Details

analyze358.0ms (13.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
31.2%	68.6%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	57.7%	1.7%	9
54.6%	41.3%	4%	10
59.3%	36.7%	4%	11
61.6%	32.6%	5.8%	12
68.3%	22.7%	9%	13
71%	20%	9%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample864.0ms (33.1%)

Results

781.0ms	8256×	body	128	valid
65.0ms	734×	body	128	invalid

Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess21.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`associate-/l*_binary64`
6×	`associate-/r/_binary64`
1×	`swap-x-y`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	22	28
2	30	28
3	36	28
4	38	28
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	13	7
3	16	7
4	17	7

Stop Event

1×

saturated

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
	6.4b	(*.f64 x (/.f64 y z))
▶	4.9b	(/.f64 (*.f64 x y) z)

Compiler

Compiled 45 to 27 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 (*.f64 x y) z)

series12.0ms (0.5%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(/.f64 (*.f64 x y) z)	z	-inf
2.0ms	(/.f64 (*.f64 x y) z)	x	-inf
2.0ms	(/.f64 (*.f64 x y) z)	y	-inf
1.0ms	(/.f64 (*.f64 x y) z)	x	0
1.0ms	(/.f64 (*.f64 x y) z)	x	inf

rewrite39.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`log1p-expm1-u_binary64`
659×	`expm1-log1p-u_binary64`
367×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1745	7

Stop Event

1×	node limit

Counts

1 → 46

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	252
1	9	252
2	13	252
3	16	252
4	17	252

Stop Event

1×

saturated

Counts

82 → 48

prune32.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Error

Counts

50 → 7

Alt Table

Status	Error	Program
	5.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) 1) (/.f64 (cbrt.f64 (*.f64 x y)) z))
	6.5b	(.f64 x (.f64 y (/.f64 1 z)))
	29.1b	(.f64 (/.f64 (sqrt.f64 (.f64 x y)) 1) (/.f64 (sqrt.f64 (*.f64 x y)) z))
▶	5.3b	(*.f64 y (/.f64 x z))
	34.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 x z) y) 3))
✓	4.9b	(/.f64 (*.f64 x y) z)
	5.4b	(*.f64 (/.f64 x (pow.f64 (cbrt.f64 z) 2)) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 643 to 276 computations (57.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.1b	(*.f64 y (/.f64 x z))

series13.0ms (0.5%)

Counts

1 → 36

Calls

9 calls:

3.0ms	(*.f64 y (/.f64 x z))	z	inf
2.0ms	(*.f64 y (/.f64 x z))	y	-inf
2.0ms	(*.f64 y (/.f64 x z))	x	-inf
1.0ms	(*.f64 y (/.f64 x z))	y	0
1.0ms	(*.f64 y (/.f64 x z))	x	inf

rewrite34.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`log1p-expm1-u_binary64`
628×	`expm1-log1p-u_binary64`
349×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1686	7

Stop Event

1×	node limit

Counts

1 → 27

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	252
1	9	252
2	13	252
3	16	252
4	17	252

Stop Event

1×

saturated

Counts

63 → 28

prune21.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	28	7	35

Error

Counts

35 → 7

Alt Table

Status	Error	Program
	5.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) 1) (/.f64 (cbrt.f64 (*.f64 x y)) z))
	6.5b	(.f64 x (.f64 y (/.f64 1 z)))
	29.1b	(.f64 (/.f64 (sqrt.f64 (.f64 x y)) 1) (/.f64 (sqrt.f64 (*.f64 x y)) z))
✓	5.3b	(*.f64 y (/.f64 x z))
	34.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 x z) y) 3))
✓	4.9b	(/.f64 (*.f64 x y) z)
▶	5.4b	(*.f64 (/.f64 x (pow.f64 (cbrt.f64 z) 2)) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 399 to 187 computations (53.1% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (cbrt.f64 z))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)
✓	4.4b	(*.f64 (/.f64 x (pow.f64 (cbrt.f64 z) 2)) (/.f64 y (cbrt.f64 z)))

series188.0ms (7.2%)

Counts

4 → 48

Calls

21 calls:

66.0ms	(*.f64 (/.f64 x (pow.f64 (cbrt.f64 z) 2)) (/.f64 y (cbrt.f64 z)))	z	-inf
21.0ms	(/.f64 y (cbrt.f64 z))	y	0
21.0ms	(/.f64 y (cbrt.f64 z))	y	-inf
20.0ms	(/.f64 y (cbrt.f64 z))	y	inf
18.0ms	(pow.f64 (cbrt.f64 z) 2)	z	-inf

rewrite61.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

556×	`log-prod_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
171×	`log-pow_binary64`
167×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	216	22
2	2961	22

Stop Event

1×	node limit

Counts

4 → 142

simplify77.0ms (3%)

Algorithm

1×	egg-herbie

Rules

728×	`sqr-pow_binary64`
438×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	360
1	23	360
2	36	360
3	58	360
4	119	360
5	319	360
6	1165	360
7	1854	360
8	1944	360
9	2080	360
10	2241	360
11	2478	360
12	2803	360
13	3227	360
14	3730	360
15	4328	360

Stop Event

1×	node limit

Counts

190 → 146

prune90.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	172	7	179

Error

Counts

179 → 7

Alt Table

Status	Error	Program
	5.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) 1) (/.f64 (cbrt.f64 (*.f64 x y)) z))
	6.5b	(.f64 x (.f64 y (/.f64 1 z)))
▶	5.1b	(/.f64 1 (/.f64 z (*.f64 x y)))
✓	5.3b	(*.f64 y (/.f64 x z))
	6.7b	(/.f64 x (/.f64 z y))
✓	4.9b	(/.f64 (*.f64 x y) z)
✓	5.4b	(*.f64 (/.f64 x (pow.f64 (cbrt.f64 z) 2)) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 2545 to 1156 computations (54.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (/.f64 z (*.f64 x y)))
✓	4.8b	(/.f64 z (*.f64 x y))

series39.0ms (1.5%)

Counts

2 → 72

Calls

18 calls:

12.0ms	(/.f64 z (*.f64 x y))	x	inf
3.0ms	(/.f64 1 (/.f64 z (*.f64 x y)))	y	0
2.0ms	(/.f64 z (*.f64 x y))	z	-inf
2.0ms	(/.f64 z (*.f64 x y))	z	0
2.0ms	(/.f64 z (*.f64 x y))	z	inf

rewrite52.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

806×	`log1p-expm1-u_binary64`
806×	`expm1-log1p-u_binary64`
89×	`egg-rr`
83×	`add-sqr-sqrt_binary64`
76×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	14
2	2239	14

Stop Event

1×	node limit

Counts

2 → 89

simplify21.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/r*_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	504
1	12	504
2	16	504
3	19	504
4	20	504

Stop Event

1×

saturated

Counts

161 → 93

prune52.0ms (2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	93	7	100

Error

Counts

100 → 7

Alt Table

Status	Error	Program
	5.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) 1) (/.f64 (cbrt.f64 (*.f64 x y)) z))
	6.5b	(.f64 x (.f64 y (/.f64 1 z)))
✓	5.1b	(/.f64 1 (/.f64 z (*.f64 x y)))
✓	5.3b	(*.f64 y (/.f64 x z))
	6.7b	(/.f64 x (/.f64 z y))
✓	4.9b	(/.f64 (*.f64 x y) z)
✓	5.4b	(*.f64 (/.f64 x (pow.f64 (cbrt.f64 z) 2)) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 1085 to 469 computations (56.8% saved)

regimes357.0ms (13.7%)

Accuracy

Total 2.0b remaining (99.4%)

Threshold costs 0b (0%)

Counts

39 → 4

Compiler

Compiled 2554 to 1731 computations (32.2% saved)

bsearch1.0ms (0%)

Algorithm

3×	left-value

Calls

3 calls:

0.0ms	(*.f64 x y)
0.0ms	(*.f64 x y)
0.0ms	(*.f64 x y)

Steps

Iters	Point		Range
1.4951491249076507e+235	∈ [	1.4951491249076507e+235	,	2.059548393489365e+236	]
3.8895485895542e-310	∈ [	3.8895485895542e-310	,	4.645688179799266e-305	]
-1.761720498107075e-142	∈ [	-1.761720498107075e-142	,	-4.092476467215253e-144	]

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	55
1	22	55

Stop Event

1×

saturated

end217.0ms (8.3%)

Stop Event

1×

fuel

Compiler

Compiled 240 to 121 computations (49.6% saved)

Details

analyze358.0ms (13.7%)

sample864.0ms (33.1%)

preprocess21.0ms (0.8%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series12.0ms (0.5%)

rewrite39.0ms (1.5%)

simplify13.0ms (0.5%)

prune32.0ms (1.2%)

localize3.0ms (0.1%)

series13.0ms (0.5%)

rewrite34.0ms (1.3%)

simplify14.0ms (0.5%)

prune21.0ms (0.8%)

localize7.0ms (0.3%)

series188.0ms (7.2%)

rewrite61.0ms (2.3%)

simplify77.0ms (3%)

prune90.0ms (3.5%)

localize5.0ms (0.2%)

series39.0ms (1.5%)

rewrite52.0ms (2%)

simplify21.0ms (0.8%)

prune52.0ms (2%)

regimes357.0ms (13.7%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end217.0ms (8.3%)

Profiling