Details

analyze1.9s (28.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.8s (27.1%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
461.0ms	2971×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-neg_binary64`
641×	`fma-def_binary64`
211×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	123	21
3	423	21
4	908	21
5	1463	21
6	2155	21
7	2547	21
8	3019	21
9	3134	21
10	3138	21
11	3138	21
12	3138	21

Stop Event

1×

saturated

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
	2.7b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
▶	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
✓	0.2b	(.f64 (.f64 y 9) z)
✓	0.3b	(.f64 (.f64 a 27) b)
✓	6.9b	(.f64 (.f64 (*.f64 y 9) z) t)

series36.0ms (0.6%)

Counts

4 → 132

Calls

4 calls:

14.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
13.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
4.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 y 9) z)

rewrite75.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

318×	`log1p-udef_binary64`
177×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
168×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	365	40
2	4532	40

Stop Event

1×	node limit

Counts

4 → 94

Calls

4 calls:

67.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
67.0ms	(.f64 (.f64 y 9) z)
67.0ms	(.f64 (.f64 a 27) b)
67.0ms	(.f64 (.f64 (*.f64 y 9) z) t)

simplify88.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
290×	`fma-neg_binary64`
132×	`distribute-rgt-neg-in_binary64`
131×	`cancel-sign-sub-inv_binary64`
92×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	1362
1	44	1290
2	107	1290
3	265	1290
4	458	1290
5	639	1290
6	840	1290
7	1086	1290
8	1314	1290
9	1985	1290
10	2238	1290
11	2268	1290
12	2268	1290

Stop Event

1×

saturated

Counts

226 → 105

prune111.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	100	7	107

Error

0.0b

Counts

107 → 7

Alt Table

Status	Error	Program
	2.7b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
	19.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 3)))
	2.7b	(+.f64 (fma.f64 t (.f64 y (.f64 z -9)) (.f64 2 x)) (.f64 (*.f64 a 27) b))
	29.7b	(+.f64 (.f64 z (.f64 t (.f64 y -9))) (.f64 (*.f64 a 27) b))
	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
▶	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))

Compiler

Compiled 3034 to 1921 computations (36.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
✓	0.2b	(.f64 9 (.f64 y (*.f64 t z)))
	0.3b	(.f64 (.f64 a 27) b)
✓	7.1b	(.f64 y (.f64 t z))

series40.0ms (0.6%)

Counts

3 → 48

Calls

3 calls:

16.0ms	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
13.0ms	(.f64 y (.f64 t z))
10.0ms	(.f64 9 (.f64 y (*.f64 t z)))

rewrite74.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`fma-def_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
197×	`log-pow_binary64`
196×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	266	31
2	3401	31

Stop Event

1×	node limit

Counts

3 → 196

Calls

3 calls:

70.0ms	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
70.0ms	(.f64 9 (.f64 y (*.f64 t z)))
70.0ms	(.f64 y (.f64 t z))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
290×	`fma-neg_binary64`
129×	`cancel-sign-sub-inv_binary64`
127×	`distribute-rgt-neg-in_binary64`
97×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	666
1	30	594
2	84	594
3	253	594
4	454	594
5	637	594
6	838	594
7	1085	594
8	1311	594
9	1982	594
10	2235	594
11	2265	594
12	2265	594

Stop Event

1×

saturated

Counts

244 → 201

prune214.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	220	5	225

Error

0.0b

Counts

225 → 5

Alt Table

Status	Error	Program
	2.7b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
	19.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 3)))
	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
▶	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 27 (.f64 a b)))
	5.2b	(+.f64 (fma.f64 (.f64 -9 (.f64 y t)) z (.f64 x 2)) (.f64 (*.f64 a 27) b))

Compiler

Compiled 7014 to 3586 computations (48.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z))))
	0.2b	(.f64 9 (.f64 y (*.f64 t z)))
✓	0.3b	(.f64 27 (.f64 a b))
	7.1b	(.f64 y (.f64 t z))

series5.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

5.0ms

(*.f64 27 (*.f64 a b))

rewrite34.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
386×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
153×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1405	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

33.0ms

(*.f64 27 (*.f64 a b))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

17 → 17

prune188.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	218	5	223

Error

0.0b

Counts

223 → 5

Alt Table

Status	Error	Program
	2.7b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
	19.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 3)))
▶	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	5.1b	(+.f64 (fma.f64 (.f64 -9 (.f64 y t)) z (.f64 x 2)) (.f64 27 (*.f64 a b)))
✓	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 27 (.f64 a b)))

Compiler

Compiled 7013 to 3377 computations (51.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t))
✓	0.2b	(.f64 9 (.f64 y z))
	0.3b	(.f64 (.f64 a 27) b)
✓	6.9b	(.f64 (.f64 9 (*.f64 y z)) t)

series35.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

16.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t))
15.0ms	(.f64 (.f64 9 (*.f64 y z)) t)
4.0ms	(.f64 9 (.f64 y z))

rewrite69.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

419×	`fma-def_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
198×	`log-pow_binary64`
192×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	265	31
2	3395	31

Stop Event

1×	node limit

Counts

3 → 192

Calls

3 calls:

64.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t))
64.0ms	(.f64 9 (.f64 y z))
64.0ms	(.f64 (.f64 9 (*.f64 y z)) t)

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
290×	`fma-neg_binary64`
129×	`distribute-rgt-neg-in_binary64`
129×	`cancel-sign-sub-inv_binary64`
84×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	1026
1	30	954
2	84	954
3	253	954
4	454	954
5	624	954
6	825	954
7	1072	954
8	1298	954
9	1969	954
10	2222	954
11	2252	954
12	2252	954

Stop Event

1×

saturated

Counts

276 → 199

prune198.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	216	5	221

Error

0.0b

Counts

221 → 5

Alt Table

Status	Error	Program
	2.7b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
	19.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 3)))
✓	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	5.1b	(+.f64 (fma.f64 (.f64 -9 (.f64 y t)) z (.f64 x 2)) (.f64 27 (*.f64 a b)))
✓	2.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 27 (.f64 a b)))

Compiler

Compiled 6850 to 3579 computations (47.8% saved)

regimes680.0ms (10.4%)

Accuracy

Total 0.5b remaining (95.8%)

Threshold costs 0.5b (95.8%)

Counts

34 → 2

Compiler

Compiled 11746 to 8676 computations (26.1% saved)

bsearch20.0ms (0.3%)

Steps

Iters	Range		Point
4	3.3134778096922914e+27	5.350806889313648e+27	4.7492635233917384e+27

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	54
1	46	54
2	64	54
3	78	54
4	88	54
5	94	54
6	96	54

Stop Event

1×

saturated

end729.0ms (11.2%)

Compiler: Compiled 373 to 265 computations (29% saved)

Details

analyze1.9s (28.9%)

sample1.8s (27.1%)

simplify60.0ms (0.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series36.0ms (0.6%)

rewrite75.0ms (1.1%)

simplify88.0ms (1.3%)

prune111.0ms (1.7%)

localize11.0ms (0.2%)

series40.0ms (0.6%)

rewrite74.0ms (1.1%)

simplify75.0ms (1.1%)

prune214.0ms (3.3%)

localize11.0ms (0.2%)

series5.0ms (0.1%)

rewrite34.0ms (0.5%)

simplify7.0ms (0.1%)

prune188.0ms (2.9%)

localize17.0ms (0.3%)

series35.0ms (0.5%)

rewrite69.0ms (1.1%)

simplify78.0ms (1.2%)

prune198.0ms (3%)

regimes680.0ms (10.4%)

bsearch20.0ms (0.3%)

simplify4.0ms (0.1%)

end729.0ms (11.2%)

Profiling