Details

analyze1.5s (25.7%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0.4%	98.9%	0.7%	13
0.6%	98.6%	0.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.5s (25.9%)

Results

1.1s	8256×	body	128	valid
279.0ms	391×	body	8192	exit
37.0ms	323×	body	128	invalid

Compiler

Compiled 27 to 17 computations (37% saved)

simplify116.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.4b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	1.4b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series125.0ms (2.1%)

Counts

2 → 84

Calls

2 calls:

95.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
29.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

12.0ms	(/.f64 (-.f64 x y) (-.f64 z y))
10.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

simplify163.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune180.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

Counts

194 → 9

Alt Table

Status	Error	Program
	2.4b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	34.6b	(cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 x y) (-.f64 z y))) 3))
	20.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	11.8b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	8.9b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
▶	1.4b	(.f64 1 (.f64 t (/.f64 (-.f64 x y) (-.f64 z y))))
	29.8b	(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (-.f64 z y) (sqrt.f64 (-.f64 x y)))) t)
	1.5b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	30.7b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 4695 to 1377 computations (70.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	1.4b	(*.f64 t (/.f64 (-.f64 x y) (-.f64 z y)))

series39.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

39.0ms

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

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

1 → 52

Calls

1 calls:

13.0ms

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

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-def_binary64`
339×	`associate-/r*_binary64`
309×	`fma-neg_binary64`
251×	`cancel-sign-sub-inv_binary64`
199×	`associate-/r/_binary64`

Counts

100 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	2399
1	507	2282
2	2022	2050
3	4773	2050
4	4982	2050

prune172.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	182	9	191

Error

Counts

191 → 9

Alt Table

Status	Error	Program
	2.4b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	34.6b	(cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 x y) (-.f64 z y))) 3))
	20.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	11.8b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	8.9b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
✓	1.4b	(.f64 1 (.f64 t (/.f64 (-.f64 x y) (-.f64 z y))))
	29.8b	(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (-.f64 z y) (sqrt.f64 (-.f64 x y)))) t)
▶	1.5b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
	30.7b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))

Compiler

Compiled 4717 to 1682 computations (64.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
✓	1.4b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

series85.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

37.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
24.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
23.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite91.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
335×	`add-sqr-sqrt_binary64`
323×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
98×	`associate-l_binary64`

Counts

3 → 332

Calls

3 calls:

23.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
12.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
8.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify241.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

543×	`sub-neg_binary64`
246×	`associate-/l*_binary64`
241×	`fma-neg_binary64`
211×	`+-commutative_binary64`
210×	`associate--l+_binary64`

Counts

452 → 498

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	10707
1	1107	10159
2	4250	9700
3	5224	9700

prune351.0ms (5.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	496	2	498
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	501	6	507

Error

Counts

507 → 6

Alt Table

Status	Error	Program
	1.5b	(*.f64 (/.f64 1 (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y)))) t)
	11.8b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	34.6b	(cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 x y) (-.f64 z y))) 3))
▶	1.4b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	8.9b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
✓	1.4b	(.f64 1 (.f64 t (/.f64 (-.f64 x y) (-.f64 z y))))

Compiler

Compiled 12489 to 4010 computations (67.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	1.3b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

series46.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

45.0ms

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

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

1 → 144

Calls

1 calls:

12.0ms

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

simplify129.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

925×	`times-frac_binary64`
628×	`fma-def_binary64`
239×	`associate-/r/_binary64`
193×	`associate-/l/_binary64`
168×	`associate-*l/_binary64`

Counts

192 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	5536
1	818	5389
2	3076	5259
3	4983	5259

prune150.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	306	5	311

Error

Counts

311 → 5

Alt Table

Status	Error	Program
	34.6b	(cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 x y) (-.f64 z y))) 3))
	11.8b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	8.9b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
✓	1.4b	(.f64 1 (.f64 t (/.f64 (-.f64 x y) (-.f64 z y))))
	1.4b	(/.f64 t (-.f64 (/.f64 z (-.f64 x y)) (/.f64 y (-.f64 x y))))

Compiler

Compiled 7217 to 1658 computations (77% saved)

regimes691.0ms (11.7%)

Accuracy

Total 2.1b remaining (99.2%)

Threshold costs 0b (0%)

Counts

113 → 1

Compiler

Compiled 13687 to 8126 computations (40.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	14	19
2	23	19
3	27	19
4	29	19
5	29	19

end66.0ms (1.1%)

Compiler: Compiled 110 to 66 computations (40% saved)

Details

analyze1.5s (25.7%)

sample1.5s (25.9%)

simplify116.0ms (2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series125.0ms (2.1%)

rewrite32.0ms (0.5%)

simplify163.0ms (2.8%)

prune180.0ms (3%)

localize10.0ms (0.2%)

series39.0ms (0.7%)

rewrite18.0ms (0.3%)

simplify93.0ms (1.6%)

prune172.0ms (2.9%)

localize8.0ms (0.1%)

series85.0ms (1.4%)

rewrite91.0ms (1.5%)

simplify241.0ms (4.1%)

prune351.0ms (5.9%)

localize8.0ms (0.1%)

series46.0ms (0.8%)

rewrite39.0ms (0.7%)

simplify129.0ms (2.2%)

prune150.0ms (2.5%)

regimes691.0ms (11.7%)

simplify3.0ms (0%)

end66.0ms (1.1%)

Profiling