Details

analyze960.0ms (23.1%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (29.7%)

Results

932.0ms	8256×	body	128	valid
241.0ms	2188×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
729×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	32	11
3	79	11
4	180	11
5	345	11
6	572	11
7	1043	11
8	1973	11
9	2951	11
10	3462	11
11	3509	11
12	3539	11
13	3544	11
14	3544	11

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (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

2.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	2.1b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))
✓	5.5b	(*.f64 (-.f64 y x) (/.f64 z t))

series37.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

19.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))
17.0ms	(*.f64 (-.f64 y x) (/.f64 z t))

rewrite58.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

383×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
189×	`fma-neg_binary64`
173×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	205	21
2	3129	21

Stop Event

1×	node limit

Counts

2 → 102

Calls

2 calls:

56.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))
56.0ms	(*.f64 (-.f64 y x) (/.f64 z t))

simplify94.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
730×	`fma-neg_binary64`
221×	`cancel-sign-sub-inv_binary64`
158×	`distribute-rgt-in_binary64`
121×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	1371
1	96	1020
2	220	1020
3	524	948
4	1107	948
5	2066	948
6	3201	948
7	3898	948
8	3925	948
9	3955	948
10	3960	948
11	3960	948

Stop Event

1×

saturated

Counts

198 → 119

prune83.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
	4.8b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 z x)) t))
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (pow.f64 t -1) x)
	4.9b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 (-.f64 y x) z))))
▶	1.9b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
	2.1b	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))

Compiler

Compiled 1910 to 574 computations (69.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
✓	5.7b	(/.f64 (-.f64 y x) (/.f64 t z))

series38.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

20.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
18.0ms	(/.f64 (-.f64 y x) (/.f64 t z))

rewrite65.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

407×	`fma-def_binary64`
272×	`fma-neg_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
143×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	214	21
2	3545	21

Stop Event

1×	node limit

Counts

2 → 143

Calls

2 calls:

62.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
62.0ms	(/.f64 (-.f64 y x) (/.f64 t z))

simplify99.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
730×	`fma-neg_binary64`
221×	`cancel-sign-sub-inv_binary64`
158×	`distribute-rgt-in_binary64`
121×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	1371
1	96	1020
2	220	1020
3	524	948
4	1107	948
5	2066	948
6	3201	948
7	3898	948
8	3925	948
9	3955	948
10	3960	948
11	3960	948

Stop Event

1×

saturated

Counts

239 → 159

prune110.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
	4.8b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 z x)) t))
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (pow.f64 t -1) x)
✓	1.9b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
▶	1.9b	(+.f64 x (pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1))
	2.1b	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))

Compiler

Compiled 2653 to 721 computations (72.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1))
✓	0.5b	(pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1)
✓	5.5b	(/.f64 (/.f64 t z) (-.f64 y x))

series244.0ms (5.9%)

Counts

3 → 144

Calls

3 calls:

113.0ms	(pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1)
97.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1))
34.0ms	(/.f64 (/.f64 t z) (-.f64 y x))

rewrite70.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

350×	`fma-def_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
198×	`fma-neg_binary64`
156×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	253	33
2	3816	31

Stop Event

1×	node limit

Counts

3 → 156

Calls

3 calls:

67.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1))
67.0ms	(pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1)
67.0ms	(/.f64 (/.f64 t z) (-.f64 y x))

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

548×	`fma-neg_binary64`
414×	`times-frac_binary64`
328×	`associate-/l*_binary64`
255×	`distribute-rgt-neg-in_binary64`
250×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	2262
1	241	1986
2	754	1941
3	3452	1941

Stop Event

1×	node limit

Counts

300 → 190

prune111.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	190	5	195

Error

Counts

195 → 5

Alt Table

Status	Error	Program
	4.8b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 z x)) t))
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (pow.f64 t -1) x)
✓	1.9b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
✓	1.9b	(+.f64 x (pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1))
▶	2.1b	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))

Compiler

Compiled 3225 to 1078 computations (66.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))
✓	3.6b	(*.f64 (neg.f64 x) (/.f64 z t))
✓	3.9b	(fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t)))

series65.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

25.0ms	(fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t)))
22.0ms	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))
17.0ms	(*.f64 (neg.f64 x) (/.f64 z t))

rewrite60.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
295×	`fma-def_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
168×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	44
1	221	30
2	3217	28

Stop Event

1×	node limit

Counts

3 → 133

Calls

3 calls:

58.0ms	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))
58.0ms	(*.f64 (neg.f64 x) (/.f64 z t))
58.0ms	(fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t)))

simplify106.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
715×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`
123×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	1695
1	88	1344
2	213	1344
3	508	1344
4	1072	1272
5	2050	1272
6	3237	1272
7	3935	1272
8	3962	1272
9	3992	1272
10	3997	1272
11	3997	1272

Stop Event

1×

saturated

Counts

265 → 150

prune85.0ms (2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
	4.8b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 z x)) t))
	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (pow.f64 t -1) x)
✓	1.9b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))
✓	1.9b	(+.f64 x (pow.f64 (/.f64 (/.f64 t z) (-.f64 y x)) -1))
✓	2.1b	(+.f64 x (fma.f64 y (/.f64 z t) (*.f64 (neg.f64 x) (/.f64 z t))))

Compiler

Compiled 2369 to 629 computations (73.4% saved)

regimes404.0ms (9.7%)

Accuracy

Total 2.0b remaining (99%)

Threshold costs 0b (0%)

Counts

67 → 1

Compiler

Compiled 6095 to 3888 computations (36.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	17	13
3	19	13
4	20	13

Stop Event

1×

saturated

end84.0ms (2%)

Compiler: Compiled 100 to 61 computations (39% saved)

Details

analyze960.0ms (23.1%)

sample1.2s (29.7%)

simplify46.0ms (1.1%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series37.0ms (0.9%)

rewrite58.0ms (1.4%)

simplify94.0ms (2.3%)

prune83.0ms (2%)

localize6.0ms (0.1%)

series38.0ms (0.9%)

rewrite65.0ms (1.6%)

simplify99.0ms (2.4%)

prune110.0ms (2.6%)

localize8.0ms (0.2%)

series244.0ms (5.9%)

rewrite70.0ms (1.7%)

simplify62.0ms (1.5%)

prune111.0ms (2.7%)

localize7.0ms (0.2%)

series65.0ms (1.6%)

rewrite60.0ms (1.5%)

simplify106.0ms (2.5%)

prune85.0ms (2%)

regimes404.0ms (9.7%)

simplify3.0ms (0.1%)

end84.0ms (2%)

Profiling