Details

analyze1.7s (33.5%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
1.7%	98.1%	0.2%	13
2%	97%	1%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.5s (29.4%)

Results

1.1s	8256×	body	128	valid
334.0ms	2502×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

preprocess37.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

1038×	`fma-def_binary64`
598×	`times-frac_binary64`
349×	`associate-/l*_binary64`
218×	`fma-neg_binary64`
163×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	175
1	112	161
2	245	161
3	542	147
4	1271	147
5	2535	147
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
399×	`div-sub_binary64`
329×	`cancel-sign-sub-inv_binary64`
299×	`fma-def_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	56	23
3	121	21
4	283	21
5	539	21
6	1172	20
7	3469	20

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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
	9.6b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	7.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))

Compiler

Compiled 113 to 79 computations (30.1% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.2b	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)

series11.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

3.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)	t	-inf
2.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)	z	inf
2.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)	z	-inf
1.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)	z	0
1.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)	t	0

rewrite41.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

453×	`log-prod_binary64`
181×	`log1p-udef_binary64`
180×	`expm1-udef_binary64`
153×	`log-pow_binary64`
147×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	216	14
2	2713	14

Stop Event

1×	node limit

Counts

1 → 26

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-neg_binary64`
545×	`fma-def_binary64`
207×	`cancel-sign-sub-inv_binary64`
86×	`associate-/l*_binary64`
79×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	321
1	42	321
2	70	321
3	90	321
4	128	267
5	228	267
6	393	267
7	751	267
8	1544	267
9	2685	267
10	3141	267
11	3155	267

Stop Event

1×

saturated

Counts

50 → 35

prune30.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Error

0.0b

Counts

37 → 3

Alt Table

Status	Error	Program
✓	7.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
▶	0.1b	(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))
	0.1b	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))

Compiler

Compiled 761 to 507 computations (33.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)
✓	0.1b	(/.f64 (+.f64 2 (/.f64 2 z)) t)

series42.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

24.0ms	(+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)	z	-inf
2.0ms	(/.f64 (+.f64 2 (/.f64 2 z)) t)	t	-inf
2.0ms	(/.f64 (+.f64 2 (/.f64 2 z)) t)	t	inf
2.0ms	(+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)	z	0
2.0ms	(/.f64 (+.f64 2 (/.f64 2 z)) t)	t	0

rewrite51.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`log-prod_binary64`
222×	`prod-diff_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
173×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	212	23
2	2893	23

Stop Event

1×	node limit

Counts

2 → 81

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
541×	`fma-def_binary64`
207×	`cancel-sign-sub-inv_binary64`
86×	`associate-/l*_binary64`
80×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	612
1	42	612
2	70	612
3	90	612
4	128	492
5	228	492
6	393	492
7	751	492
8	1537	492
9	2682	492
10	3138	492
11	3152	492

Stop Event

1×

saturated

Counts

129 → 92

prune79.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
✓	7.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
✓	0.1b	(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
	0.7b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t)) -2))

Compiler

Compiled 1976 to 1387 computations (29.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2)
✓	0.0b	(.f64 2 (/.f64 1 (.f64 t z)))
✓	0.0b	(+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z))))
✓	0.6b	(/.f64 1 (*.f64 t z))

series43.0ms (0.9%)

Counts

4 → 45

Calls

24 calls:

4.0ms	(/.f64 1 (*.f64 t z))	z	0
3.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2)	z	inf
2.0ms	(.f64 2 (/.f64 1 (.f64 t z)))	t	0
2.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2)	z	0
2.0ms	(+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z))))	t	0

rewrite76.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`fma-def_binary64`
317×	`fma-neg_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
188×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	274	43
2	3779	43

Stop Event

1×	node limit

Counts

4 → 188

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

24×	`fma-def_binary64`
19×	`associate-/r/_binary64`
17×	`*-commutative_binary64`
14×	`associate-/l*_binary64`
12×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	336
1	29	336
2	41	336
3	55	336
4	79	336
5	105	336
6	127	336
7	171	336
8	182	336
9	184	336

Stop Event

1×

saturated

Counts

233 → 194

prune198.0ms (3.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	194	4	198

Error

Counts

198 → 4

Alt Table

Status	Error	Program
✓	7.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
✓	0.1b	(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
▶	0.7b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t)) -2))

Compiler

Compiled 4434 to 2745 computations (38.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 (cbrt.f64 t) 2))
✓	0.3b	(/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t))
✓	0.5b	(pow.f64 (cbrt.f64 t) 2)
✓	0.6b	(cbrt.f64 t)

series114.0ms (2.3%)

Counts

4 → 12

Calls

15 calls:

19.0ms	(/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t))	t	-inf
19.0ms	(pow.f64 (cbrt.f64 t) 2)	t	-inf
17.0ms	(/.f64 1 (pow.f64 (cbrt.f64 t) 2))	t	-inf
12.0ms	(/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t))	z	-inf
11.0ms	(/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t))	z	0

rewrite63.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`log-prod_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
180×	`log-pow_binary64`
159×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	243	27
2	3097	27

Stop Event

1×	node limit

Counts

4 → 118

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-def_binary64`
451×	`associate-/r*_binary64`
381×	`unswap-sqr_binary64`
368×	`*-commutative_binary64`
327×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	240
1	30	192
2	69	165
3	195	165
4	572	165
5	1095	165
6	1950	165
7	3708	165
8	4395	165
9	4560	165
10	4705	165
11	4938	165

Stop Event

1×	node limit

Counts

130 → 124

prune120.0ms (2.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	150	4	154

Error

Counts

154 → 4

Alt Table

Status	Error	Program
✓	7.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
✓	0.1b	(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
✓	0.7b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 t) 2)) (/.f64 (+.f64 2 (/.f64 2 z)) (cbrt.f64 t)) -2))

Compiler

Compiled 3734 to 2342 computations (37.3% saved)

regimes636.0ms (12.6%)

Accuracy

Total 0.1b remaining (73.7%)

Threshold costs 0.1b (73.7%)

Counts

78 → 1

Compiler

Compiled 10932 to 8273 computations (24.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	16	23

Stop Event

1×

saturated

end83.0ms (1.6%)

Stop Event

1×

done

Compiler

Compiled 122 to 92 computations (24.6% saved)

Iter	Nodes	Cost
0	16	336
1	29	336
2	41	336
3	55	336
4	79	336
5	105	336
6	127	336
7	171	336
8	182	336
9	184	336

Iter	Nodes	Cost
0	16	336
1	29	336
2	41	336
3	55	336
4	79	336
5	105	336
6	127	336
7	171	336
8	182	336
9	184	336

Details

analyze1.7s (33.5%)

sample1.5s (29.4%)

preprocess37.0ms (0.7%)

simplify25.0ms (0.5%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series11.0ms (0.2%)

rewrite41.0ms (0.8%)

simplify46.0ms (0.9%)

prune30.0ms (0.6%)

localize8.0ms (0.2%)

series42.0ms (0.8%)

rewrite51.0ms (1%)

simplify57.0ms (1.1%)

prune79.0ms (1.6%)

localize12.0ms (0.2%)

series43.0ms (0.9%)

rewrite76.0ms (1.5%)

simplify26.0ms (0.5%)

prune198.0ms (3.9%)

localize13.0ms (0.3%)

series114.0ms (2.3%)

rewrite63.0ms (1.2%)

simplify56.0ms (1.1%)

prune120.0ms (2.4%)

regimes636.0ms (12.6%)

simplify3.0ms (0.1%)

end83.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	16	336
1	29	336
2	41	336
3	55	336
4	79	336
5	105	336
6	127	336
7	171	336
8	182	336
9	184	336