Details

analyze149.0ms (2.5%)

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
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample764.0ms (12.7%)

Results

671.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify113.0ms (1.9%)

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

1.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.7b	(*.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))
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series58.0ms (1%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
23.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite26.0ms (0.4%)

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:

11.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
6.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify129.0ms (2.1%)

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

prune135.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	185	8	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	9	194

Error

Counts

194 → 9

Alt Table

Status	Error	Program
	32.7b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
	9.5b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	2.7b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	42.3b	(-.f64 (fma.f64 (/.f64 (.f64 t x) z) (/.f64 y z) (fma.f64 (/.f64 (.f64 y y) (pow.f64 z 3)) (.f64 t x) (-.f64 (/.f64 (.f64 t (-.f64 x y)) z) (/.f64 (.f64 y (.f64 y t)) (.f64 z z))))) (.f64 (pow.f64 (/.f64 y z) 3) t))
	31.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 z z) (.f64 y y))) (.f64 (+.f64 z y) t))
	2.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	11.7b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
▶	1.8b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 4754 to 1391 computations (70.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
✓	1.7b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)

series61.0ms (1%)

Counts

3 → 108

Calls

3 calls:

33.0ms	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
19.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
8.0ms	(/.f64 1 (-.f64 z y))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`
24×	`associate-r_binary64`

Counts

3 → 125

Calls

3 calls:

11.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
9.0ms	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
4.0ms	(/.f64 1 (-.f64 z y))

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
441×	`cancel-sign-sub-inv_binary64`
364×	`sub-neg_binary64`
202×	`associate-l_binary64`
191×	`fma-neg_binary64`

Counts

233 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	5123
1	791	4796
2	2905	4505
3	5071	4505

prune176.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	245	9	254

Error

Counts

254 → 9

Alt Table

Status	Error	Program
	2.6b	(.f64 (.f64 (-.f64 x y) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (cbrt.f64 (-.f64 z y)))) t)
	9.5b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	2.7b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	42.3b	(-.f64 (fma.f64 (/.f64 (.f64 t x) z) (/.f64 y z) (fma.f64 (/.f64 (.f64 y y) (pow.f64 z 3)) (.f64 t x) (-.f64 (/.f64 (.f64 t (-.f64 x y)) z) (/.f64 (.f64 y (.f64 y t)) (.f64 z z))))) (.f64 (pow.f64 (/.f64 y z) 3) t))
	31.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 z z) (.f64 y y))) (.f64 (+.f64 z y) t))
▶	2.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	11.7b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.8b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 5698 to 2212 computations (61.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
✓	5.8b	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

series1.3s (21.8%)

Counts

4 → 168

Calls

4 calls:

598.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
473.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
200.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))
44.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))

rewrite125.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

304×	`*-un-lft-identity_binary64`
251×	`add-sqr-sqrt_binary64`
248×	`cbrt-prod_binary64`
205×	`times-frac_binary64`
96×	`distribute-lft-out--_binary64`

Counts

4 → 285

Calls

4 calls:

30.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
26.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
11.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
5.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

simplify294.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

331×	`associate-r_binary64`
329×	`fma-def_binary64`
275×	`associate-+r+_binary64`
181×	`associate-/l*_binary64`
173×	`associate-*r/_binary64`

Counts

453 → 461

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1820	27927
1	5310	27927

prune864.0ms (14.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	659	2	661
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	662	8	670

Error

Counts

670 → 8

Alt Table

Status	Error	Program
	2.6b	(.f64 (.f64 (-.f64 x y) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (cbrt.f64 (-.f64 z y)))) t)
	9.5b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	31.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 z z) (.f64 y y))) (.f64 (+.f64 z y) t))
▶	2.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (/.f64 1 (-.f64 z y)))) t))
	11.7b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.8b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	5.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) t) (cbrt.f64 (-.f64 z y))))

Compiler

Compiled 54306 to 24001 computations (55.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
✓	0.6b	(cbrt.f64 (-.f64 x y))
✓	0.6b	(cbrt.f64 (/.f64 1 (-.f64 z y)))
	5.8b	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

series66.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(cbrt.f64 (-.f64 x y))
32.0ms	(cbrt.f64 (/.f64 1 (-.f64 z y)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-prod_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 49

Calls

2 calls:

3.0ms	(cbrt.f64 (/.f64 1 (-.f64 z y)))
2.0ms	(cbrt.f64 (-.f64 x y))

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-def_binary64`
426×	`times-frac_binary64`
299×	`cancel-sign-sub-inv_binary64`
290×	`fma-neg_binary64`
211×	`neg-mul-1_binary64`

Counts

97 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	271	2513
1	698	2465
2	2081	2384
3	4694	2266
4	5048	2266

prune686.0ms (11.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	489	0	489
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	489	8	497

Error

Counts

497 → 8

Alt Table

Status	Error	Program
	2.6b	(.f64 (.f64 (-.f64 x y) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z y)) (cbrt.f64 (-.f64 z y)))) (cbrt.f64 (-.f64 z y)))) t)
	9.5b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
	31.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 z z) (.f64 y y))) (.f64 (+.f64 z y) t))
✓	2.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (/.f64 1 (-.f64 z y)))) t))
	11.7b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	1.8b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	5.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) t) (cbrt.f64 (-.f64 z y))))

Compiler

Compiled 39402 to 19237 computations (51.2% saved)

regimes689.0ms (11.4%)

Accuracy

Total 2.0b remaining (99.1%)

Threshold costs 0b (0%)

Counts

118 → 1

Compiler

Compiled 18976 to 9770 computations (48.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13
5	22	13

end85.0ms (1.4%)

Compiler: Compiled 195 to 105 computations (46.2% saved)

Details

analyze149.0ms (2.5%)

sample764.0ms (12.7%)

simplify113.0ms (1.9%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series58.0ms (1%)

rewrite26.0ms (0.4%)

simplify129.0ms (2.1%)

prune135.0ms (2.2%)

localize7.0ms (0.1%)

series61.0ms (1%)

rewrite32.0ms (0.5%)

simplify104.0ms (1.7%)

prune176.0ms (2.9%)

localize10.0ms (0.2%)

series1.3s (21.8%)

rewrite125.0ms (2.1%)

simplify294.0ms (4.9%)

prune864.0ms (14.3%)

localize15.0ms (0.3%)

series66.0ms (1.1%)

rewrite8.0ms (0.1%)

simplify97.0ms (1.6%)

prune686.0ms (11.4%)

regimes689.0ms (11.4%)

simplify5.0ms (0.1%)

end85.0ms (1.4%)

Profiling