Details

analyze1.1s (22%)

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
12.5%	87.3%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
23.4%	76.4%	0.2%	11
31.6%	68.2%	0.2%	12
34.5%	64.9%	0.6%	13
40.3%	59.2%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.5s (28.6%)

Results

1.0s	8256×	body	128	valid
391.0ms	3204×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

587×	`div-sub_binary64`
387×	`fma-def_binary64`
326×	`fma-neg_binary64`
244×	`distribute-neg-frac_binary64`
227×	`associate-/l*_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	59	22
3	116	22
4	255	20
5	552	16
6	1238	14
7	3482	14
8	4716	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
✓	0.2b	(.f64 (.f64 z 3) y)
✓	0.2b	(/.f64 y (*.f64 z 3))
✓	8.4b	(/.f64 t (.f64 (.f64 z 3) y))

series44.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

18.0ms	(/.f64 t (.f64 (.f64 z 3) y))
16.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
6.0ms	(/.f64 y (*.f64 z 3))
4.0ms	(.f64 (.f64 z 3) y)

rewrite97.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`prod-diff_binary64`
232×	`log1p-udef_binary64`
229×	`egg-rr`
127×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	246	34
2	3668	34

Stop Event

1×	node limit

Counts

4 → 229

Calls

4 calls:

92.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
92.0ms	(.f64 (.f64 z 3) y)
92.0ms	(/.f64 y (*.f64 z 3))
92.0ms	(/.f64 t (.f64 (.f64 z 3) y))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
543×	`fma-neg_binary64`
526×	`times-frac_binary64`
343×	`div-sub_binary64`
280×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	999
1	35	999
2	78	945
3	132	945
4	197	945
5	263	945
6	349	945
7	437	945
8	528	945
9	748	945
10	1618	945
11	4094	945

Stop Event

1×	node limit

Counts

349 → 238

prune253.0ms (5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	231	7	238
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	232	8	240

Error

0.0b

Counts

240 → 8

Alt Table

Status	Error	Program
	4.5b	(+.f64 (-.f64 x (pow.f64 (.f64 3 (/.f64 z y)) -1)) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	1.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (*.f64 t (/.f64 1/3 z)) (/.f64 1 y)))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.5b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
	4.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (pow.f64 (cbrt.f64 t) 2) 1) (/.f64 (cbrt.f64 t) (.f64 z (.f64 3 y)))))
	4.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 1 z) (/.f64 t (*.f64 3 y))))
	35.8b	(+.f64 (-.f64 x (.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 7711 to 4808 computations (37.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 t (/.f64 1/3 z))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.4b	(/.f64 1/3 z)
✓	4.1b	(.f64 (.f64 t (/.f64 1/3 z)) (/.f64 1 y))

series26.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

19.0ms	(.f64 (.f64 t (/.f64 1/3 z)) (/.f64 1 y))
6.0ms	(*.f64 t (/.f64 1/3 z))
1.0ms	(/.f64 1/3 z)

rewrite55.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`log-prod_binary64`
257×	`pow2_binary64`
183×	`pow1/3_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	211	21
2	2675	21

Stop Event

1×	node limit

Counts

3 → 98

Calls

3 calls:

52.0ms	(*.f64 t (/.f64 1/3 z))
52.0ms	(/.f64 1/3 z)
52.0ms	(.f64 (.f64 t (/.f64 1/3 z)) (/.f64 1 y))

simplify20.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

16×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
7×	`*-commutative_binary64`
7×	`associate-/r/_binary64`
6×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	528
1	18	528
2	37	528
3	60	528
4	83	528
5	83	528

Stop Event

1×

saturated

Counts

158 → 102

prune178.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	140	9	149

Error

0.0b

Counts

149 → 9

Alt Table

Status	Error	Program
▶	1.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 t (*.f64 z 3)) (/.f64 1 y)))
	4.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (pow.f64 (cbrt.f64 t) 2) 1) (/.f64 (cbrt.f64 t) (.f64 z (.f64 3 y)))))
	4.5b	(+.f64 (-.f64 x (pow.f64 (.f64 3 (/.f64 z y)) -1)) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	1.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (*.f64 t (/.f64 1/3 z)) (/.f64 1 y)))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.5b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
	4.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 1 z) (/.f64 t (*.f64 3 y))))
	35.8b	(+.f64 (-.f64 x (.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 3226 to 2147 computations (33.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
✓	0.2b	(/.f64 t (*.f64 z 3))
	0.2b	(/.f64 y (*.f64 z 3))
✓	4.1b	(.f64 (/.f64 t (.f64 z 3)) (/.f64 1 y))

series21.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(.f64 (/.f64 t (.f64 z 3)) (/.f64 1 y))
6.0ms	(/.f64 t (*.f64 z 3))

rewrite49.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
172×	`log-div_binary64`
161×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	213	17
2	2939	17

Stop Event

1×	node limit

Counts

2 → 108

Calls

2 calls:

47.0ms	(/.f64 t (*.f64 z 3))
47.0ms	(.f64 (/.f64 t (.f64 z 3)) (/.f64 1 y))

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

16×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
7×	`*-commutative_binary64`
7×	`associate-/r/_binary64`
6×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	528
1	18	528
2	37	528
3	60	528
4	83	528
5	83	528

Stop Event

1×

saturated

Counts

168 → 110

prune297.0ms (5.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	288	7	295

Error

0.0b

Counts

295 → 7

Alt Table

Status	Error	Program
▶	1.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 y 3)))
	4.5b	(+.f64 (-.f64 x (pow.f64 (.f64 3 (/.f64 z y)) -1)) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	1.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (*.f64 t (/.f64 1/3 z)) (/.f64 1 y)))
	4.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.5b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.4b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 (/.f64 t y) 3) z))
	35.8b	(+.f64 (-.f64 x (.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 8981 to 5701 computations (36.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 y 3)))
	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
	0.2b	(/.f64 y (*.f64 z 3))
✓	4.1b	(/.f64 (/.f64 t z) (*.f64 y 3))

series40.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

25.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 y 3)))
15.0ms	(/.f64 (/.f64 t z) (*.f64 y 3))

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

158×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`
150×	`add-cbrt-cube_binary64`
147×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	304	29

Stop Event

1×	node limit

Counts

2 → 108

Calls

2 calls:

36.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 y 3)))
36.0ms	(/.f64 (/.f64 t z) (*.f64 y 3))

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

481×	`fma-neg_binary64`
479×	`fma-def_binary64`
269×	`cancel-sign-sub-inv_binary64`
264×	`div-sub_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	1141
1	58	1003
2	123	997
3	219	931
4	395	931
5	711	931
6	1258	931
7	2111	931
8	3600	931

Stop Event

1×	node limit

Counts

192 → 121

prune247.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	4	1	5
Picked	0	1	1
Done	1	0	1
Total	299	5	304

Error

Counts

304 → 5

Alt Table

Status	Error	Program
	4.5b	(-.f64 x (/.f64 (-.f64 (/.f64 y z) (/.f64 t (*.f64 y z))) 3))
	28.0b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)
✓	1.9b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 y 3)))
	4.5b	(fma.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z) x)
	4.5b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 9440 to 5318 computations (43.7% saved)

regimes803.0ms (15.8%)

Accuracy

Total 0.9b remaining (98.2%)

Threshold costs 0.9b (98.2%)

Counts

92 → 3

Compiler

Compiled 11219 to 7850 computations (30% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	117
1	57	115
2	71	115
3	80	115
4	85	115
5	86	115

Stop Event

1×

saturated

end88.0ms (1.7%)

Compiler: Compiled 250 to 165 computations (34% saved)

Details

analyze1.1s (22%)

sample1.5s (28.6%)

simplify33.0ms (0.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series44.0ms (0.9%)

rewrite97.0ms (1.9%)

simplify77.0ms (1.5%)

prune253.0ms (5%)

localize10.0ms (0.2%)

series26.0ms (0.5%)

rewrite55.0ms (1.1%)

simplify20.0ms (0.4%)

prune178.0ms (3.5%)

localize9.0ms (0.2%)

series21.0ms (0.4%)

rewrite49.0ms (1%)

simplify23.0ms (0.5%)

prune297.0ms (5.9%)

localize9.0ms (0.2%)

series40.0ms (0.8%)

rewrite39.0ms (0.8%)

simplify64.0ms (1.3%)

prune247.0ms (4.9%)

regimes803.0ms (15.8%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end88.0ms (1.7%)

Profiling