Details

analyze458.0ms (9.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.2s (25.3%)

Results

930.0ms	8256×	body	128	valid
79.0ms	712×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (0.1%)

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

5.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.3b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series15.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64`

Counts

1 → 52

Calls

1 calls:

6.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Rules

412×	`unsub-neg_binary64`
396×	`exp-prod_binary64`
359×	`distribute-rgt-in_binary64`
334×	`distribute-lft-in_binary64`
331×	`fma-def_binary64`

Counts

88 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1249
1	225	1167
2	784	1113
3	2358	1057
4	3941	1057
5	4982	1057
6	4909	1057

prune65.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Error

0.0b

Counts

76 → 5

Alt Table

Status	Error	Program
	5.6b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 (.f64 z 1))) x) (.f64 (fma.f64 (neg.f64 z) 1 (*.f64 z 1)) x))
	6.5b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
▶	1.8b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	5.3b	(.f64 (.f64 x 1) (-.f64 (fma.f64 y z 1) z))
	23.7b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 1632 to 788 computations (51.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	3.8b	(.f64 y (.f64 z x))

series31.0ms (0.7%)

Counts

3 → 60

Calls

3 calls:

11.0ms	(.f64 y (.f64 z x))
10.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
10.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
4.0ms	(+.f64 (.f64 y (.f64 z x)) x)
4.0ms	(.f64 y (.f64 z x))

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
502×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
279×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

116 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1397
1	285	1233
2	896	1196
3	2752	1195
4	4487	1195
5	4963	1195

prune73.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Error

0.0b

Counts

108 → 6

Alt Table

Status	Error	Program
▶	2.2b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))) x) (*.f64 z x))
	28.2b	(.f64 (-.f64 (.f64 y x) x) z)
	6.5b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
	42.3b	(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 (fma.f64 z y 1) (fma.f64 z y 1)) (.f64 z z))) (*.f64 x (+.f64 z (fma.f64 z y 1))))
✓	1.8b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	5.3b	(-.f64 (+.f64 (.f64 (.f64 y z) x) x) (*.f64 z x))

Compiler

Compiled 1950 to 556 computations (71.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	2.0b	(.f64 (cbrt.f64 y) (.f64 z x))
✓	2.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

series532.0ms (11.2%)

Counts

4 → 96

Calls

4 calls:

442.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
32.0ms	(cbrt.f64 y)
21.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

rewrite75.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
1.0ms	(cbrt.f64 y)

simplify123.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
621×	`distribute-rgt-in_binary64`
464×	`*-commutative_binary64`
327×	`sqr-pow_binary64`
233×	`associate-l_binary64`

Counts

204 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	1885
1	239	1657
2	914	1619
3	1620	1605
4	2950	1511
5	4929	1511

prune124.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	182	6	188

Error

Counts

188 → 6

Alt Table

Status	Error	Program
	28.2b	(.f64 (-.f64 (.f64 y x) x) z)
	31.0b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y)))) (.f64 (cbrt.f64 y) (.f64 z x))) x) (.f64 z x))
▶	1.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) z) x)) x) (*.f64 z x))
	6.5b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
✓	1.8b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	5.3b	(-.f64 (+.f64 (.f64 (.f64 y z) x) x) (*.f64 z x))

Compiler

Compiled 4304 to 1122 computations (73.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
	0.6b	(cbrt.f64 y)
✓	2.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) z) x))
✓	2.2b	(.f64 (.f64 (cbrt.f64 y) z) x)

series468.0ms (9.9%)

Counts

2 → 72

Calls

2 calls:

446.0ms	(.f64 (.f64 (cbrt.f64 y) z) x)
22.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) z) x))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
28×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`

Counts

2 → 50

Calls

2 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) z) x))
5.0ms	(.f64 (.f64 (cbrt.f64 y) z) x)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

542×	`fma-def_binary64`
430×	`*-commutative_binary64`
291×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`
267×	`unswap-sqr_binary64`

Counts

122 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1691
1	210	1081
2	758	1075
3	1397	1075
4	2634	1075
5	4922	1075

prune130.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	175	6	181

Error

Counts

181 → 6

Alt Table

Status	Error	Program
	28.2b	(.f64 (-.f64 (.f64 y x) x) z)
	31.0b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (sqrt.f64 y)) (cbrt.f64 (sqrt.f64 y)))) (.f64 (cbrt.f64 y) (.f64 z x))) x) (.f64 z x))
✓	1.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) z) x)) x) (*.f64 z x))
	6.5b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
✓	1.8b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	5.3b	(-.f64 (+.f64 (.f64 (.f64 y z) x) x) (*.f64 z x))

Compiler

Compiled 4040 to 1041 computations (74.2% saved)

regimes915.0ms (19.3%)

Accuracy

Total 0.1b remaining (84.2%)

Threshold costs 0.1b (84.2%)

Counts

96 → 3

Compiler

Compiled 14228 to 8090 computations (43.1% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 10 to 8 computations (20% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

47×	`distribute-rgt-neg-in_binary64`
41×	`cancel-sign-sub-inv_binary64`
32×	`neg-sub0_binary64`
32×	`neg-mul-1_binary64`
30×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	43	53
2	63	53
3	79	53
4	93	53
5	104	53
6	120	53
7	135	53
8	148	53
9	170	53
10	195	53
11	212	53
12	229	53
13	246	53
14	253	53
15	255	53
16	251	53

end145.0ms (3.1%)

Compiler: Compiled 195 to 119 computations (39% saved)

Iter	Nodes	Cost
0	22	53
1	43	53
2	63	53
3	79	53
4	93	53
5	104	53
6	120	53
7	135	53
8	148	53
9	170	53
10	195	53
11	212	53
12	229	53
13	246	53
14	253	53
15	255	53
16	251	53

Iter	Nodes	Cost
0	22	53
1	43	53
2	63	53
3	79	53
4	93	53
5	104	53
6	120	53
7	135	53
8	148	53
9	170	53
10	195	53
11	212	53
12	229	53
13	246	53
14	253	53
15	255	53
16	251	53

Details

analyze458.0ms (9.7%)

sample1.2s (25.3%)

simplify43.0ms (0.9%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series15.0ms (0.3%)

rewrite10.0ms (0.2%)

simplify96.0ms (2%)

prune65.0ms (1.4%)

localize6.0ms (0.1%)

series31.0ms (0.7%)

rewrite16.0ms (0.3%)

simplify86.0ms (1.8%)

prune73.0ms (1.5%)

localize11.0ms (0.2%)

series532.0ms (11.2%)

rewrite75.0ms (1.6%)

simplify123.0ms (2.6%)

prune124.0ms (2.6%)

localize12.0ms (0.3%)

series468.0ms (9.9%)

rewrite17.0ms (0.4%)

simplify70.0ms (1.5%)

prune130.0ms (2.7%)

regimes915.0ms (19.3%)

bsearch3.0ms (0.1%)

simplify11.0ms (0.2%)

end145.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	22	53
1	43	53
2	63	53
3	79	53
4	93	53
5	104	53
6	120	53
7	135	53
8	148	53
9	170	53
10	195	53
11	212	53
12	229	53
13	246	53
14	253	53
15	255	53
16	251	53