Details

analyze4.0ms (0.2%)

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)

sample1.2s (46.4%)

Infinites

0% of outputs are infinite.

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify19.0ms (0.7%)

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

prune2.0ms (0.1%)

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)

localize13.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(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))

simplify61.0ms (2.3%)

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

prune13.0ms (0.5%)

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))))
▶	0.5b	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

Compiler

Compiled 322 to 196 computations (39.1% saved)

localize20.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.5b	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

series11.0ms (0.4%)

Counts

2 → 32

Calls

2 calls:

6.0ms	(exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
4.0ms	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`exp-prod_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`
4×	`log-prod_binary32`

Counts

2 → 32

Calls

2 calls:

1.0ms	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
1.0ms	(exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))

simplify102.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary32`
567×	`associate-l_binary32`
491×	`associate-r_binary32`
306×	`associate-+l+_binary32`
194×	`associate--l+_binary32`

Counts

64 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	972
1	271	845
2	922	805
3	4711	799
4	4974	799
5	5000	799
6	4980	799

prune57.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	107	3	110

Error

Counts

110 → 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))))
✓	0.5b	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

Compiler

Compiled 1618 to 1071 computations (33.8% saved)

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.2b	(.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))))
✓	0.4b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

series115.0ms (4.3%)

Counts

3 → 72

Calls

3 calls:

81.0ms

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

29.0ms

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

5.0ms

(*.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))))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary32`
24×	`add-sqr-sqrt_binary32`
23×	`cbrt-prod_binary32`
16×	`pow1/3_binary32`
14×	`*-un-lft-identity_binary32`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.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))))

5.0ms

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

1.0ms

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

simplify164.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-def_binary32`
380×	`associate-/r*_binary32`
308×	`associate-l_binary32`
252×	`times-frac_binary32`
173×	`*-commutative_binary32`

Counts

165 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	555	7876
1	1800	7105
2	4988	7101
3	5000	7101

prune558.0ms (20.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	447	0	447
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	447	3	450

Error

Counts

450 → 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))))
✓	0.5b	(log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

Compiler

Compiled 22180 to 15035 computations (32.2% saved)

regimes189.0ms (7.1%)

Accuracy

Total 0.0b remaining (39.5%)

Threshold costs 0.0b (39.5%)

Counts

26 → 1

Compiler

Compiled 1949 to 1400 computations (28.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	14	8
3	16	8
4	17	8
5	16	8

end44.0ms (1.7%)

Compiler: Compiled 64 to 43 computations (32.8% saved)

Details

analyze4.0ms (0.2%)

sample1.2s (46.4%)

simplify19.0ms (0.7%)

prune2.0ms (0.1%)

localize13.0ms (0.5%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify61.0ms (2.3%)

prune13.0ms (0.5%)

localize20.0ms (0.8%)

series11.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify102.0ms (3.8%)

prune57.0ms (2.2%)

localize25.0ms (0.9%)

series115.0ms (4.3%)

rewrite17.0ms (0.7%)

simplify164.0ms (6.2%)

prune558.0ms (20.9%)

regimes189.0ms (7.1%)

simplify2.0ms (0.1%)

end44.0ms (1.7%)

Profiling