Details

analyze606.0ms (17%)

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
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.3s (37.2%)

Symmetry

(sort x y)

Results

947.0ms	8256×	body	128	valid
319.0ms	2954×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify23.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-neg_binary64`
579×	`fma-def_binary64`
349×	`div-sub_binary64`
329×	`cancel-sign-sub-inv_binary64`
297×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	74	13
4	155	13
5	299	13
6	610	13
7	1305	13
8	2658	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(*.f64 (-.f64 z (+.f64 x y)) (/.f64 -1/2 t))
▶	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 74 to 49 computations (33.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series29.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

25.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
4.0ms	(-.f64 (+.f64 x y) z)

rewrite72.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`fma-def_binary64`
245×	`fma-neg_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
165×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	232	20
2	3583	20

Stop Event

1×	node limit

Counts

2 → 165

Calls

2 calls:

69.0ms	(-.f64 (+.f64 x y) z)
69.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

simplify46.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-neg_binary64`
434×	`fma-def_binary64`
293×	`div-sub_binary64`
208×	`cancel-sign-sub-inv_binary64`
183×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1141
1	111	946
2	272	907
3	559	790
4	1407	790
5	3110	790

Stop Event

1×	node limit

Counts

249 → 190

prune127.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	189	3	192

Error

Counts

192 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
	1.2b	(pow.f64 (cbrt.f64 (*.f64 (+.f64 x (-.f64 y z)) (/.f64 1/2 t))) 3)
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 3135 to 1372 computations (56.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (/.f64 y t))
✓	0.0b	(*.f64 1/2 (/.f64 x t))
✓	0.0b	(*.f64 1/2 (/.f64 z t))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

series46.0ms (1.3%)

Counts

4 → 39

Calls

4 calls:

28.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
6.0ms	(*.f64 1/2 (/.f64 x t))
6.0ms	(*.f64 1/2 (/.f64 y t))
6.0ms	(*.f64 1/2 (/.f64 z t))

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

168×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`
156×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	43
1	328	40

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

35.0ms	(*.f64 1/2 (/.f64 y t))
35.0ms	(*.f64 1/2 (/.f64 x t))
35.0ms	(*.f64 1/2 (/.f64 z t))
35.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

simplify35.0ms (1%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
386×	`fma-def_binary64`
248×	`div-sub_binary64`
241×	`distribute-rgt-in_binary64`
207×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	741
1	85	651
2	223	471
3	491	462
4	1282	462
5	2942	462

Stop Event

1×	node limit

Counts

160 → 136

prune126.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	136	3	139

Error

Counts

139 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
▶	0.2b	(+.f64 (/.f64 1/2 (/.f64 t x)) (/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 2979 to 1477 computations (50.4% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 (/.f64 t x)) (/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t))
✓	0.0b	(/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t)
✓	0.7b	(/.f64 1/2 (/.f64 t x))

series50.0ms (1.4%)

Counts

3 → 100

Calls

3 calls:

29.0ms	(+.f64 (/.f64 1/2 (/.f64 t x)) (/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t))
14.0ms	(/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t)
6.0ms	(/.f64 1/2 (/.f64 t x))

rewrite40.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

165×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
157×	`add-cbrt-cube_binary64`
154×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	319	34

Stop Event

1×	node limit

Counts

3 → 122

Calls

3 calls:

38.0ms	(+.f64 (/.f64 1/2 (/.f64 t x)) (/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t))
38.0ms	(/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t)
38.0ms	(/.f64 1/2 (/.f64 t x))

simplify52.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
361×	`fma-neg_binary64`
302×	`div-sub_binary64`
277×	`cancel-sign-sub-inv_binary64`
212×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	1201
1	104	1084
2	277	1015
3	649	1009
4	1761	1009
5	3775	1009

Stop Event

1×	node limit

Counts

222 → 139

prune97.0ms (2.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	0.2b	(+.f64 (/.f64 1/2 (/.f64 t x)) (/.f64 (-.f64 (.f64 1/2 y) (.f64 1/2 z)) t))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 2834 to 1515 computations (46.5% saved)

regimes758.0ms (21.2%)

Accuracy

Total 0.0b remaining (78.9%)

Threshold costs 0.0b (78.9%)

Counts

92 → 1

Compiler

Compiled 12011 to 8560 computations (28.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	20	23

Stop Event

1×

saturated

end67.0ms (1.9%)

Remove: (sort x y)
Compiler: Compiled 133 to 94 computations (29.3% saved)

Details

analyze606.0ms (17%)

sample1.3s (37.2%)

simplify23.0ms (0.7%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series29.0ms (0.8%)

rewrite72.0ms (2%)

simplify46.0ms (1.3%)

prune127.0ms (3.6%)

localize10.0ms (0.3%)

series46.0ms (1.3%)

rewrite37.0ms (1%)

simplify35.0ms (1%)

prune126.0ms (3.5%)

localize9.0ms (0.3%)

series50.0ms (1.4%)

rewrite40.0ms (1.1%)

simplify52.0ms (1.5%)

prune97.0ms (2.7%)

regimes758.0ms (21.2%)

simplify2.0ms (0.1%)

end67.0ms (1.9%)

Profiling