Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample561.0ms (13.5%)

Symmetry

(sort a b)

Results

522.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify15.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

284×	`fma-def_binary64`
35×	`associate-l_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`
19×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

prune2.0ms (0%)

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

12.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))

Compiler

Compiled 38 to 20 computations (47.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.6b	(.f64 (.f64 (*.f64 a a) b) b)
✓	8.2b	(.f64 (.f64 a a) b)

series21.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(.f64 (.f64 (*.f64 a a) b) b)
8.0ms	(.f64 (.f64 a a) b)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

6.0ms	(.f64 (.f64 (*.f64 a a) b) b)
4.0ms	(.f64 (.f64 a a) b)

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
359×	`unswap-sqr_binary64`
354×	`associate-/l/_binary64`
272×	`sqr-pow_binary64`
262×	`associate-/r/_binary64`

Counts

92 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	983
1	142	854
2	480	830
3	782	812
4	1506	801
5	2460	801
6	4674	801
7	4916	801

prune46.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Error

0.1b

Counts

57 → 8

Alt Table

Status	Error	Program
	12.1b	(neg.f64 (.f64 b (.f64 (*.f64 a a) b)))
	18.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
▶	0.2b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	14.6b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	3.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	21.7b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (sqrt.f64 b)) (sqrt.f64 b)))
	15.2b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))

Compiler

Compiled 910 to 330 computations (63.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 a b) (*.f64 a b))

series11.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(*.f64 (*.f64 a b) (*.f64 a b))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary64`
17×	`pow-prod-down_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

1 → 36

Calls

1 calls:

5.0ms

(*.f64 (*.f64 a b) (*.f64 a b))

simplify79.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

654×	`associate-l_binary64`
551×	`fma-def_binary64`
352×	`associate-r_binary64`
341×	`associate-/l*_binary64`
311×	`associate-/l/_binary64`

Counts

60 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	613
1	92	508
2	315	474
3	1009	474
4	1436	372
5	2353	372
6	4908	372
7	4999	372
8	4954	372

prune35.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	31	11	42

Error

0.0b

Counts

42 → 11

Alt Table

Status	Error	Program
	12.1b	(neg.f64 (.f64 b (.f64 (*.f64 a a) b)))
	18.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
✓	0.2b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	14.6b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
▶	0.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	2.2b	(neg.f64 (exp.f64 (log.f64 (.f64 (.f64 a b) (*.f64 a b)))))
	3.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	21.7b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (sqrt.f64 b)) (sqrt.f64 b)))
	10.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	3.1b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))

Compiler

Compiled 688 to 302 computations (56.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
✓	0.2b	(pow.f64 (*.f64 a b) 2)
✓	0.3b	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
✓	32.5b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.1s (26.7%)

Counts

4 → 96

Calls

4 calls:

549.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
544.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))
14.0ms	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
8.0ms	(pow.f64 (*.f64 a b) 2)

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`pow1_binary64`
20×	`unswap-sqr_binary64`
18×	`associate-r_binary64`

Counts

4 → 142

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
7.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
2.0ms	(pow.f64 (*.f64 a b) 2)
1.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

simplify171.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-def_binary64`
708×	`unswap-sqr_binary64`
612×	`exp-prod_binary64`
576×	`fma-neg_binary64`
540×	`log-prod_binary64`

Counts

238 → 193

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	184	3987
1	321	3345
2	776	2770
3	1650	2453
4	3874	2219
5	4832	2215
6	4391	2210
7	5217	2210

prune382.0ms (9.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	301	4	305
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	303	13	316

Error

0.0b

Counts

316 → 13

Alt Table

Status	Error	Program
	12.1b	(neg.f64 (.f64 b (.f64 (*.f64 a a) b)))
	18.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
✓	0.2b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	14.6b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	0.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))))
	11.1b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	3.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	21.7b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (sqrt.f64 b)) (sqrt.f64 b)))
▶	0.5b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))))
	0.6b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	10.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	3.1b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))

Compiler

Compiled 8339 to 5015 computations (39.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (*.f64 a b) 2)
	0.3b	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
✓	2.5b	(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
	32.5b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series365.0ms (8.7%)

Counts

1 → 24

Calls

1 calls:

364.0ms

(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
9×	`sqrt-prod_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`rem-sqrt-square_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 25

Calls

1 calls:

2.0ms

(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))

simplify96.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-neg_binary64`
674×	`unswap-sqr_binary64`
303×	`fma-def_binary64`
219×	`associate-l_binary64`
184×	`associate-r_binary64`

Counts

49 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	656
1	119	648
2	191	586
3	478	474
4	1514	474
5	4289	474
6	4796	474
7	4990	474
8	5139	474

prune656.0ms (15.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	388	1	389
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	388	14	402

Error

0.0b

Counts

402 → 14

Alt Table

Status	Error	Program
	12.1b	(neg.f64 (.f64 b (.f64 (*.f64 a a) b)))
	18.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
✓	0.2b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	14.6b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	1.3b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (exp.f64 (log.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))))))
	3.1b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	0.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))))
	11.1b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	3.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	21.7b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (sqrt.f64 b)) (sqrt.f64 b)))
✓	0.5b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))))
	0.6b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	10.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))

Compiler

Compiled 13907 to 8579 computations (38.3% saved)

regimes289.0ms (6.9%)

Accuracy

Total 0.2b remaining (89.5%)

Threshold costs 0.2b (89.5%)

Counts

59 → 1

Compiler

Compiled 7156 to 4538 computations (36.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
2	14	9
3	15	9
4	15	9

end162.0ms (3.9%)

Remove: (sort a b)
Compiler: Compiled 266 to 175 computations (34.2% saved)

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

Details

analyze1.0ms (0%)

sample561.0ms (13.5%)

simplify15.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series21.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify77.0ms (1.9%)

prune46.0ms (1.1%)

localize5.0ms (0.1%)

series11.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify79.0ms (1.9%)

prune35.0ms (0.8%)

localize8.0ms (0.2%)

series1.1s (26.7%)

rewrite31.0ms (0.7%)

simplify171.0ms (4.1%)

prune382.0ms (9.2%)

localize10.0ms (0.2%)

series365.0ms (8.7%)

rewrite3.0ms (0.1%)

simplify96.0ms (2.3%)

prune656.0ms (15.7%)

regimes289.0ms (6.9%)

simplify2.0ms (0.1%)

end162.0ms (3.9%)

Profiling

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12