Details

analyze765.0ms (14.1%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (18.7%)

Results

930.0ms	8256×	body	128	valid
65.0ms	624×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess13.0ms (0.2%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	91
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13

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

14.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.1b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	13.3b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series37.0ms (0.7%)

Counts

2 → 84

Calls

21 calls:

7.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))	y	-inf
3.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))	t	-inf
3.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))	t	inf
2.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))	t	0
2.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))	z	0

rewrite37.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log1p-expm1-u_binary64`
801×	`expm1-log1p-u_binary64`
180×	`log1p-udef_binary64`
99×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	177	20
2	2012	20

Stop Event

1×	node limit

Counts

2 → 30

simplify446.0ms (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	89	1893
1	114	1893
2	133	1893
3	156	1893
4	189	1893
5	223	1893
6	263	1893
7	306	1893
8	356	1893
9	409	1893
10	469	1893
11	532	1893
12	602	1893
13	675	1893
14	755	1893
15	838	1893
16	928	1893
17	1021	1893
18	1121	1893
19	1224	1893
20	1334	1893
21	1447	1893
22	1567	1893
23	1690	1893
24	1820	1893
25	1953	1893
26	2093	1893
27	2236	1893
28	2244	1893
29	2248	1893
30	2248	1893
31	2396	1893
32	2545	1893
33	2705	1893
34	2868	1893
35	3038	1893
36	3211	1893
37	3391	1893
38	3574	1893
39	3764	1893
40	3957	1893
41	4005	1893
42	4009	1893
43	4009	1893
44	4202	1893
45	4402	1893
46	4609	1893
47	4823	1893

Stop Event

1×	node limit

Counts

114 → 65

prune46.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	56	9	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	9	66

Error

6.3b

Counts

66 → 9

Alt Table

Status	Error	Program
	14.9b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))
	52.0b	(cbrt.f64 (/.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3) (pow.f64 (-.f64 t z) 3)))
	36.7b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))) 2)
▶	14.1b	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))
	39.6b	(-.f64 (+.f64 (/.f64 (.f64 t x) z) x) (/.f64 (.f64 y x) z))
	41.3b	x
	36.0b	(.f64 -1 (/.f64 (.f64 z x) (-.f64 t z)))
	53.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (-.f64 y z) 3))) (-.f64 t z))
	40.9b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 x (-.f64 y z))) 2) (-.f64 t z))

Compiler

Compiled 1787 to 686 computations (61.6% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.4b	(-.f64 (.f64 y x) (.f64 z x))
✓	13.3b	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))

series46.0ms (0.9%)

Counts

2 → 66

Calls

21 calls:

8.0ms	(-.f64 (.f64 y x) (.f64 z x))	z	-inf
4.0ms	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))	z	0
3.0ms	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))	t	-inf
3.0ms	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))	z	-inf
3.0ms	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))	x	0

rewrite45.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

393×	`unpow-prod-down_binary64`
301×	`pow2_binary64`
294×	`log-prod_binary64`
212×	`pow1/3_binary64`
210×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	204	26
2	2361	26

Stop Event

1×	node limit

Counts

2 → 67

simplify420.0ms (7.8%)

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	94	1746
1	119	1746
2	138	1746
3	163	1746
4	197	1746
5	231	1746
6	271	1746
7	314	1746
8	364	1746
9	417	1746
10	477	1746
11	540	1746
12	610	1746
13	683	1746
14	763	1746
15	846	1746
16	936	1746
17	1029	1746
18	1129	1746
19	1232	1746
20	1342	1746
21	1455	1746
22	1575	1746
23	1698	1746
24	1828	1746
25	1961	1746
26	2101	1746
27	2244	1746
28	2252	1746
29	2256	1746
30	2256	1746
31	2404	1746
32	2553	1746
33	2713	1746
34	2876	1746
35	3046	1746
36	3219	1746
37	3399	1746
38	3582	1746
39	3772	1746
40	3965	1746
41	4013	1746
42	4017	1746
43	4017	1746
44	4210	1746
45	4410	1746
46	4617	1746
47	4831	1746

Stop Event

1×	node limit

Counts

133 → 103

prune66.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	101	11	112

Error

6.3b

Counts

112 → 11

Alt Table

Status	Error	Program
✓	14.1b	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))
	35.1b	(/.f64 (+.f64 (-.f64 (.f64 y x) (.f64 x z)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x z))) (sqrt.f64 (.f64 x z)) (*.f64 x z))) (-.f64 t z))
▶	14.9b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))
	52.0b	(cbrt.f64 (/.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3) (pow.f64 (-.f64 t z) 3)))
	36.7b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))) 2)
	30.7b	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y x) (.f64 x z)) (-.f64 t z))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y x) (*.f64 x z)) (-.f64 t z)) 2)))
	39.6b	(-.f64 (+.f64 (/.f64 (.f64 t x) z) x) (/.f64 (.f64 y x) z))
	41.3b	x
	36.0b	(.f64 -1 (/.f64 (.f64 z x) (-.f64 t z)))
	53.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (-.f64 y z) 3))) (-.f64 t z))
	40.9b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 x (-.f64 y z))) 2) (-.f64 t z))

Compiler

Compiled 2862 to 943 computations (67.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (-.f64 y z))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3)
✓	13.3b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))
✓	14.8b	(cbrt.f64 (*.f64 x (-.f64 y z)))

series406.0ms (7.5%)

Counts

3 → 64

Calls

30 calls:

145.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3)	z	0
58.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3)	y	0
50.0ms	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))	x	-inf
30.0ms	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))	y	-inf
20.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3)	y	-inf

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`unpow-prod-down_binary64`
297×	`pow2_binary64`
294×	`log-prod_binary64`
209×	`pow1/3_binary64`
209×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	237	29
2	2455	29

Stop Event

1×	node limit

Counts

3 → 70

simplify398.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

1696×	`sqr-pow_binary64`
444×	`pow-sqr_binary64`
75×	`cube-mult_binary64`
75×	`unpow3_binary64`
72×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	192	2614
1	321	2614
2	426	2614
3	536	2614
4	658	2614
5	780	2614
6	911	2614
7	1047	2614
8	1193	2614
9	1344	2614
10	1505	2614
11	1671	2614
12	1847	2614
13	2028	2614
14	2219	2614
15	2415	2614
16	2621	2614
17	2663	2614
18	2695	2614
19	2695	2614
20	2871	2614
21	3081	2614
22	3308	2614
23	3540	2614
24	3782	2614
25	4029	2614
26	4286	2614
27	4548	2614
28	4820	2614
29	4832	2614
30	4838	2614
31	4838	2614

Stop Event

1×	node limit

Counts

134 → 127

prune110.0ms (2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	143	13	156

Error

6.3b

Counts

156 → 13

Alt Table

Status	Error	Program
	36.7b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))) 2)
	36.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 -1 (.f64 z x))) 3) (-.f64 t z))
✓	14.1b	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))
	35.1b	(/.f64 (+.f64 (-.f64 (.f64 y x) (.f64 x z)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x z))) (sqrt.f64 (.f64 x z)) (*.f64 x z))) (-.f64 t z))
	39.6b	(-.f64 (+.f64 (/.f64 (.f64 t x) z) x) (/.f64 (.f64 y x) z))
▶	15.0b	(/.f64 (pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3) (-.f64 t z))
	53.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (-.f64 y z) 3))) (-.f64 t z))
	48.6b	(/.f64 (pow.f64 (.f64 (cbrt.f64 -1) (pow.f64 (.f64 z x) 1/3)) 3) (-.f64 t z))
✓	14.9b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))
	52.0b	(cbrt.f64 (/.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3) (pow.f64 (-.f64 t z) 3)))
	30.7b	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y x) (.f64 x z)) (-.f64 t z))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y x) (*.f64 x z)) (-.f64 t z)) 2)))
	41.3b	x
	40.9b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 x (-.f64 y z))) 2) (-.f64 t z))

Compiler

Compiled 4211 to 2016 computations (52.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3)
✓	0.6b	(cbrt.f64 (-.f64 y z))
✓	0.6b	(cbrt.f64 x)
✓	13.3b	(/.f64 (pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3) (-.f64 t z))

series407.0ms (7.5%)

Counts

4 → 64

Calls

30 calls:

144.0ms	(pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3)	z	0
57.0ms	(pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3)	y	0
55.0ms	(/.f64 (pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3) (-.f64 t z))	x	-inf
29.0ms	(/.f64 (pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3) (-.f64 t z))	y	-inf
19.0ms	(pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3)	x	-inf

rewrite47.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

332×	`log-prod_binary64`
235×	`log-pow_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
231×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	257	29
2	2754	29

Stop Event

1×	node limit

Counts

4 → 78

simplify394.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1644×	`sqr-pow_binary64`
507×	`pow-sqr_binary64`
75×	`cube-prod_binary64`
75×	`cube-mult_binary64`
75×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	190	2524
1	313	2524
2	411	2524
3	514	2524
4	629	2524
5	744	2524
6	868	2524
7	997	2524
8	1136	2524
9	1280	2524
10	1434	2524
11	1593	2524
12	1762	2524
13	1936	2524
14	2120	2524
15	2309	2524
16	2508	2524
17	2712	2524
18	2724	2524
19	2730	2524
20	2730	2524
21	2941	2524
22	3154	2524
23	3383	2524
24	3617	2524
25	3861	2524
26	4110	2524
27	4369	2524
28	4633	2524
29	4691	2524
30	4697	2524
31	4697	2524
32	4956	2524

Stop Event

1×	node limit

Counts

142 → 135

prune93.0ms (1.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	134	14	148

Error

6.3b

Counts

148 → 14

Alt Table

Status	Error	Program
	36.7b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))) 2)
	36.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 -1 (.f64 z x))) 3) (-.f64 t z))
✓	14.1b	(/.f64 (-.f64 (.f64 y x) (.f64 z x)) (-.f64 t z))
	35.1b	(/.f64 (+.f64 (-.f64 (.f64 y x) (.f64 x z)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x z))) (sqrt.f64 (.f64 x z)) (*.f64 x z))) (-.f64 t z))
	39.6b	(-.f64 (+.f64 (/.f64 (.f64 t x) z) x) (/.f64 (.f64 y x) z))
	30.7b	(.f64 (cbrt.f64 (/.f64 (.f64 (-.f64 y z) x) (-.f64 t z))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 (-.f64 y z) x) (-.f64 t z)) 2)))
✓	15.0b	(/.f64 (pow.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 x)) 3) (-.f64 t z))
	53.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (-.f64 y z) 3))) (-.f64 t z))
	48.6b	(/.f64 (pow.f64 (.f64 (cbrt.f64 -1) (pow.f64 (.f64 z x) 1/3)) 3) (-.f64 t z))
✓	14.9b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 y z))) 3) (-.f64 t z))
	52.0b	(cbrt.f64 (/.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3) (pow.f64 (-.f64 t z) 3)))
	41.3b	x
	36.4b	(/.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 z)) (cbrt.f64 x)) 3) (-.f64 t z))
	40.9b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 x (-.f64 y z))) 2) (-.f64 t z))

Compiler

Compiled 3819 to 1844 computations (51.7% saved)

regimes341.0ms (6.3%)

Accuracy

Total 0.5b remaining (8.8%)

Threshold costs 0.5b (8.8%)

Counts

44 → 3

Compiler

Compiled 3824 to 2421 computations (36.7% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

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

Steps

Iters	Point		Range
1.710510294576776e+291	∈ [	1.710510294576776e+291	,	#hash((type . real) (value . +inf))	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-8.672960660683467e+307	]

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54

Stop Event

1×

saturated

end177.0ms (3.3%)

Stop Event

1×

fuel

Compiler

Compiled 328 to 196 computations (40.2% saved)

Details

analyze765.0ms (14.1%)

sample1.0s (18.7%)

preprocess13.0ms (0.2%)

simplify4.0ms (0.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series37.0ms (0.7%)

rewrite37.0ms (0.7%)

simplify446.0ms (8.2%)

prune46.0ms (0.9%)

localize15.0ms (0.3%)

series46.0ms (0.9%)

rewrite45.0ms (0.8%)

simplify420.0ms (7.8%)

prune66.0ms (1.2%)

localize11.0ms (0.2%)

series406.0ms (7.5%)

rewrite53.0ms (1%)

simplify398.0ms (7.4%)

prune110.0ms (2%)

localize10.0ms (0.2%)

series407.0ms (7.5%)

rewrite47.0ms (0.9%)

simplify394.0ms (7.3%)

prune93.0ms (1.7%)

regimes341.0ms (6.3%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

end177.0ms (3.3%)

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