Details

analyze1.1s (13.6%)

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
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
5.8%	94%	0.2%	9
7.6%	92.2%	0.2%	10
11.6%	88.2%	0.2%	11
18.5%	81.3%	0.2%	12
32.3%	66.9%	0.8%	13
37%	62.2%	0.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (15.2%)

Symmetry

(sort x y)

Results

970.0ms	8256×	body	128	valid
174.0ms	1542×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify169.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1483×	`associate-/l/_binary64`
1068×	`associate-/l*_binary64`
1015×	`associate-/r/_binary64`
675×	`*-commutative_binary64`
404×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	10
2	41	7
3	91	7
4	366	7
5	1228	7
6	1212	7
7	1225	7
8	1238	7
9	1245	7
10	1252	7
11	1259	7
12	1266	7
13	1273	7
14	1280	7
15	1287	7
16	1294	7
17	1301	7
18	1308	7
19	1315	7
20	1322	7
21	3032	7
22	2753	7
23	2781	7
24	2833	7
25	2977	7
26	3074	7
27	3494	7
28	3743	7
29	4033	7
30	4473	7
31	5028	7

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(*.f64 x (/.f64 y z))

Compiler

Compiled 36 to 21 computations (41.7% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.7b	(*.f64 x (/.f64 y z))

series12.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(*.f64 x (/.f64 y z))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

6.0ms

(*.f64 x (/.f64 y z))

simplify113.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

736×	`fabs-mul_binary64`
732×	`sqr-pow_binary64`
503×	`pow-sqr_binary64`
384×	`associate-/l/_binary64`
307×	`unswap-sqr_binary64`

Counts

70 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	642
1	162	597
2	526	597
3	1312	597
4	2135	597
5	2239	597
6	2445	597
7	2751	597
8	3643	597
9	4500	597
10	4489	597
11	5931	597

prune42.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	41	9	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	10	51

Error

0.0b

Counts

51 → 10

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 x y) (/.f64 1 z))
✓	5.8b	(*.f64 x (/.f64 y z))
	19.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	7.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) z)) (cbrt.f64 (/.f64 (.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
	31.3b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
	6.3b	(/.f64 (*.f64 y x) z)
	31.6b	(.f64 (.f64 x (sqrt.f64 (/.f64 y z))) (sqrt.f64 (/.f64 y z)))
	6.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	6.3b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
▶	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))

Compiler

Compiled 847 to 328 computations (61.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 y)
✓	1.2b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.2s (14.2%)

Counts

4 → 72

Calls

4 calls:

1.1s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
31.0ms	(cbrt.f64 y)
30.0ms	(cbrt.f64 z)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
24×	`add-exp-log_binary64`
22×	`cbrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 100

Calls

4 calls:

11.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 z)

simplify112.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-*l/_binary64`
774×	`fma-def_binary64`
371×	`fma-neg_binary64`
245×	`unswap-sqr_binary64`
188×	`associate-/r/_binary64`

Counts

172 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2641
1	385	1963
2	1420	1783
3	4099	1777
4	4957	1777
5	5012	1777

prune145.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	223	13	236

Error

Counts

236 → 13

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 x y) (/.f64 1 z))
▶	1.9b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
✓	5.8b	(*.f64 x (/.f64 y z))
	6.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (expm1.f64 (log1p.f64 (cbrt.f64 y))) (cbrt.f64 z)))
	19.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	7.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) z)) (cbrt.f64 (/.f64 (.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
	31.3b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
	6.3b	(/.f64 (*.f64 y x) z)
	31.6b	(.f64 (.f64 x (sqrt.f64 (/.f64 y z))) (sqrt.f64 (/.f64 y z)))
	1.9b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
	6.3b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
✓	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))

Compiler

Compiled 5825 to 1588 computations (72.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 y)
✓	0.6b	(cbrt.f64 (cbrt.f64 y))
✓	1.2b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.3s (15.9%)

Counts

2 → 48

Calls

2 calls:

1.0s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
251.0ms	(cbrt.f64 (cbrt.f64 y))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-exp-log_binary64`
25×	`cbrt-unprod_binary64`
25×	`prod-exp_binary64`
22×	`add-cbrt-cube_binary64`
9×	`cbrt-prod_binary64`

Counts

2 → 55

Calls

2 calls:

19.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
1.0ms	(cbrt.f64 (cbrt.f64 y))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

832×	`associate-*l/_binary64`
723×	`associate-/r*_binary64`
318×	`fma-def_binary64`
205×	`associate-/r/_binary64`
167×	`associate-/l/_binary64`

Counts

103 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2344
1	384	1744
2	1399	1520
3	4929	1510
4	5133	1510

prune184.0ms (2.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	269	13	282

Error

Counts

282 → 13

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 x y) (/.f64 1 z))
✓	1.9b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
✓	5.8b	(*.f64 x (/.f64 y z))
	6.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (expm1.f64 (log1p.f64 (cbrt.f64 y))) (cbrt.f64 z)))
	19.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	7.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) z)) (cbrt.f64 (/.f64 (.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
	31.3b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
	6.3b	(/.f64 (*.f64 y x) z)
	31.6b	(.f64 (.f64 x (sqrt.f64 (/.f64 y z))) (sqrt.f64 (/.f64 y z)))
▶	1.9b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
	6.3b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
✓	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))

Compiler

Compiled 9219 to 1890 computations (79.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 z))
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 y)
✓	1.2b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))))))

series1.3s (15.6%)

Counts

2 → 48

Calls

2 calls:

1.0s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))))))
247.0ms	(cbrt.f64 (cbrt.f64 z))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-exp-log_binary64`
25×	`cbrt-unprod_binary64`
25×	`prod-exp_binary64`
22×	`add-cbrt-cube_binary64`
9×	`cbrt-prod_binary64`

Counts

2 → 55

Calls

2 calls:

15.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))))))
1.0ms	(cbrt.f64 (cbrt.f64 z))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

812×	`associate-*l/_binary64`
448×	`fma-def_binary64`
385×	`*-commutative_binary64`
281×	`associate-/l/_binary64`
258×	`log-prod_binary64`

Counts

103 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2344
1	384	1744
2	1390	1520
3	4313	1510
4	4969	1510

prune174.0ms (2.1%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	9	9
Picked	0	1	1
Done	0	3	3
Total	267	13	280

Error

Counts

280 → 13

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 x y) (/.f64 1 z))
✓	1.9b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
✓	5.8b	(*.f64 x (/.f64 y z))
	6.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 y z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (expm1.f64 (log1p.f64 (cbrt.f64 y))) (cbrt.f64 z)))
	19.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	7.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) z)) (cbrt.f64 (/.f64 (.f64 y x) z))) (cbrt.f64 (/.f64 (*.f64 y x) z)))
	31.3b	(.f64 (.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 z))) (/.f64 (cbrt.f64 y) (sqrt.f64 z)))
	6.3b	(/.f64 (*.f64 y x) z)
	31.6b	(.f64 (.f64 x (sqrt.f64 (/.f64 y z))) (sqrt.f64 (/.f64 y z)))
✓	1.9b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
	6.3b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 y (cbrt.f64 z)))
✓	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))

Compiler

Compiled 8996 to 1784 computations (80.2% saved)

regimes550.0ms (6.7%)

Accuracy

Total 2.0b remaining (98.8%)

Threshold costs 0b (0%)

Counts

33 → 1

Compiler

Compiled 4423 to 2450 computations (44.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	15	29
2	15	29

end286.0ms (3.5%)

Compiler: Compiled 335 to 184 computations (45.1% saved)

Details

analyze1.1s (13.6%)

sample1.2s (15.2%)

simplify169.0ms (2.1%)

prune3.0ms (0%)

localize3.0ms (0%)

series12.0ms (0.1%)

rewrite8.0ms (0.1%)

simplify113.0ms (1.4%)

prune42.0ms (0.5%)

localize10.0ms (0.1%)

series1.2s (14.2%)

rewrite21.0ms (0.3%)

simplify112.0ms (1.4%)

prune145.0ms (1.8%)

localize14.0ms (0.2%)

series1.3s (15.9%)

rewrite26.0ms (0.3%)

simplify79.0ms (1%)

prune184.0ms (2.3%)

localize14.0ms (0.2%)

series1.3s (15.6%)

rewrite24.0ms (0.3%)

simplify82.0ms (1%)

prune174.0ms (2.1%)

regimes550.0ms (6.7%)

simplify3.0ms (0%)

end286.0ms (3.5%)

Profiling