Details

analyze568.0ms (9.6%)

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
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (18.2%)

Symmetry

(sort z t)

Results

894.0ms	8256×	body	128	valid
35.0ms	356×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

2.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.4b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	2.4b	(/.f64 x (-.f64 y (*.f64 z t)))

series35.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.f64 y (*.f64 z t))

rewrite74.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

642×	`prod-diff_binary64`
490×	`log-prod_binary64`
207×	`fma-def_binary64`
178×	`egg-rr`
170×	`expm1-udef_binary64`

Counts

2 → 178

Calls

2 calls:

68.0ms	(-.f64 y (*.f64 z t))
68.0ms	(/.f64 x (-.f64 y (*.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	177	17
2	2393	17
3	5465	17
0	0	0
1	0	0

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
715×	`times-frac_binary64`
452×	`associate-/l*_binary64`
299×	`associate-/r*_binary64`
236×	`associate-l_binary64`

Counts

262 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	1604
1	176	1544
2	676	1492
3	4187	1492
4	5019	1492

prune143.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	189	9	198
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Error

2.4b

Counts

199 → 9

Alt Table

Status	Error	Program
▶	2.4b	(/.f64 x (fma.f64 z (neg.f64 t) y))
	26.7b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 z t))) 3))
	3.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 y (.f64 z t))) 2)) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	32.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	2.8b	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
	3.4b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	46.9b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (fma.f64 y y (.f64 (.f64 z t) (fma.f64 z t y))))
	32.8b	(.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (-.f64 y (.f64 z t))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (-.f64 y (*.f64 z t)))))

Compiler

Compiled 4248 to 1163 computations (72.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(/.f64 x (fma.f64 z (neg.f64 t) y))

series32.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

31.0ms

(/.f64 x (fma.f64 z (neg.f64 t) y))

rewrite47.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

721×	`log1p-expm1-u_binary64`
721×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`

Counts

1 → 34

Calls

1 calls:

46.0ms

(/.f64 x (fma.f64 z (neg.f64 t) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	166	8
2	1871	8
3	4965	8
0	0	0
1	0	0

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
715×	`times-frac_binary64`
452×	`associate-/l*_binary64`
299×	`associate-/r*_binary64`
231×	`associate-l_binary64`

Counts

82 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	1381
1	172	1321
2	670	1269
3	4181	1269
4	5013	1269

prune41.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	50	9	59

Error

2.4b

Counts

59 → 9

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (fma.f64 z (neg.f64 t) y))
	26.7b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 z t))) 3))
	3.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 y (.f64 z t))) 2)) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	32.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
▶	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	2.8b	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
	3.4b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	46.9b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (fma.f64 y y (.f64 (.f64 z t) (fma.f64 z t y))))
	32.8b	(.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (-.f64 y (.f64 z t))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (-.f64 y (*.f64 z t)))))

Compiler

Compiled 1062 to 473 computations (55.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.3b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	2.5b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series46.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
15.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite145.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

662×	`prod-diff_binary64`
520×	`fma-udef_binary64`
344×	`fma-def_binary64`
189×	`fma-neg_binary64`
188×	`expm1-udef_binary64`

Counts

2 → 52

Calls

2 calls:

144.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))
144.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	213	20
2	2611	20
3	4786	20
4	4779	20
5	4991	20
6	4945	20
0	0	0
1	0	0

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

922×	`times-frac_binary64`
598×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
327×	`fma-def_binary64`
145×	`associate-*l/_binary64`

Counts

136 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	2470
1	242	2380
2	933	2258
3	4963	2258
4	5020	2258

prune153.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	226	8	234

Error

2.4b

Counts

234 → 8

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (fma.f64 z (neg.f64 t) y))
	26.7b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 z t))) 3))
	3.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 y (.f64 z t))) 2)) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
✓	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	32.6b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
▶	2.8b	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
	3.4b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	46.9b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (fma.f64 y y (.f64 (.f64 z t) (fma.f64 z t y))))

Compiler

Compiled 4892 to 1685 computations (65.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y)
✓	0.4b	(pow.f64 (cbrt.f64 (*.f64 z t)) 2)
✓	2.4b	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
✓	13.8b	(cbrt.f64 (*.f64 z t))

series2.6s (42.9%)

Counts

4 → 132

Calls

4 calls:

1.2s	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
744.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y)
322.0ms	(cbrt.f64 (*.f64 z t))
313.0ms	(pow.f64 (cbrt.f64 (*.f64 z t)) 2)

rewrite89.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

530×	`log-prod_binary64`
314×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
179×	`pow3_binary64`

Counts

4 → 145

Calls

4 calls:

86.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y)
86.0ms	(pow.f64 (cbrt.f64 (*.f64 z t)) 2)
86.0ms	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
86.0ms	(cbrt.f64 (*.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	247	32
2	2592	28
3	5000	28
4	5107	28
0	0	0
1	0	0

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

715×	`times-frac_binary64`
452×	`associate-/l*_binary64`
301×	`associate-/r*_binary64`
292×	`associate-l_binary64`
275×	`associate-r_binary64`

Counts

277 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	2472
1	313	2460
2	896	2290
3	5031	2290

prune173.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	252	8	260

Error

2.4b

Counts

260 → 8

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (fma.f64 z (neg.f64 t) y))
	26.7b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 z t))) 3))
	3.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 y (.f64 z t))) 2)) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
✓	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	32.6b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
✓	2.8b	(/.f64 x (fma.f64 (pow.f64 (cbrt.f64 (.f64 z t)) 2) (neg.f64 (cbrt.f64 (.f64 z t))) y))
	3.4b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	46.9b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (fma.f64 y y (.f64 (.f64 z t) (fma.f64 z t y))))

Compiler

Compiled 4514 to 1841 computations (59.2% saved)

regimes331.0ms (5.6%)

Accuracy

Total 0.1b remaining (2.3%)

Threshold costs 0.1b (2.3%)

Counts

44 → 1

Compiler

Compiled 6005 to 3689 computations (38.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	12	10
2	14	10
3	15	10
4	15	10

end98.0ms (1.6%)

Remove: (sort z t)
Compiler: Compiled 179 to 111 computations (38% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Details

analyze568.0ms (9.6%)

sample1.1s (18.2%)

simplify13.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series35.0ms (0.6%)

rewrite74.0ms (1.2%)

simplify71.0ms (1.2%)

prune143.0ms (2.4%)

localize5.0ms (0.1%)

series32.0ms (0.5%)

rewrite47.0ms (0.8%)

simplify59.0ms (1%)

prune41.0ms (0.7%)

localize9.0ms (0.2%)

series46.0ms (0.8%)

rewrite145.0ms (2.4%)

simplify92.0ms (1.5%)

prune153.0ms (2.6%)

localize10.0ms (0.2%)

series2.6s (42.9%)

rewrite89.0ms (1.5%)

simplify63.0ms (1.1%)

prune173.0ms (2.9%)

regimes331.0ms (5.6%)

simplify2.0ms (0%)

end98.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10