	24

Stop Event

1×	node limit

Counts

2 → 77

Calls

2 calls:

51.0ms	(/.f64 (-.f64 t z) (-.f64 a z))
51.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a z)) x)

simplify53.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
652×	`times-frac_binary64`
495×	`cancel-sign-sub-inv_binary64`
324×	`sub-neg_binary64`
153×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2928
1	568	2919
2	1954	2272

Stop Event

1×	node limit

Counts

173 → 153

prune129.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	5	154

Error

0.0b

Counts

154 → 5

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) 1) x)
	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
	11.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 y z) (-.f64 a z)))
	1.6b	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)
	51.6b	(/.f64 y (/.f64 (-.f64 a z) t))

Compiler

Compiled 3508 to 1224 computations (65.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) (-.f64 a z))
✓	1.0b	(fma.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) 1) x)

series33.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

33.0ms

(fma.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) 1) x)

rewrite45.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

366×	`fma-def_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
203×	`fma-neg_binary64`
127×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	253	14
2	3521	14

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

45.0ms

(fma.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) 1) x)

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

524×	`times-frac_binary64`
509×	`associate--l+_binary64`
470×	`fma-def_binary64`
453×	`associate-/l*_binary64`
296×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1832
1	383	1832
2	1244	1333

Stop Event

1×	node limit

Counts

86 → 70

prune117.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	153	5	158

Error

0.0b

Counts

158 → 5

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) 1) x)
	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
	11.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 y z) (-.f64 a z)))
▶	1.6b	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)
	51.6b	(/.f64 y (/.f64 (-.f64 a z) t))

Compiler

Compiled 3655 to 1367 computations (62.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z))))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 t z)) 2)
✓	0.6b	(cbrt.f64 (-.f64 t z))
✓	1.0b	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)

series167.0ms (3.4%)

Counts

4 → 112

Calls

4 calls:

55.0ms	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)
49.0ms	(pow.f64 (cbrt.f64 (-.f64 t z)) 2)
35.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z))))
28.0ms	(cbrt.f64 (-.f64 t z))

rewrite69.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`prod-diff_binary64`
167×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`
158×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	45
1	341	39
2	4392	39

Stop Event

1×	node limit

Counts

4 → 92

Calls

4 calls:

67.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z))))
67.0ms	(pow.f64 (cbrt.f64 (-.f64 t z)) 2)
67.0ms	(cbrt.f64 (-.f64 t z))
67.0ms	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
710×	`cancel-sign-sub-inv_binary64`
373×	`sub-neg_binary64`
211×	`fma-neg_binary64`
177×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	3760
1	866	3745
2	2981	3700

Stop Event

1×	node limit

Counts

204 → 201

prune186.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	243	6	249

Error

0.0b

Counts

249 → 6

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 y (pow.f64 (/.f64 (-.f64 t z) (-.f64 a z)) 1) x)
▶	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
	11.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 y z) (-.f64 a z)))
✓	1.6b	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)
	43.2b	(-.f64 (/.f64 y (/.f64 (-.f64 a z) t)) (/.f64 (*.f64 y z) (-.f64 a z)))
	12.2b	(-.f64 x (/.f64 y (/.f64 (-.f64 a z) z)))

Compiler

Compiled 7190 to 3331 computations (53.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	10.3b	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))

series93.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

49.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
30.0ms	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))
14.0ms	(/.f64 y (-.f64 a z))

rewrite65.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

539×	`fma-def_binary64`
258×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	34
2	3913	34

Stop Event

1×	node limit

Counts

3 → 134

Calls

3 calls:

63.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
63.0ms	(/.f64 y (-.f64 a z))
63.0ms	(*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z))

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
685×	`times-frac_binary64`
538×	`cancel-sign-sub-inv_binary64`
277×	`sub-neg_binary64`
149×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3945
1	627	3837
2	1948	3086

Stop Event

1×	node limit

Counts

266 → 233

prune167.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	3	0	3
Picked	0	1	1
Done	1	1	2
Total	235	4	239

Error

0.0b

Counts

239 → 4

Alt Table

Status	Error	Program
✓	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a z)) (-.f64 t z)))
✓	1.6b	(fma.f64 y (.f64 (pow.f64 (cbrt.f64 (-.f64 t z)) 2) (.f64 (cbrt.f64 (-.f64 t z)) (/.f64 1 (-.f64 a z)))) x)
	2.7b	(+.f64 x (/.f64 (-.f64 t z) (/.f64 (-.f64 a z) y)))
	1.1b	(+.f64 x (/.f64 y (/.f64 (-.f64 a z) (-.f64 t z))))

Compiler

Compiled 5269 to 1662 computations (68.5% saved)

regimes877.0ms (18%)

Accuracy

Total 1.2b remaining (98.6%)

Threshold costs 0b (0%)

Counts

120 → 1

Compiler

Compiled 16804 to 10612 computations (36.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	15	16
2	21	16
3	23	16
4	24	16

Stop Event

1×

saturated

end64.0ms (1.3%)

Compiler: Compiled 105 to 65 computations (38.1% saved)

Details

analyze1.3s (26.6%)

sample1.2s (23.8%)

simplify24.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series57.0ms (1.2%)

rewrite52.0ms (1.1%)

simplify53.0ms (1.1%)

prune129.0ms (2.6%)

localize8.0ms (0.2%)

series33.0ms (0.7%)

rewrite45.0ms (0.9%)

simplify36.0ms (0.7%)

prune117.0ms (2.4%)

localize13.0ms (0.3%)

series167.0ms (3.4%)

rewrite69.0ms (1.4%)

simplify69.0ms (1.4%)

prune186.0ms (3.8%)

localize10.0ms (0.2%)

series93.0ms (1.9%)

rewrite65.0ms (1.3%)

simplify67.0ms (1.4%)

prune167.0ms (3.4%)

regimes877.0ms (18%)

simplify3.0ms (0.1%)

end64.0ms (1.3%)

Profiling