Details

analyze123.0ms (2.8%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample813.0ms (18.4%)

Results

734.0ms	8256×	body	128	valid
14.0ms	172×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify26.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 51

Calls

1 calls:

10.0ms

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

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
433×	`exp-prod_binary64`
400×	`*-commutative_binary64`
343×	`fma-def_binary64`
288×	`associate-+r+_binary64`

Counts

75 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1085
1	223	985
2	948	871
3	2323	814
4	4186	814
5	4991	814
6	4915	814
7	4901	814

prune61.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Error

0.0b

Counts

74 → 7

Alt Table

Status	Error	Program
	25.5b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	11.6b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
	13.9b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	33.8b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x y) (-.f64 1 y)) (.f64 (.f64 x y) (-.f64 1 y))) (.f64 (.f64 x y) (-.f64 1 y))))
▶	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	30.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))

Compiler

Compiled 1482 to 648 computations (56.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (pow.f64 y 2))
✓	4.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

series14.0ms (0.3%)

Counts

2 → 15

Calls

2 calls:

12.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
2.0ms	(-.f64 y (pow.f64 y 2))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`
14×	`unpow-prod-down_binary64`

Counts

2 → 82

Calls

2 calls:

6.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
6.0ms	(-.f64 y (pow.f64 y 2))

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

967×	`fma-neg_binary64`
456×	`fma-def_binary64`
377×	`exp-prod_binary64`
263×	`cancel-sign-sub-inv_binary64`
232×	`difference-of-squares_binary64`

Counts

97 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1889
1	261	1074
2	791	924
3	2087	924
4	3779	924
5	4661	924
6	4794	924

prune97.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	123	8	131

Error

0.0b

Counts

131 → 8

Alt Table

Status	Error	Program
▶	5.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2)))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	13.9b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	25.5b	(.f64 (/.f64 (-.f64 (.f64 y y) (pow.f64 y 4)) (fma.f64 y y y)) x)
	34.9b	(.f64 (.f64 (-.f64 y (pow.f64 y 2)) (sqrt.f64 x)) (sqrt.f64 x))
	30.4b	(.f64 (+.f64 (sqrt.f64 y) y) (.f64 (-.f64 (sqrt.f64 y) y) x))
	30.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))

Compiler

Compiled 2394 to 1327 computations (44.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x)
✓	0.6b	(*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2))))
✓	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2)))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
✓	4.6b	(cbrt.f64 (-.f64 y (pow.f64 y 2)))

series505.0ms (11.5%)

Counts

4 → 72

Calls

4 calls:

452.0ms	(*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x)
23.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2)))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
17.0ms	(*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2))))
12.0ms	(cbrt.f64 (-.f64 y (pow.f64 y 2)))

rewrite61.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`cbrt-div_binary64`
64×	`add-sqr-sqrt_binary64`
63×	`cbrt-prod_binary64`
40×	`*-un-lft-identity_binary64`
36×	`associate-*l/_binary64`

Counts

4 → 173

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2)))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
14.0ms	(*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2))))
7.0ms	(*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x)
3.0ms	(cbrt.f64 (-.f64 y (pow.f64 y 2)))

simplify218.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

494×	`cancel-sign-sub-inv_binary64`
476×	`fma-neg_binary64`
422×	`associate-l_binary64`
395×	`associate-r_binary64`
274×	`unswap-sqr_binary64`

Counts

245 → 339

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	358	6465
1	906	5511
2	2814	5344
3	4443	5169
4	4878	5163
5	4995	5163
6	5005	5163

prune412.0ms (9.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	452	1	453
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	452	9	461

Error

0.0b

Counts

461 → 9

Alt Table

Status	Error	Program
✓	5.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2)))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
▶	5.3b	(.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2))))) (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	13.9b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	4.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	25.5b	(.f64 (/.f64 (-.f64 (.f64 y y) (pow.f64 y 4)) (fma.f64 y y y)) x)
	34.9b	(.f64 (.f64 (-.f64 y (pow.f64 y 2)) (sqrt.f64 x)) (sqrt.f64 x))
	30.4b	(.f64 (+.f64 (sqrt.f64 y) y) (.f64 (-.f64 (sqrt.f64 y) y) x))
	30.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))

Compiler

Compiled 15402 to 9881 computations (35.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2)))))
✓	0.6b	(cbrt.f64 y)
✓	0.7b	(.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2))))) (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
	4.6b	(cbrt.f64 (-.f64 y (pow.f64 y 2)))

series963.0ms (21.8%)

Counts

3 → 48

Calls

3 calls:

915.0ms

(*.f64 (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2))))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))

30.0ms

(cbrt.f64 y)

17.0ms

(*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2)))))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-div_binary64`
42×	`associate-*r/_binary64`
34×	`associate-*l/_binary64`
33×	`flip--_binary64`
33×	`flip3--_binary64`

Counts

3 → 101

Calls

3 calls:

16.0ms

(*.f64 (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2))))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))

11.0ms

(*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2)))))

2.0ms

(cbrt.f64 y)

simplify128.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

609×	`associate-l_binary64`
545×	`fma-def_binary64`
468×	`associate-r_binary64`
329×	`fma-neg_binary64`
272×	`*-commutative_binary64`

Counts

149 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	4924
1	737	4411
2	2676	4134
3	4765	4134
4	4946	4134

prune270.0ms (6.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	0	5	5
Picked	1	0	1
Done	1	2	3
Total	310	8	318

Error

0.0b

Counts

318 → 8

Alt Table

Status	Error	Program
✓	5.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) (cbrt.f64 (-.f64 y (pow.f64 y 2)))) (*.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	5.6b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 y (pow.f64 y 2))))) (.f64 (cbrt.f64 (-.f64 y (pow.f64 y 2))) x))
	30.4b	(.f64 (+.f64 (sqrt.f64 y) y) (.f64 (-.f64 (sqrt.f64 y) y) x))
	13.9b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	25.5b	(.f64 (/.f64 (-.f64 (.f64 y y) (pow.f64 y 4)) (fma.f64 y y y)) x)
	34.9b	(.f64 (.f64 (-.f64 y (pow.f64 y 2)) (sqrt.f64 x)) (sqrt.f64 x))
	30.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))

Compiler

Compiled 11028 to 6915 computations (37.3% saved)

regimes307.0ms (7%)

Accuracy

Total 0.1b remaining (65.9%)

Threshold costs 0.1b (65.9%)

Counts

93 → 1

Compiler

Compiled 6381 to 4286 computations (32.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	19	10
4	20	10
5	19	10

end99.0ms (2.3%)

Compiler: Compiled 157 to 101 computations (35.7% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze123.0ms (2.8%)

sample813.0ms (18.4%)

simplify26.0ms (0.6%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite14.0ms (0.3%)

simplify104.0ms (2.4%)

prune61.0ms (1.4%)

localize4.0ms (0.1%)

series14.0ms (0.3%)

rewrite16.0ms (0.4%)

simplify93.0ms (2.1%)

prune97.0ms (2.2%)

localize9.0ms (0.2%)

series505.0ms (11.5%)

rewrite61.0ms (1.4%)

simplify218.0ms (4.9%)

prune412.0ms (9.3%)

localize12.0ms (0.3%)

series963.0ms (21.8%)

rewrite45.0ms (1%)

simplify128.0ms (2.9%)

prune270.0ms (6.1%)

regimes307.0ms (7%)

simplify2.0ms (0.1%)

end99.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10