Details

analyze434.0ms (8.4%)

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 (22.8%)

Results

922.0ms	8256×	body	128	valid
64.0ms	689×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify42.0ms (0.8%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

3.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 44 to 31 computations (29.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

series10.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

10.0ms

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

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`
5×	`distribute-lft-in_binary64`
5×	`distribute-rgt-in_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

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

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

583×	`associate-+l+_binary64`
346×	`associate-l_binary64`
314×	`associate-+r+_binary64`
263×	`associate-r_binary64`
253×	`distribute-rgt-in_binary64`

Counts

68 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1079
1	176	889
2	568	819
3	1879	801
4	4795	801
5	4789	801

prune48.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	5	60

Error

0.0b

Counts

60 → 5

Alt Table

Status	Error	Program
	17.9b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 (-.f64 1 y) z) (.f64 (-.f64 1 y) z)))) (+.f64 1 (.f64 (-.f64 1 y) z)))
	23.3b	(/.f64 (.f64 x (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (-.f64 1 y) z) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (-.f64 1 y) z) (.f64 (-.f64 1 y) z)) (.f64 1 (.f64 (-.f64 1 y) z)))))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	3.7b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z))))
▶	3.1b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 1190 to 777 computations (34.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	5.0b	(.f64 y (.f64 z x))

series22.0ms (0.4%)

Counts

2 → 30

Calls

2 calls:

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

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 42

Calls

2 calls:

11.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
3.0ms	(.f64 y (.f64 z x))

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-l_binary64`
514×	`fma-neg_binary64`
505×	`associate-r_binary64`
337×	`fma-def_binary64`
271×	`distribute-rgt-in_binary64`

Counts

72 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1032
1	237	823
2	766	798
3	3183	797
4	4553	797
5	4999	797
6	4931	797

prune45.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	79	4	83

Error

0.0b

Counts

83 → 4

Alt Table

Status	Error	Program
▶	3.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))
	31.7b	(.f64 (-.f64 (.f64 y x) x) z)
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
✓	3.1b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 1387 to 383 computations (72.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (*.f64 z x))))
	5.0b	(.f64 y (.f64 z x))
✓	11.7b	(cbrt.f64 (.f64 y (.f64 z x)))

series1.8s (35.7%)

Counts

3 → 108

Calls

3 calls:

1.2s

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

562.0ms

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

48.0ms

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

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

7.0ms

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

4.0ms

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

4.0ms

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

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

640×	`unswap-sqr_binary64`
348×	`fma-neg_binary64`
314×	`exp-sum_binary64`
297×	`exp-prod_binary64`
260×	`unsub-neg_binary64`

Counts

187 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	3163
1	387	2879
2	865	2337
3	2290	2071
4	5245	2071

prune181.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	256	5	261

Error

0.0b

Counts

261 → 5

Alt Table

Status	Error	Program
✓	3.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))
	31.7b	(.f64 (-.f64 (.f64 y x) x) z)
▶	3.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
✓	3.1b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 7890 to 1707 computations (78.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 y)
	5.0b	(.f64 y (.f64 z x))
✓	10.6b	(cbrt.f64 (*.f64 z x))
	11.7b	(cbrt.f64 (.f64 y (.f64 z x)))

series346.0ms (6.7%)

Counts

2 → 36

Calls

2 calls:

317.0ms	(cbrt.f64 (*.f64 z x))
29.0ms	(cbrt.f64 y)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 24

Calls

2 calls:

2.0ms	(cbrt.f64 (*.f64 z x))
1.0ms	(cbrt.f64 y)

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

566×	`log-prod_binary64`
386×	`fma-def_binary64`
369×	`fma-neg_binary64`
314×	`distribute-rgt-in_binary64`
297×	`times-frac_binary64`

Counts

60 → 37

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	66	601
1	118	597
2	209	541
3	514	429
4	1385	425
5	3544	423
6	4842	423
7	5209	423

prune104.0ms (2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	143	5	148

Error

0.0b

Counts

148 → 5

Alt Table

Status	Error	Program
✓	3.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))
	31.7b	(.f64 (-.f64 (.f64 y x) x) z)
✓	3.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))) x) (*.f64 z x))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
✓	3.1b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 4657 to 1027 computations (77.9% saved)

regimes399.0ms (7.7%)

Accuracy

Total 0.1b remaining (89.6%)

Threshold costs 0.1b (89.6%)

Counts

39 → 3

Compiler

Compiled 5867 to 3831 computations (34.7% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

46×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
29×	`distribute-lft-neg-in_binary64`
26×	`distribute-lft-neg-out_binary64`
26×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	57
1	34	57
2	52	57
3	68	57
4	83	57
5	95	57
6	111	57
7	126	57
8	139	57
9	157	57
10	184	57
11	210	57
12	226	57
13	230	57
14	226	57

end74.0ms (1.4%)

Compiler: Compiled 179 to 93 computations (48% saved)

Iter	Nodes	Cost
0	19	57
1	34	57
2	52	57
3	68	57
4	83	57
5	95	57
6	111	57
7	126	57
8	139	57
9	157	57
10	184	57
11	210	57
12	226	57
13	230	57
14	226	57

Iter	Nodes	Cost
0	19	57
1	34	57
2	52	57
3	68	57
4	83	57
5	95	57
6	111	57
7	126	57
8	139	57
9	157	57
10	184	57
11	210	57
12	226	57
13	230	57
14	226	57

Details

analyze434.0ms (8.4%)

sample1.2s (22.8%)

simplify42.0ms (0.8%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify76.0ms (1.5%)

prune48.0ms (0.9%)

localize5.0ms (0.1%)

series22.0ms (0.4%)

rewrite16.0ms (0.3%)

simplify94.0ms (1.8%)

prune45.0ms (0.9%)

localize10.0ms (0.2%)

series1.8s (35.7%)

rewrite19.0ms (0.4%)

simplify89.0ms (1.7%)

prune181.0ms (3.5%)

localize13.0ms (0.3%)

series346.0ms (6.7%)

rewrite3.0ms (0.1%)

simplify80.0ms (1.5%)

prune104.0ms (2%)

regimes399.0ms (7.7%)

bsearch4.0ms (0.1%)

simplify10.0ms (0.2%)

end74.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	19	57
1	34	57
2	52	57
3	68	57
4	83	57
5	95	57
6	111	57
7	126	57
8	139	57
9	157	57
10	184	57
11	210	57
12	226	57
13	230	57
14	226	57