Details

analyze602.0ms (17.7%)

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)

sample986.0ms (29%)

Symmetry

(sort z t)

Results

901.0ms	8256×	body	128	valid
32.0ms	328×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	26	10
3	43	10
4	63	10
5	97	10
6	154	10
7	207	10
8	271	10
9	356	10
10	406	10
11	412	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (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

2.1b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	2.1b	(/.f64 x (-.f64 y (*.f64 z t)))

series37.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.f64 y (*.f64 z t))

rewrite74.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`prod-diff_binary64`
207×	`fma-def_binary64`
170×	`egg-rr`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	177	17
2	2543	17

Stop Event

1×	node limit

Counts

2 → 170

Calls

2 calls:

67.0ms	(-.f64 y (*.f64 z t))
67.0ms	(/.f64 x (-.f64 y (*.f64 z t)))

simplify62.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	1604
1	179	1544
2	694	1492
3	4852	1492

Stop Event

1×	node limit

Counts

254 → 190

prune134.0ms (3.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Error

0.0b

Counts

191 → 9

Alt Table

Status	Error	Program
	36.6b	(/.f64 (neg.f64 (/.f64 x z)) t)
	2.6b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	25.0b	(pow.f64 (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 2)
	3.0b	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 3)
	33.7b	(/.f64 x (pow.f64 (sqrt.f64 (-.f64 y (*.f64 z t))) 2))
	35.1b	(.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)))))
	3.1b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	2.1b	(/.f64 x (fma.f64 z (neg.f64 t) y))

Compiler

Compiled 4060 to 1389 computations (65.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.1b	(/.f64 x (fma.f64 z (neg.f64 t) y))

series29.0ms (0.9%)

Counts

1 → 48

Calls

1 calls:

29.0ms

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

rewrite37.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`log1p-expm1-u_binary64`
721×	`expm1-log1p-u_binary64`
141×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`
87×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	166	8
2	2183	8

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

36.0ms

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

simplify47.0ms (1.4%)

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`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	1381
1	175	1321
2	686	1269
3	4850	1269

Stop Event

1×	node limit

Counts

81 → 49

prune33.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	49	9	58

Error

0.0b

Counts

58 → 9

Alt Table

Status	Error	Program
	36.6b	(/.f64 (neg.f64 (/.f64 x z)) t)
	2.6b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	25.0b	(pow.f64 (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 2)
	3.0b	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 3)
	33.7b	(/.f64 x (pow.f64 (sqrt.f64 (-.f64 y (*.f64 z t))) 2))
	35.1b	(.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)))))
	3.1b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
▶	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	2.1b	(/.f64 x (fma.f64 z (neg.f64 t) y))

Compiler

Compiled 998 to 466 computations (53.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.2b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series41.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

27.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
14.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite45.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`prod-diff_binary64`
212×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
108×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	213	20
2	2836	20

Stop Event

1×	node limit

Counts

2 → 51

Calls

2 calls:

44.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))
44.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	2470
1	245	2380
2	952	2258

Stop Event

1×	node limit

Counts

135 → 82

prune135.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	224	6	230

Error

0.0b

Counts

230 → 6

Alt Table

Status	Error	Program
▶	2.6b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	35.4b	(*.f64 x (/.f64 (/.f64 -1 z) t))
	36.6b	(/.f64 (neg.f64 (/.f64 x z)) t)
	3.0b	(pow.f64 (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 3)
✓	2.1b	(/.f64 x (fma.f64 z (neg.f64 t) y))
	34.7b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))

Compiler

Compiled 4711 to 1873 computations (60.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.7b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
✓	2.0b	(/.f64 (-.f64 y (*.f64 z t)) x)

series49.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

32.0ms	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
18.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite108.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

878×	`prod-diff_binary64`
296×	`egg-rr`
201×	`log1p-udef_binary64`
115×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	222	20
2	3163	20

Stop Event

1×	node limit

Counts

2 → 296

Calls

2 calls:

98.0ms	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
98.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

887×	`fma-neg_binary64`
715×	`times-frac_binary64`
464×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
236×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	1840
1	203	1780
2	742	1728
3	5000	1728

Stop Event

1×	node limit

Counts

392 → 320

prune285.0ms (8.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	458	1	459
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	459	6	465

Error

Counts

465 → 6

Alt Table

Status	Error	Program
✓	2.6b	(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
	35.4b	(*.f64 x (/.f64 (/.f64 -1 z) t))
	14.3b	(pow.f64 (+.f64 (fma.f64 y (/.f64 1 x) (neg.f64 (.f64 (/.f64 z x) (/.f64 t 1)))) (fma.f64 (neg.f64 (/.f64 z x)) (/.f64 t 1) (.f64 (/.f64 z x) (/.f64 t 1)))) -1)
✓	2.1b	(/.f64 x (fma.f64 z (neg.f64 t) y))
	36.6b	(/.f64 (neg.f64 (/.f64 x z)) t)
	34.7b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))

Compiler

Compiled 15576 to 5094 computations (67.3% saved)

regimes460.0ms (13.5%)

Accuracy

Total 1.3b remaining (99.2%)

Threshold costs 0b (0%)

Counts

56 → 2

Compiler

Compiled 7662 to 4795 computations (37.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	27	28
2	35	28
3	41	28
4	43	28

Stop Event

1×

saturated

end80.0ms (2.4%)

Remove: (sort z t)
Compiler: Compiled 187 to 118 computations (36.9% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	26	10
3	43	10
4	63	10
5	97	10
6	154	10
7	207	10
8	271	10
9	356	10
10	406	10
11	412	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	26	10
3	43	10
4	63	10
5	97	10
6	154	10
7	207	10
8	271	10
9	356	10
10	406	10
11	412	10

Details

analyze602.0ms (17.7%)

sample986.0ms (29%)

simplify11.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series37.0ms (1.1%)

rewrite74.0ms (2.2%)

simplify62.0ms (1.8%)

prune134.0ms (3.9%)

localize5.0ms (0.2%)

series29.0ms (0.9%)

rewrite37.0ms (1.1%)

simplify47.0ms (1.4%)

prune33.0ms (1%)

localize6.0ms (0.2%)

series41.0ms (1.2%)

rewrite45.0ms (1.3%)

simplify51.0ms (1.5%)

prune135.0ms (4%)

localize6.0ms (0.2%)

series49.0ms (1.5%)

rewrite108.0ms (3.2%)

simplify64.0ms (1.9%)

prune285.0ms (8.4%)

regimes460.0ms (13.5%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end80.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	26	10
3	43	10
4	63	10
5	97	10
6	154	10
7	207	10
8	271	10
9	356	10
10	406	10
11	412	10