Details

analyze6.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample1.6s (7%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-def_binary32`
155×	`fma-neg_binary32`
47×	`cancel-sign-sub-inv_binary32`
34×	`sub-neg_binary32`
26×	`unsub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	8
2	35	8
3	63	8
4	142	8
5	262	8
6	381	8
7	434	8
8	458	8
9	463	8
10	428	8

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize14.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(fma.f32 ux maxCos (-.f32 1 ux))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary32`
1×	`add-sqr-sqrt_binary32`
1×	`add-cube-cbrt_binary32`
1×	`add-cbrt-cube_binary32`
1×	`add-exp-log_binary32`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f32 ux maxCos (-.f32 1 ux))

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-neg_binary32`
470×	`times-frac_binary32`
313×	`distribute-rgt-in_binary32`
309×	`neg-sub0_binary32`
301×	`distribute-lft-in_binary32`

Counts

34 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	331
1	45	278
2	99	277
3	292	277
4	1097	277
5	2072	277
6	4492	277
7	5251	277

prune18.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
	0.6b	(.f32 (.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
▶	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 320 to 194 computations (39.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 maxCos ux)
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.0b	(-.f32 (*.f32 maxCos ux) ux)
✓	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series10.3s (44.2%)

Counts

4 → 63

Calls

4 calls:

10.3s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
19.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
7.0ms	(*.f32 maxCos ux)
4.0ms	(-.f32 (*.f32 maxCos ux) ux)

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`
7×	`add-log-exp_binary32`
6×	`add-cbrt-cube_binary32`

Counts

4 → 66

Calls

4 calls:

3.0ms	(-.f32 (*.f32 maxCos ux) ux)
3.0ms	(*.f32 maxCos ux)
1.0ms	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
1.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

370×	`fma-neg_binary32`
309×	`sub-neg_binary32`
275×	`cancel-sign-sub-inv_binary32`
225×	`fma-def_binary32`
216×	`unswap-sqr_binary32`

Counts

129 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	2451
1	768	2173
2	3179	2084
3	4920	2084

prune127.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	174	2	176

Error

Counts

176 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 3119 to 1599 computations (48.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f32 maxCos ux)
✓	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
	0.0b	(-.f32 (*.f32 maxCos ux) ux)
	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series10.6s (45.6%)

Counts

1 → 24

Calls

1 calls:

10.6s

(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`pow-unpow_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-sqr-sqrt_binary32`
3×	`unpow-prod-down_binary32`
3×	`add-cube-cbrt_binary32`

Counts

1 → 20

Calls

1 calls:

2.0ms

(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-neg_binary32`
642×	`fma-def_binary32`
512×	`div-sub_binary32`
422×	`log-prod_binary32`
335×	`log-div_binary32`

Counts

44 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	592
1	169	515
2	355	509
3	940	509
4	2625	509
5	4705	509
6	4925	509
7	4962	509
8	4772	509

prune102.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	179	2	181

Error

Counts

181 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 3358 to 1588 computations (52.7% saved)

regimes97.0ms (0.4%)

Accuracy

Total 0.0b remaining (86.7%)

Threshold costs 0.0b (86.7%)

Counts

26 → 1

Compiler

Compiled 1094 to 817 computations (25.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
2×	`*-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end36.0ms (0.2%)

Compiler: Compiled 40 to 28 computations (30% saved)

Details

analyze6.0ms (0%)

sample1.6s (7%)

simplify21.0ms (0.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series5.0ms (0%)

rewrite1.0ms (0%)

simplify60.0ms (0.3%)

prune18.0ms (0.1%)

localize20.0ms (0.1%)

series10.3s (44.2%)

rewrite10.0ms (0%)

simplify84.0ms (0.4%)

prune127.0ms (0.5%)

localize25.0ms (0.1%)

series10.6s (45.6%)

rewrite2.0ms (0%)

simplify108.0ms (0.5%)

prune102.0ms (0.4%)

regimes97.0ms (0.4%)

simplify3.0ms (0%)

end36.0ms (0.2%)

Profiling