Details

analyze1.2s (9.6%)

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%	74.8%	25.2%	5
0%	74.8%	25.2%	6
0%	74.8%	25.2%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	62.3%	37.7%	10
0%	56.1%	43.9%	11
0%	56.1%	43.9%	12
1.6%	54.5%	43.9%	13
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample2.7s (21.3%)

Symmetry

(sort x y)

Results

1.4s	8253×	body	128	valid
1.1s	2369×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify284.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

5327×	`fma-def_binary64`
866×	`fma-neg_binary64`
705×	`sub-neg_binary64`
654×	`unsub-neg_binary64`
445×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	101	22
3	269	21
4	805	20
5	2079	20
6	2787	20
7	3848	20
8	4164	20
9	4306	20
10	4090	20
11	4094	20
12	4190	20
13	4488	20
14	4581	20
15	4587	20
16	4587	20
17	4593	20
18	4599	20
19	4599	20
20	4617	20
21	4601	20
22	4601	20
23	9364	20

prune6.0ms (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

0.0b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series254.0ms (2%)

Counts

2 → 80

Calls

2 calls:

225.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
29.0ms	(-.f64 1 (log.f64 t))

rewrite71.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

759×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
151×	`add-log-exp_binary64`

Counts

2 → 54

Calls

2 calls:

69.0ms	(-.f64 1 (log.f64 t))
69.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	319	26
2	3918	26
3	5360	26
0	0	0
1	0	0

simplify214.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
691×	`associate--l+_binary64`
521×	`neg-mul-1_binary64`
509×	`+-commutative_binary64`
433×	`associate-+l-_binary64`

Counts

134 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	1491
1	177	1490
2	489	1373
3	1507	1309
4	3645	1309
5	4151	1309
6	4804	1309
7	5037	1309

prune183.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.3b	(fma.f64 z (*.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) (pow.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) 2)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	27.2b	(pow.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) 2)
	1.3b	(*.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) 2))

Compiler

Compiled 1708 to 907 computations (46.9% saved)

localize33.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.5b	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t)))
✓	0.5b	(pow.f64 (log.f64 t) 2)

series1.3s (10.2%)

Counts

3 → 88

Calls

3 calls:

1.0s	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
144.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t)))
89.0ms	(pow.f64 (log.f64 t) 2)

rewrite108.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

431×	`prod-diff_binary64`
207×	`add-sqr-sqrt_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
195×	`add-log-exp_binary64`

Counts

3 → 103

Calls

3 calls:

104.0ms	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
104.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t)))
104.0ms	(pow.f64 (log.f64 t) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	54
1	417	32
2	4781	32
3	5701	32
0	0	0
1	0	0

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-neg_binary64`
553×	`cancel-sign-sub-inv_binary64`
543×	`times-frac_binary64`
362×	`sub-neg_binary64`
294×	`div-sub_binary64`

Counts

191 → 135

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	3424
1	280	3255
2	735	3082
3	2457	2630
4	4793	2626
5	4859	2626

prune313.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (/.f64 z (+.f64 1 (log.f64 t))) (+.f64 (.f64 a b) (+.f64 y x))) (+.f64 (/.f64 (.f64 z (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (*.f64 1/2 b)))
▶	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	27.2b	(pow.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) 2)
	1.3b	(*.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) 2))

Compiler

Compiled 5455 to 3316 computations (39.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.3b	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))))
✓	0.6b	(fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))
✓	0.7b	(pow.f64 (log.f64 t) 3)

series1.9s (15.2%)

Counts

4 → 104

Calls

4 calls:

1.6s	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
210.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))))
73.0ms	(fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))
28.0ms	(pow.f64 (log.f64 t) 3)

rewrite134.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

238×	`prod-diff_binary64`
220×	`add-sqr-sqrt_binary64`
210×	`log1p-expm1-u_binary64`
210×	`expm1-log1p-u_binary64`
205×	`add-log-exp_binary64`

Counts

4 → 125

Calls

4 calls:

127.0ms	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
127.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))))
127.0ms	(fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))
127.0ms	(pow.f64 (log.f64 t) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	81
1	439	81
2	4824	81
3	5255	81
0	0	0
1	0	0

simplify152.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-neg_binary64`
494×	`associate-+l+_binary64`
411×	`associate--l+_binary64`
280×	`fma-def_binary64`
237×	`associate-r_binary64`

Counts

229 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	5818
1	371	5609
2	1213	5180
3	4642	5132
4	5307	5132

prune284.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (/.f64 z (+.f64 1 (+.f64 (pow.f64 (log.f64 t) 2) (log.f64 t)))) (+.f64 (.f64 a b) (+.f64 y x))) (+.f64 (/.f64 (.f64 z (pow.f64 (log.f64 t) 3)) (+.f64 1 (+.f64 (pow.f64 (log.f64 t) 2) (log.f64 t)))) (*.f64 1/2 b)))
▶	0.1b	(-.f64 (+.f64 (/.f64 z (+.f64 1 (log.f64 t))) (+.f64 (.f64 a b) (+.f64 y x))) (+.f64 (/.f64 (.f64 z (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (*.f64 1/2 b)))
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	27.2b	(pow.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) 2)

Compiler

Compiled 9256 to 4578 computations (50.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (pow.f64 (log.f64 t) 2))
✓	0.3b	(/.f64 z (+.f64 1 (log.f64 t)))
✓	0.4b	(/.f64 (*.f64 z (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t)))
	0.5b	(pow.f64 (log.f64 t) 2)

series1.1s (8.6%)

Counts

3 → 24

Calls

3 calls:

589.0ms	(/.f64 (*.f64 z (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t)))
254.0ms	(/.f64 z (+.f64 1 (log.f64 t)))
227.0ms	(*.f64 z (pow.f64 (log.f64 t) 2))

rewrite75.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

570×	`log-prod_binary64`
276×	`prod-diff_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
187×	`fma-def_binary64`

Counts

3 → 104

Calls

3 calls:

72.0ms	(*.f64 z (pow.f64 (log.f64 t) 2))
72.0ms	(/.f64 z (+.f64 1 (log.f64 t)))
72.0ms	(/.f64 (*.f64 z (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	232	35
2	2880	35
3	5570	35
0	0	0
1	0	0

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

878×	`div-sub_binary64`
862×	`sub-neg_binary64`
280×	`cancel-sign-sub-inv_binary64`
278×	`times-frac_binary64`
208×	`associate-r_binary64`

Counts

128 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	344
1	50	312
2	110	280
3	386	280
4	2165	280
5	4454	280
6	5478	280

prune173.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	128	4	132

Error

Counts

132 → 4

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (/.f64 z (+.f64 1 (+.f64 (pow.f64 (log.f64 t) 2) (log.f64 t)))) (+.f64 (.f64 a b) (+.f64 y x))) (+.f64 (/.f64 (.f64 z (pow.f64 (log.f64 t) 3)) (+.f64 1 (+.f64 (pow.f64 (log.f64 t) 2) (log.f64 t)))) (*.f64 1/2 b)))
✓	0.1b	(-.f64 (+.f64 (/.f64 z (+.f64 1 (log.f64 t))) (+.f64 (.f64 a b) (+.f64 y x))) (+.f64 (/.f64 (.f64 z (pow.f64 (log.f64 t) 2)) (+.f64 1 (log.f64 t))) (*.f64 1/2 b)))
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	27.2b	(pow.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) 2)

Compiler

Compiled 4678 to 2410 computations (48.5% saved)

regimes1.8s (14.2%)

Accuracy

Total 0.0b remaining (56.7%)

Threshold costs 0.0b (56.7%)

Counts

125 → 1

Compiler

Compiled 42865 to 29750 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`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	15	20
1	23	20
2	28	20
3	30	20
4	31	20
5	29	20

end109.0ms (0.9%)

Remove: (sort x y)
Compiler: Compiled 217 to 147 computations (32.3% saved)

Details

analyze1.2s (9.6%)

sample2.7s (21.3%)

simplify284.0ms (2.3%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

series254.0ms (2%)

rewrite71.0ms (0.6%)

simplify214.0ms (1.7%)

prune183.0ms (1.5%)

localize33.0ms (0.3%)

series1.3s (10.2%)

rewrite108.0ms (0.9%)

simplify117.0ms (0.9%)

prune313.0ms (2.5%)

localize18.0ms (0.1%)

series1.9s (15.2%)

rewrite134.0ms (1.1%)

simplify152.0ms (1.2%)

prune284.0ms (2.3%)

localize19.0ms (0.2%)

series1.1s (8.6%)

rewrite75.0ms (0.6%)

simplify63.0ms (0.5%)

prune173.0ms (1.4%)

regimes1.8s (14.2%)

simplify3.0ms (0%)

end109.0ms (0.9%)

Profiling