Details

analyze1.6s (29.6%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.6s (29.1%)

Results

1.1s	8256×	body	128	valid
442.0ms	2536×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify26.0ms (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
	12.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	7.1b	(+.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
✓	0.0b	(/.f64 (+.f64 z 1) t)
✓	6.7b	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)

series44.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

28.0ms	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
10.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)
5.0ms	(/.f64 (+.f64 z 1) t)

rewrite65.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`log1p-udef_binary64`
272×	`expm1-udef_binary64`
154×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	310	41
2	4210	41

Stop Event

1×	node limit

Counts

3 → 92

Calls

3 calls:

63.0ms	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
63.0ms	(/.f64 (+.f64 z 1) t)
63.0ms	(fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2)

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1038×	`fma-neg_binary64`
497×	`fma-def_binary64`
240×	`associate-/r*_binary64`
211×	`div-sub_binary64`
207×	`sub-neg_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	32	1452
1	69	1452
2	119	1452
3	161	1452
4	225	1281
5	427	1281
6	823	1281
7	1878	1281
8	3489	1218
9	4605	1218
10	4917	1218

Stop Event

1×	node limit

Counts

188 → 113

prune125.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Error

0.0b

Counts

115 → 6

Alt Table

Status	Error	Program
	7.5b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (*.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) 2)) -2))
▶	0.0b	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
	7.5b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 z 1)) 2) (pow.f64 (cbrt.f64 t) 2)) (cbrt.f64 (/.f64 (+.f64 z 1) t))) -2))
	27.4b	(+.f64 (/.f64 x y) (/.f64 (/.f64 2 t) z))
	7.2b	(fma.f64 x (/.f64 1 y) (fma.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t) -2))
	33.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (pow.f64 (sqrt.f64 (/.f64 (+.f64 z 1) t)) 2) -2))

Compiler

Compiled 2577 to 1671 computations (35.2% saved)

localize11.0ms (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 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
✓	0.3b	(/.f64 1 (*.f64 t z))

series58.0ms (1%)

Counts

4 → 78

Calls

4 calls:

32.0ms	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
10.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2)
8.0ms	(/.f64 1 (*.f64 t z))
8.0ms	(.f64 2 (/.f64 1 (.f64 t z)))

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

184×	`add-sqr-sqrt_binary64`
176×	`log1p-expm1-u_binary64`
176×	`expm1-log1p-u_binary64`
175×	`add-cbrt-cube_binary64`
170×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	370	52

Stop Event

1×	node limit

Counts

4 → 142

Calls

4 calls:

49.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2)
49.0ms	(.f64 2 (/.f64 1 (.f64 t z)))
49.0ms	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (/.f64 1 (*.f64 t z)))) 2))
49.0ms	(/.f64 1 (*.f64 t z))

simplify136.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-neg_binary64`
724×	`fma-def_binary64`
188×	`sub-neg_binary64`
152×	`cancel-sign-sub-inv_binary64`
126×	`cancel-sign-sub_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	1110
1	63	1110
2	113	1110
3	155	1110
4	219	993
5	419	993
6	815	993
7	1752	993
8	2975	993
9	3781	993
10	4125	993
11	4207	993
12	4252	993
13	4262	993
14	4539	993
15	4544	993
16	4544	993

Stop Event

1×

saturated

Counts

220 → 156

prune155.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	157	5	162

Error

Counts

162 → 5

Alt Table

Status	Error	Program
	7.5b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (*.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) 2)) -2))
▶	0.1b	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2))
	29.6b	(+.f64 (/.f64 x y) (-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (.f64 2 (*.f64 (/.f64 (pow.f64 t -1/2) 1) (/.f64 (pow.f64 t -1/2) z)))) 2))
	33.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (pow.f64 (sqrt.f64 (/.f64 (+.f64 z 1) t)) 2) -2))
	0.1b	(fma.f64 x (/.f64 1 y) (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 t z)) -2)))

Compiler

Compiled 4321 to 2766 computations (36% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2))
✓	0.0b	(fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2)
✓	0.2b	(/.f64 (pow.f64 t -1) z)

series46.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

30.0ms	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2))
9.0ms	(fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2)
7.0ms	(/.f64 (pow.f64 t -1) z)

rewrite64.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	312	47
2	4332	47

Stop Event

1×	node limit

Counts

3 → 91

Calls

3 calls:

62.0ms	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2))
62.0ms	(fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2)
62.0ms	(/.f64 (pow.f64 t -1) z)

simplify167.0ms (3%)

Algorithm

1×	egg-herbie

Rules

965×	`fma-neg_binary64`
731×	`fma-def_binary64`
188×	`sub-neg_binary64`
152×	`cancel-sign-sub-inv_binary64`
129×	`cancel-sign-sub_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	1398
1	63	1398
2	113	1398
3	155	1398
4	219	1227
5	419	1227
6	813	1227
7	1750	1227
8	2985	1227
9	3798	1227
10	4166	1227
11	4248	1227
12	4293	1227
13	4303	1227
14	4580	1227
15	4585	1227
16	4585	1227

Stop Event

1×

saturated

Counts

187 → 107

prune93.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

Counts

112 → 5

Alt Table

Status	Error	Program
	29.6b	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (*.f64 (/.f64 (pow.f64 t -1/2) 1) (/.f64 (pow.f64 t -1/2) z))) -2))
	7.5b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (*.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) 2)) -2))
✓	0.1b	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2))
	33.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (pow.f64 (sqrt.f64 (/.f64 (+.f64 z 1) t)) 2) -2))
▶	0.1b	(fma.f64 x (/.f64 1 y) (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 t z)) -2)))

Compiler

Compiled 2666 to 1805 computations (32.3% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (*.f64 t z)) -2)
✓	0.1b	(fma.f64 x (/.f64 1 y) (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 t z)) -2)))
✓	0.3b	(/.f64 2 (*.f64 t z))

series48.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

35.0ms	(fma.f64 x (/.f64 1 y) (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 t z)) -2)))
8.0ms	(/.f64 2 (*.f64 t z))
6.0ms	(+.f64 (/.f64 2 (*.f64 t z)) -2)

rewrite68.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`
155×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	332	39
2	4537	39

Stop Event

1×	node limit

Counts

3 → 91

Calls

3 calls:

66.0ms	(+.f64 (/.f64 2 (*.f64 t z)) -2)
66.0ms	(fma.f64 x (/.f64 1 y) (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 t z)) -2)))
66.0ms	(/.f64 2 (*.f64 t z))

simplify137.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
731×	`fma-def_binary64`
187×	`sub-neg_binary64`
152×	`cancel-sign-sub-inv_binary64`
125×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	1107
1	62	1107
2	114	1107
3	162	1107
4	226	990
5	426	990
6	821	990
7	1757	990
8	2985	990
9	3795	990
10	4156	990
11	4238	990
12	4283	990
13	4293	990
14	4570	990
15	4575	990
16	4575	990

Stop Event

1×

saturated

Counts

163 → 106

prune91.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	106	5	111

Error

Counts

111 → 5

Alt Table

Status	Error	Program
	29.6b	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (*.f64 (/.f64 (pow.f64 t -1/2) 1) (/.f64 (pow.f64 t -1/2) z))) -2))
	7.5b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (*.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 z 1) t)) 2)) -2))
✓	0.1b	(+.f64 (/.f64 x y) (fma.f64 2 (+.f64 (pow.f64 t -1) (/.f64 (pow.f64 t -1) z)) -2))
	33.6b	(+.f64 (/.f64 x y) (fma.f64 (/.f64 2 z) (pow.f64 (sqrt.f64 (/.f64 (+.f64 z 1) t)) 2) -2))
✓	0.1b	(fma.f64 x (/.f64 1 y) (+.f64 (/.f64 2 t) (+.f64 (/.f64 2 (*.f64 t z)) -2)))

Compiler

Compiled 2297 to 1603 computations (30.2% saved)

regimes675.0ms (12.1%)

Accuracy

Total 0.1b remaining (73.3%)

Threshold costs 0.1b (73.3%)

Counts

92 → 1

Compiler

Compiled 13601 to 10182 computations (25.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	18	23

Stop Event

1×

saturated

end107.0ms (1.9%)

Compiler: Compiled 155 to 117 computations (24.5% saved)

Details

analyze1.6s (29.6%)

sample1.6s (29.1%)

simplify26.0ms (0.5%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series44.0ms (0.8%)

rewrite65.0ms (1.2%)

simplify94.0ms (1.7%)

prune125.0ms (2.2%)

localize11.0ms (0.2%)

series58.0ms (1%)

rewrite53.0ms (1%)

simplify136.0ms (2.4%)

prune155.0ms (2.8%)

localize9.0ms (0.2%)

series46.0ms (0.8%)

rewrite64.0ms (1.1%)

simplify167.0ms (3%)

prune93.0ms (1.7%)

localize12.0ms (0.2%)

series48.0ms (0.9%)

rewrite68.0ms (1.2%)

simplify137.0ms (2.5%)

prune91.0ms (1.6%)

regimes675.0ms (12.1%)

simplify3.0ms (0%)

end107.0ms (1.9%)

Profiling