Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

sample523.0ms (30%)

Infinites

0% of outputs are infinite.

Results

469.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify13.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

57×	`fma-neg_binary64`
53×	`fma-def_binary64`
22×	`cancel-sign-sub-inv_binary64`
15×	`sub-neg_binary64`
11×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	15	7
3	24	7
4	36	7
5	60	5
6	93	5
7	116	5
8	146	5
9	168	5
10	200	5
11	213	5
12	216	5
13	178	5

prune3.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y -1/200 x)
▶	0.0b	(-.f64 x (/.f64 y 200))

Compiler

Compiled 37 to 25 computations (32.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y 200))

series4.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(-.f64 x (/.f64 y 200))

rewrite14.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

1 → 71

Calls

1 calls:

8.0ms

(-.f64 x (/.f64 y 200))

simplify97.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1018×	`fma-def_binary64`
389×	`associate-*l/_binary64`
363×	`associate-*r/_binary64`
296×	`associate-/l*_binary64`
229×	`fma-neg_binary64`

Counts

95 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1175
1	425	964
2	970	590
3	3361	590
4	4093	590
5	4958	590
6	4602	590

prune73.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	89	4	93

Error

Counts

93 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y -1/200 x)
	41.9b	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))
	0.6b	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
✓	0.0b	(-.f64 x (/.f64 y 200))

Compiler

Compiled 2215 to 1453 computations (34.4% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y -1/200 x)

series4.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

3.0ms

(fma.f64 y -1/200 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y -1/200 x)

simplify74.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
539×	`neg-sub0_binary64`
512×	`unsub-neg_binary64`
503×	`neg-mul-1_binary64`
490×	`associate-l_binary64`

Counts

34 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	229
1	26	182
2	50	182
3	162	182
4	598	182
5	2353	182
6	3574	182
7	4429	182
8	4963	182

prune9.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	16	4	20

Error

Counts

20 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y -1/200 x)
	41.9b	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))
▶	0.6b	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
✓	0.0b	(-.f64 x (/.f64 y 200))

Compiler

Compiled 178 to 123 computations (30.9% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
✓	0.3b	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200)))
✓	0.6b	(*.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))
✓	0.6b	(cbrt.f64 (/.f64 y 200))

series140.0ms (8%)

Counts

4 → 60

Calls

4 calls:

45.0ms	(*.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))
43.0ms	(cbrt.f64 (/.f64 y 200))
30.0ms	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
21.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200)))

rewrite40.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
84×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`

Counts

4 → 167

Calls

4 calls:

14.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200)))
10.0ms	(*.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))
2.0ms	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
2.0ms	(cbrt.f64 (/.f64 y 200))

simplify160.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

358×	`fma-neg_binary64`
286×	`neg-sub0_binary64`
281×	`neg-mul-1_binary64`
253×	`associate-l_binary64`
235×	`associate-r_binary64`

Counts

227 → 264

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3619
1	451	3405
2	1494	3159
3	3834	3116
4	4908	3116
5	4931	3116

prune255.0ms (14.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	334	4	338

Error

Counts

338 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y -1/200 x)
▶	41.9b	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))
✓	0.6b	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
✓	0.0b	(-.f64 x (/.f64 y 200))

Compiler

Compiled 7835 to 6001 computations (23.4% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (fma.f64 -1/200 y x) 3)
✓	0.1b	(fma.f64 -1/200 y x)
✓	41.9b	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))

series16.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

9.0ms	(pow.f64 (fma.f64 -1/200 y x) 3)
3.0ms	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))
3.0ms	(fma.f64 -1/200 y x)

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 58

Calls

3 calls:

1.0ms	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))
1.0ms	(pow.f64 (fma.f64 -1/200 y x) 3)
0.0ms	(fma.f64 -1/200 y x)

simplify86.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
496×	`exp-prod_binary64`
395×	`associate-l_binary64`
340×	`cancel-sign-sub-inv_binary64`
328×	`log-prod_binary64`

Counts

130 → 92

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	1404
1	169	1233
2	476	1196
3	2126	1139
4	4667	1136
5	5088	1136

prune42.0ms (2.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	92	4	96

Error

Counts

96 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y -1/200 x)
✓	41.9b	(cbrt.f64 (pow.f64 (fma.f64 -1/200 y x) 3))
✓	0.6b	(+.f64 x (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 y 200)) (cbrt.f64 (/.f64 y 200)))) (cbrt.f64 (/.f64 y 200))))
✓	0.0b	(-.f64 x (/.f64 y 200))

Compiler

Compiled 1133 to 826 computations (27.1% saved)

regimes107.0ms (6.1%)

Accuracy

Total 0.0b remaining (79.9%)

Threshold costs 0.0b (79.9%)

Counts

23 → 1

Compiler

Compiled 2144 to 1582 computations (26.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`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	6	7
1	8	7
2	15	7
3	19	7
4	22	7
5	23	7
6	23	7

end56.0ms (3.2%)

Compiler: Compiled 55 to 41 computations (25.5% saved)

Iter	Nodes	Cost
0	6	7
1	8	7
2	15	7
3	24	7
4	36	7
5	60	5
6	93	5
7	116	5
8	146	5
9	168	5
10	200	5
11	213	5
12	216	5
13	178	5

Iter	Nodes	Cost
0	6	7
1	8	7
2	15	7
3	24	7
4	36	7
5	60	5
6	93	5
7	116	5
8	146	5
9	168	5
10	200	5
11	213	5
12	216	5
13	178	5

Details

analyze1.0ms (0.1%)

sample523.0ms (30%)

simplify13.0ms (0.7%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite14.0ms (0.8%)

simplify97.0ms (5.6%)

prune73.0ms (4.2%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0%)

simplify74.0ms (4.3%)

prune9.0ms (0.5%)

localize8.0ms (0.4%)

series140.0ms (8%)

rewrite40.0ms (2.3%)

simplify160.0ms (9.2%)

prune255.0ms (14.6%)

localize6.0ms (0.3%)

series16.0ms (0.9%)

rewrite5.0ms (0.3%)

simplify86.0ms (4.9%)

prune42.0ms (2.4%)

regimes107.0ms (6.1%)

simplify2.0ms (0.1%)

end56.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	6	7
1	8	7
2	15	7
3	24	7
4	36	7
5	60	5
6	93	5
7	116	5
8	146	5
9	168	5
10	200	5
11	213	5
12	216	5
13	178	5