Details

analyze1.2s (12.8%)

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)

sample1.3s (14.2%)

Symmetry

(sort x y)

Results

1.0s	8256×	body	128	valid
185.0ms	1661×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify167.0ms (1.9%)

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

3 alts after pruning (3 fresh and 0 done)

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

Error

7.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.1b	(*.f64 x (/.f64 y z))
	15.5b	(.f64 x (/.f64 (.f64 (/.f64 y z) t) t))

Compiler

Compiled 62 to 37 computations (40.3% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.9b	(*.f64 x (/.f64 y z))

series13.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

13.0ms

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

rewrite6.0ms (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:

5.0ms

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

simplify114.0ms (1.3%)

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

prune33.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Error

0.0b

Counts

52 → 8

Alt Table

Status	Error	Program
	19.8b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
✓	7.1b	(*.f64 x (/.f64 y z))
	16.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 y) (cbrt.f64 z)))
▶	2.3b	(.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)))
	25.8b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) z)) (sqrt.f64 (/.f64 (*.f64 y x) z)))
	6.3b	(.f64 (.f64 x y) (/.f64 1 z))
	6.2b	(/.f64 (*.f64 y x) z)
	6.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 767 to 288 computations (62.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 y)
✓	1.4b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.7s (19.1%)

Counts

4 → 72

Calls

4 calls:

1.6s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
42.0ms	(cbrt.f64 z)
40.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
32.0ms	(cbrt.f64 y)

rewrite22.0ms (0.2%)

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:

10.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
5.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 z)

simplify109.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

796×	`associate-*l/_binary64`
584×	`fma-def_binary64`
303×	`fma-neg_binary64`
256×	`log-prod_binary64`
236×	`unswap-sqr_binary64`

Counts

172 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2641
1	385	1963
2	1436	1783
3	3949	1777
4	4953	1777
5	4948	1777

prune119.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	225	9	234

Error

0.0b

Counts

234 → 9

Alt Table

Status	Error	Program
	19.8b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
✓	7.1b	(*.f64 x (/.f64 y z))
	16.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 y) (cbrt.f64 z)))
▶	2.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
✓	2.3b	(.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)))
	25.8b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) z)) (sqrt.f64 (/.f64 (*.f64 y x) z)))
	6.3b	(.f64 (.f64 x y) (/.f64 1 z))
	6.2b	(/.f64 (*.f64 y x) z)
	6.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 5627 to 1494 computations (73.4% saved)

localize54.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 y)
✓	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)
✓	1.4b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4))))

series1.6s (17.8%)

Counts

2 → 48

Calls

2 calls:

1.3s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4))))
298.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
19×	`prod-exp_binary64`
14×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`

Counts

2 → 61

Calls

2 calls:

11.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4))))
2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

849×	`associate-/r*_binary64`
670×	`associate-*l/_binary64`
184×	`fma-def_binary64`
182×	`associate-/r/_binary64`
171×	`associate-/l/_binary64`

Counts

109 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2799
1	426	2372
2	1424	2269
3	4749	2269
4	4964	2269

prune138.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	209	9	218

Error

Counts

218 → 9

Alt Table

Status	Error	Program
▶	2.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
✓	7.1b	(*.f64 x (/.f64 y z))
	19.8b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	16.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 y) (cbrt.f64 z)))
✓	2.3b	(.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)))
	25.8b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) z)) (sqrt.f64 (/.f64 (*.f64 y x) z)))
	6.3b	(.f64 (.f64 x y) (/.f64 1 z))
	6.2b	(/.f64 (*.f64 y x) z)
	6.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 6795 to 2187 computations (67.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 y)
✓	0.9b	(pow.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4)
✓	1.4b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4))))

series1.6s (17.7%)

Counts

2 → 48

Calls

2 calls:

1.3s

(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4))))

294.0ms

(pow.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
19×	`prod-exp_binary64`
14×	`add-cbrt-cube_binary64`
9×	`cbrt-unprod_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 56

Calls

2 calls:

10.0ms

(*.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4))))

5.0ms

(pow.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4)

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-*r/_binary64`
670×	`associate-*l/_binary64`
226×	`fma-def_binary64`
182×	`associate-/r/_binary64`
171×	`associate-/l/_binary64`

Counts

104 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2604
1	412	2225
2	1418	2150
3	4433	2133
4	4975	2133
5	4963	2133

prune172.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	257	9	266

Error

Counts

266 → 9

Alt Table

Status	Error	Program
✓	2.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) 4)))) (/.f64 (cbrt.f64 y) (cbrt.f64 z)))
✓	7.1b	(*.f64 x (/.f64 y z))
	19.8b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (sqrt.f64 y) z))
	16.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 y) (cbrt.f64 z)))
✓	2.3b	(.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)))
	25.8b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) z)) (sqrt.f64 (/.f64 (*.f64 y x) z)))
	6.3b	(.f64 (.f64 x y) (/.f64 1 z))
	6.2b	(/.f64 (*.f64 y x) z)
	6.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

Compiler

Compiled 10424 to 2676 computations (74.3% saved)

regimes321.0ms (3.6%)

Accuracy

Total 1.9b remaining (97.8%)

Threshold costs 0b (0%)

Counts

41 → 1

Compiler

Compiled 7204 to 4131 computations (42.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	14	31
2	14	31

end107.0ms (1.2%)

Remove: (sort x y)
Compiler: Compiled 249 to 136 computations (45.4% saved)

Details

analyze1.2s (12.8%)

sample1.3s (14.2%)

simplify167.0ms (1.9%)

prune3.0ms (0%)

localize3.0ms (0%)

series13.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify114.0ms (1.3%)

prune33.0ms (0.4%)

localize10.0ms (0.1%)

series1.7s (19.1%)

rewrite22.0ms (0.2%)

simplify109.0ms (1.2%)

prune119.0ms (1.3%)

localize54.0ms (0.6%)

series1.6s (17.8%)

rewrite18.0ms (0.2%)

simplify90.0ms (1%)

prune138.0ms (1.5%)

localize22.0ms (0.2%)

series1.6s (17.7%)

rewrite21.0ms (0.2%)

simplify115.0ms (1.3%)

prune172.0ms (1.9%)

regimes321.0ms (3.6%)

simplify3.0ms (0%)

end107.0ms (1.2%)

Profiling