Details

analyze1.3s (27.6%)

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
0%	99.8%	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
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (27.5%)

Results

1.1s	8254×	body	128	valid
102.0ms	781×	body	128	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
579×	`times-frac_binary64`
533×	`div-sub_binary64`
520×	`fma-neg_binary64`
208×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	81	14
4	191	14
5	392	14
6	833	14
7	2397	14

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
▶	0.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	9.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series53.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
17.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite53.0ms (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 z t) (-.f64 a t))
51.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
678×	`cancel-sign-sub-inv_binary64`
618×	`times-frac_binary64`
322×	`sub-neg_binary64`
175×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2919
1	553	2907
2	2057	2615

Stop Event

1×	node limit

Counts

173 → 155

prune121.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Error

0.0b

Counts

157 → 5

Alt Table

Status	Error	Program
	1.8b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) 3)
▶	0.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	1.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 a t)) z x) (*.f64 (/.f64 y (-.f64 a t)) t))
	9.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 3633 to 1210 computations (66.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	0.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series64.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

35.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
21.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
7.0ms	(/.f64 1 (-.f64 a t))

rewrite58.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`prod-diff_binary64`
133×	`add-sqr-sqrt_binary64`
125×	`add-cbrt-cube_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	259	31
2	3551	31

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

55.0ms	(/.f64 1 (-.f64 a t))
55.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
55.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-def_binary64`
681×	`cancel-sign-sub-inv_binary64`
632×	`times-frac_binary64`
329×	`sub-neg_binary64`
176×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	3411
1	609	3381
2	2245	3089

Stop Event

1×	node limit

Counts

209 → 181

prune110.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	182	4	186

Error

0.0b

Counts

186 → 4

Alt Table

Status	Error	Program
	38.2b	(-.f64 (/.f64 y (/.f64 (-.f64 a t) z)) (/.f64 t (/.f64 (-.f64 a t) y)))
✓	0.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	9.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 4012 to 1466 computations (63.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) (-.f64 a t)) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	3.8b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	8.0b	(/.f64 (*.f64 y t) (-.f64 a t))

series107.0ms (2.3%)

Counts

4 → 114

Calls

4 calls:

42.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
24.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
24.0ms	(+.f64 (/.f64 (*.f64 y z) (-.f64 a t)) x)
17.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

rewrite88.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
181×	`egg-rr`
160×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	304	58
2	4988	58

Stop Event

1×	node limit

Counts

4 → 181

Calls

4 calls:

84.0ms	(+.f64 (/.f64 (*.f64 y z) (-.f64 a t)) x)
84.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
84.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
84.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
856×	`cancel-sign-sub-inv_binary64`
638×	`times-frac_binary64`
246×	`sub-neg_binary64`
131×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3200
1	633	3200
2	2006	2827

Stop Event

1×	node limit

Counts

295 → 282

prune182.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	280	2	282
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	280	6	286

Error

Counts

286 → 6

Alt Table

Status	Error	Program
	38.2b	(-.f64 (/.f64 y (/.f64 (-.f64 a t) z)) (/.f64 t (/.f64 (-.f64 a t) y)))
✓	0.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	7.5b	(-.f64 (+.f64 (.f64 (/.f64 z (pow.f64 (cbrt.f64 (-.f64 a t)) 2)) (/.f64 y (cbrt.f64 (-.f64 a t)))) x) (/.f64 (.f64 y t) (-.f64 a t)))
	8.6b	(-.f64 (+.f64 (.f64 z (.f64 y (/.f64 1 (-.f64 a t)))) x) (/.f64 (*.f64 y t) (-.f64 a t)))
✓	9.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 8159 to 2000 computations (75.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (-.f64 a t))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 a t)) 2)
✓	2.9b	(*.f64 (/.f64 z (pow.f64 (cbrt.f64 (-.f64 a t)) 2)) (/.f64 y (cbrt.f64 (-.f64 a t))))
	8.0b	(/.f64 (*.f64 y t) (-.f64 a t))

series114.0ms (2.5%)

Counts

3 → 64

Calls

3 calls:

52.0ms	(pow.f64 (cbrt.f64 (-.f64 a t)) 2)
31.0ms	(cbrt.f64 (-.f64 a t))
30.0ms	(*.f64 (/.f64 z (pow.f64 (cbrt.f64 (-.f64 a t)) 2)) (/.f64 y (cbrt.f64 (-.f64 a t))))

rewrite60.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

413×	`prod-diff_binary64`
238×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`
128×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	267	25
2	3778	25

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

58.0ms	(cbrt.f64 (-.f64 a t))
58.0ms	(pow.f64 (cbrt.f64 (-.f64 a t)) 2)
58.0ms	(*.f64 (/.f64 z (pow.f64 (cbrt.f64 (-.f64 a t)) 2)) (/.f64 y (cbrt.f64 (-.f64 a t))))

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
538×	`times-frac_binary64`
321×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-neg-in_binary64`
196×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1858
1	540	1854
2	1954	1686

Stop Event

1×	node limit

Counts

163 → 154

prune231.0ms (5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Status	Error	Program
	8.5b	(-.f64 (+.f64 (/.f64 z (/.f64 (-.f64 a t) y)) x) (/.f64 (*.f64 y t) (-.f64 a t)))
	38.2b	(-.f64 (/.f64 y (/.f64 (-.f64 a t) z)) (/.f64 t (/.f64 (-.f64 a t) y)))
✓	0.6b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	7.5b	(-.f64 (+.f64 (.f64 (/.f64 z (pow.f64 (cbrt.f64 (-.f64 a t)) 2)) (/.f64 y (cbrt.f64 (-.f64 a t)))) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	9.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 8837 to 3527 computations (60.1% saved)

regimes473.0ms (10.2%)

Accuracy

Total 1.4b remaining (99.2%)

Threshold costs 0b (0%)

Counts

72 → 1

Compiler

Compiled 8892 to 5441 computations (38.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	22	16
2	27	16
3	29	16
4	30	16

Stop Event

1×

saturated

end73.0ms (1.6%)

Compiler: Compiled 158 to 91 computations (42.4% saved)

Details

analyze1.3s (27.6%)

sample1.3s (27.5%)

simplify23.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series53.0ms (1.1%)

rewrite53.0ms (1.1%)

simplify56.0ms (1.2%)

prune121.0ms (2.6%)

localize8.0ms (0.2%)

series64.0ms (1.4%)

rewrite58.0ms (1.3%)

simplify59.0ms (1.3%)

prune110.0ms (2.4%)

localize10.0ms (0.2%)

series107.0ms (2.3%)

rewrite88.0ms (1.9%)

simplify58.0ms (1.3%)

prune182.0ms (3.9%)

localize14.0ms (0.3%)

series114.0ms (2.5%)

rewrite60.0ms (1.3%)

simplify49.0ms (1.1%)

prune231.0ms (5%)

regimes473.0ms (10.2%)

simplify2.0ms (0%)

end73.0ms (1.6%)

Profiling