Details

analyze1.3s (14.9%)

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
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (13.2%)

Results

1.0s	8255×	body	128	valid
105.0ms	759×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess17.0ms (0.2%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
0	5	5

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16

Stop Event

1×

saturated

Counts

1 → 1

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

8.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	9.1b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

series72.0ms (0.8%)

Counts

3 → 144

Calls

36 calls:

4.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))	a	inf
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))	z	0
3.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))	a	-inf
3.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))	a	0
3.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))	t	0

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

322×	`pow2_binary64`
314×	`log-prod_binary64`
227×	`pow1/3_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	220	36
2	2529	36

Stop Event

1×	node limit

Counts

3 → 59

simplify713.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

1734×	`sqr-pow_binary64`
834×	`pow-sqr_binary64`
80×	`cube-prod_binary64`
80×	`cube-mult_binary64`
80×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	173	3729
1	198	3729
2	217	3729
3	240	3729
4	273	3729
5	307	3729
6	347	3729
7	390	3729
8	440	3729
9	493	3729
10	553	3729
11	616	3729
12	686	3729
13	759	3729
14	839	3729
15	922	3729
16	1012	3729
17	1105	3729
18	1205	3729
19	1308	3729
20	1418	3729
21	1531	3729
22	1651	3729
23	1774	3729
24	1904	3729
25	2037	3729
26	2177	3729
27	2320	3729
28	2328	3729
29	2332	3729
30	2332	3729
31	2480	3729
32	2629	3729
33	2789	3729
34	2952	3729
35	3122	3729
36	3295	3729
37	3475	3729
38	3658	3729
39	3848	3729
40	4041	3729
41	4089	3729
42	4093	3729
43	4093	3729
44	4286	3729
45	4486	3729
46	4693	3729
47	4907	3729

Stop Event

1×	node limit

Counts

203 → 133

prune94.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	126	7	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Error

0.0b

Counts

134 → 7

Alt Table

Status	Error	Program
	16.7b	(+.f64 x (.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))))
	38.2b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	26.4b	x
	21.2b	(+.f64 x y)
	10.0b	(.f64 (cbrt.f64 (+.f64 x (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t)))) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2))
	32.9b	(+.f64 x (pow.f64 (sqrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) 2))
▶	8.8b	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))

Compiler

Compiled 3847 to 1288 computations (66.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))
	0.0b	(*.f64 y (-.f64 z t))
	9.1b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

series39.0ms (0.4%)

Counts

1 → 60

Calls

15 calls:

4.0ms	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))	z	0
3.0ms	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))	a	0
3.0ms	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))	t	0
3.0ms	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))	x	0
2.0ms	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))	x	inf

rewrite36.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

323×	`log-prod_binary64`
235×	`pow1/3_binary64`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`
225×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	247	16
2	2673	16

Stop Event

1×	node limit

Counts

1 → 23

simplify426.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1734×	`sqr-pow_binary64`
834×	`pow-sqr_binary64`
80×	`cube-prod_binary64`
80×	`cube-mult_binary64`
80×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	126	1836
1	149	1836
2	167	1836
3	190	1836
4	223	1836
5	257	1836
6	297	1836
7	340	1836
8	390	1836
9	443	1836
10	503	1836
11	566	1836
12	636	1836
13	709	1836
14	789	1836
15	872	1836
16	962	1836
17	1055	1836
18	1155	1836
19	1258	1836
20	1368	1836
21	1481	1836
22	1601	1836
23	1724	1836
24	1854	1836
25	1987	1836
26	2127	1836
27	2270	1836
28	2278	1836
29	2282	1836
30	2282	1836
31	2430	1836
32	2579	1836
33	2739	1836
34	2902	1836
35	3072	1836
36	3245	1836
37	3425	1836
38	3608	1836
39	3798	1836
40	3991	1836
41	4039	1836
42	4043	1836
43	4043	1836
44	4236	1836
45	4436	1836
46	4643	1836
47	4857	1836

Stop Event

1×	node limit

Counts

83 → 60

prune105.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	135	7	142

Error

0.0b

Counts

142 → 7

Alt Table

Status	Error	Program
	16.7b	(+.f64 x (.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))))
	38.2b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	26.4b	x
	21.2b	(+.f64 x y)
▶	10.0b	(.f64 (cbrt.f64 (+.f64 x (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t)))) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2))
	32.9b	(+.f64 x (pow.f64 (sqrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) 2))
✓	8.8b	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))

Compiler

Compiled 4001 to 1428 computations (64.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (+.f64 x (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t)))) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2)
✓	0.6b	(cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))))
	9.1b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

series498.0ms (5.7%)

Counts

3 → 132

Calls

45 calls:

40.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2)	t	0
39.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2)	a	0
37.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2)	t	-inf
37.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2)	t	inf
31.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2)	a	-inf

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

367×	`log-prod_binary64`
264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
260×	`log-pow_binary64`
152×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	80
1	296	55
2	3218	55

Stop Event

1×	node limit

Counts

3 → 62

simplify1.0s (11.7%)

Algorithm

1×	egg-herbie

Rules

1481×	`sqr-pow_binary64`
272×	`fma-def_binary64`
196×	`pow-sqr_binary64`
66×	`cube-prod_binary64`
66×	`cube-mult_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1031	17893
1	1535	17893
2	1757	17893
3	1990	17893
4	2243	17893
5	2497	17893
6	2765	17893
7	3048	17893
8	3346	17893
9	3659	17893
10	3683	17893
11	3695	17893
12	3695	17893
13	4017	17893
14	4348	17893
15	4706	17893

Stop Event

1×	node limit

Counts

194 → 219

prune557.0ms (6.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	409	0	409
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	409	7	416

Error

0.0b

Counts

416 → 7

Alt Table

Status	Error	Program
▶	16.7b	(+.f64 x (.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))))
	38.2b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	26.4b	x
	21.2b	(+.f64 x y)
✓	10.0b	(.f64 (cbrt.f64 (+.f64 x (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t)))) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2))
	32.9b	(+.f64 x (pow.f64 (sqrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) 2))
✓	8.8b	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))

Compiler

Compiled 38603 to 17073 computations (55.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2)))
✓	5.4b	(cbrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	9.1b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
✓	30.1b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))

series716.0ms (8.3%)

Counts

3 → 88

Calls

36 calls:

88.0ms	(cbrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))	a	0
79.0ms	(cbrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))	a	-inf
59.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))	a	-inf
58.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))	a	inf
55.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))	a	0

rewrite47.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

316×	`log-prod_binary64`
235×	`pow1/3_binary64`
232×	`log-pow_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	272	46
2	2893	46

Stop Event

1×	node limit

Counts

3 → 64

simplify650.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

1571×	`sqr-pow_binary64`
201×	`fma-def_binary64`
52×	`unpow1/3_binary64`
49×	`pow-sqr_binary64`
24×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1066	11546
1	1685	11546
2	2045	11546
3	2401	11546
4	2766	11546
5	3132	11546
6	3504	11546
7	3540	11546
8	3555	11546
9	3564	11546
10	3570	11546
11	3576	11546
12	3932	11546
13	4288	11546
14	4656	11546

Stop Event

1×	node limit

Counts

152 → 177

prune398.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	285	7	292

Error

0.0b

Counts

292 → 7

Alt Table

Status	Error	Program
✓	16.7b	(+.f64 x (.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 2))))
	38.2b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	26.4b	x
	21.2b	(+.f64 x y)
✓	10.0b	(.f64 (cbrt.f64 (+.f64 x (/.f64 (.f64 y (-.f64 z t)) (-.f64 a t)))) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))) 2))
	32.9b	(+.f64 x (pow.f64 (sqrt.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) 2))
✓	8.8b	(+.f64 x (pow.f64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) 1))

Compiler

Compiled 20602 to 10632 computations (48.4% saved)

regimes609.0ms (7%)

Accuracy

Total 2.2b remaining (94.3%)

Threshold costs 0b (0%)

Counts

47 → 3

Compiler

Compiled 7752 to 4755 computations (38.7% saved)

bsearch2.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
0.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

Steps

Iters	Point		Range
8.964883377348856e+260	∈ [	8.964883377348856e+260	,	3.49708094385907e+279	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-2.2083046330603893e+300	]

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	90

Stop Event

1×

saturated

end93.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 263 to 119 computations (54.8% saved)

Details

analyze1.3s (14.9%)

sample1.1s (13.2%)

preprocess17.0ms (0.2%)

simplify5.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series72.0ms (0.8%)

rewrite40.0ms (0.5%)

simplify713.0ms (8.2%)

prune94.0ms (1.1%)

localize9.0ms (0.1%)

series39.0ms (0.4%)

rewrite36.0ms (0.4%)

simplify426.0ms (4.9%)

prune105.0ms (1.2%)

localize12.0ms (0.1%)

series498.0ms (5.7%)

rewrite48.0ms (0.6%)

simplify1.0s (11.7%)

prune557.0ms (6.4%)

localize15.0ms (0.2%)

series716.0ms (8.3%)

rewrite47.0ms (0.5%)

simplify650.0ms (7.5%)

prune398.0ms (4.6%)

regimes609.0ms (7%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end93.0ms (1.1%)

Profiling