Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample815.0ms (28.1%)

Infinites

24.8% of outputs are infinite.

Symmetry

(sort y t)

Results

647.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify39.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-def_binary64`
304×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
90×	`associate-l_binary64`
87×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.0b	(.f64 y (.f64 t (-.f64 x z)))
	7.8b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	4.0b	(.f64 y (.f64 t (-.f64 x z)))

series21.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

15.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

9.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

simplify113.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

449×	`*-commutative_binary64`
402×	`distribute-rgt-in_binary64`
400×	`distribute-rgt-neg-out_binary64`
379×	`distribute-lft-in_binary64`
309×	`fma-def_binary64`

Counts

208 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	2765
1	326	2564
2	1079	2402
3	3077	2078
4	4965	2078
5	4751	2078

prune94.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
	6.0b	(.f64 t (.f64 y (-.f64 x z)))
	22.4b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
▶	4.7b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
	6.7b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
✓	4.0b	(.f64 y (.f64 t (-.f64 x z)))
	4.8b	(.f64 (-.f64 x z) (.f64 y t))
	4.7b	(.f64 y (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 t) (-.f64 x z))))

Compiler

Compiled 3167 to 812 computations (74.4% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	1.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
✓	2.4b	(.f64 (cbrt.f64 y) (.f64 t (-.f64 x z)))

series470.0ms (16.2%)

Counts

4 → 120

Calls

4 calls:

369.0ms	(.f64 (cbrt.f64 y) (.f64 t (-.f64 x z)))
39.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
34.0ms	(cbrt.f64 y)
27.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))

rewrite72.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

208×	`distribute-lft-in_binary64`
208×	`distribute-rgt-in_binary64`
108×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
99×	`*-un-lft-identity_binary64`

Counts

4 → 268

Calls

4 calls:

18.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
10.0ms	(.f64 (cbrt.f64 y) (.f64 t (-.f64 x z)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify155.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

750×	`distribute-rgt-in_binary64`
697×	`associate-l_binary64`
650×	`associate-r_binary64`
420×	`fma-def_binary64`
326×	`unswap-sqr_binary64`

Counts

388 → 331

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	6052
1	558	5508
2	2084	5133
3	5116	5133

prune203.0ms (7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	366	1	367
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	368	6	374

Error

Counts

374 → 6

Alt Table

Status	Error	Program
	6.0b	(.f64 t (.f64 y (-.f64 x z)))
	22.4b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	19.4b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
	6.7b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
✓	4.0b	(.f64 y (.f64 t (-.f64 x z)))
▶	4.8b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 10170 to 1930 computations (81% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.8b	(.f64 (-.f64 x z) (.f64 y t))

series14.0ms (0.5%)

Counts

1 → 32

Calls

1 calls:

14.0ms

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

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 24

Calls

1 calls:

6.0ms

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

simplify50.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-l_binary64`
483×	`fma-def_binary64`
414×	`associate-r_binary64`
378×	`distribute-rgt-neg-out_binary64`
327×	`unsub-neg_binary64`

Counts

56 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	661
1	178	598
2	527	598
3	1835	598
4	3260	598
5	5376	598

prune26.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	42	6	48

Error

Counts

48 → 6

Alt Table

Status	Error	Program
▶	6.0b	(.f64 t (.f64 y (-.f64 x z)))
	22.4b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	19.4b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
	6.7b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
✓	4.0b	(.f64 y (.f64 t (-.f64 x z)))
✓	4.8b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 710 to 226 computations (68.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 x z))
✓	6.0b	(.f64 t (.f64 y (-.f64 x z)))

series22.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

13.0ms	(.f64 t (.f64 y (-.f64 x z)))
9.0ms	(*.f64 y (-.f64 x z))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

7.0ms	(.f64 t (.f64 y (-.f64 x z)))
5.0ms	(*.f64 y (-.f64 x z))

simplify109.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

437×	`*-commutative_binary64`
357×	`distribute-rgt-in_binary64`
338×	`distribute-lft-neg-out_binary64`
333×	`distribute-lft-in_binary64`
326×	`exp-prod_binary64`

Counts

208 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	2765
1	323	2564
2	1043	2402
3	2831	2078
4	4900	2078
5	4798	2078

prune83.0ms (2.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	153	6	159

Error

Counts

159 → 6

Alt Table

Status	Error	Program
✓	6.0b	(.f64 t (.f64 y (-.f64 x z)))
	22.4b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	19.4b	(.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
✓	4.0b	(.f64 y (.f64 t (-.f64 x z)))
✓	4.8b	(.f64 (-.f64 x z) (.f64 y t))
	18.7b	(.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (*.f64 y (-.f64 x z))))

Compiler

Compiled 3031 to 749 computations (75.3% saved)

regimes279.0ms (9.6%)

Accuracy

Total 1.1b remaining (97.7%)

Threshold costs 0b (0%)

Counts

33 → 3

Compiler

Compiled 3346 to 1862 computations (44.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	35	52
2	46	52
3	52	52
4	56	52
5	57	52
6	57	52

end236.0ms (8.1%)

Compiler: Compiled 235 to 127 computations (46% saved)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Details

analyze2.0ms (0.1%)

sample815.0ms (28.1%)

simplify39.0ms (1.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series21.0ms (0.7%)

rewrite27.0ms (0.9%)

simplify113.0ms (3.9%)

prune94.0ms (3.2%)

localize12.0ms (0.4%)

series470.0ms (16.2%)

rewrite72.0ms (2.5%)

simplify155.0ms (5.3%)

prune203.0ms (7%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify50.0ms (1.7%)

prune26.0ms (0.9%)

localize6.0ms (0.2%)

series22.0ms (0.8%)

rewrite26.0ms (0.9%)

simplify109.0ms (3.8%)

prune83.0ms (2.9%)

regimes279.0ms (9.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end236.0ms (8.1%)

Profiling

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10