Details

analyze1.2s (22.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (21.8%)

Results

1.0s	8255×	body	128	valid
88.0ms	774×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify115.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

prune3.0ms (0.1%)

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
▶	2.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	12.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	2.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series66.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

39.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
26.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune126.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	132	5	137

Error

0.0b

Counts

137 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	7.7b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	3.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	2.8b	(fma.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 z a) (cbrt.f64 (-.f64 z t)))) x)
▶	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 3400 to 1097 computations (67.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	2.2b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series93.0ms (1.7%)

Counts

3 → 132

Calls

3 calls:

49.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
22.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
22.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify213.0ms (4%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune246.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	336	5	341

Error

0.0b

Counts

341 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	7.7b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	2.4b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)
	2.8b	(fma.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 z a) (cbrt.f64 (-.f64 z t)))) x)
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 8582 to 2763 computations (67.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 1 (-.f64 z t)))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t))))
✓	2.2b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)

series74.0ms (1.4%)

Counts

4 → 144

Calls

4 calls:

41.0ms	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)
20.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t))))
10.0ms	(/.f64 1 (-.f64 z t))
3.0ms	(/.f64 1 (/.f64 1 (-.f64 z t)))

rewrite83.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

305×	`times-frac_binary64`
250×	`add-sqr-sqrt_binary64`
208×	`*-un-lft-identity_binary64`
172×	`add-exp-log_binary64`
130×	`add-cube-cbrt_binary64`

Counts

4 → 357

Calls

4 calls:

32.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t))))
7.0ms	(/.f64 1 (/.f64 1 (-.f64 z t)))
4.0ms	(/.f64 1 (-.f64 z t))
0.0ms	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)

simplify249.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

511×	`cancel-sign-sub-inv_binary64`
363×	`sub-neg_binary64`
331×	`fma-neg_binary64`
220×	`neg-mul-1_binary64`
190×	`+-commutative_binary64`

Counts

501 → 533

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	380	8373
1	875	7951
2	3065	7309
3	4394	7306
4	5020	7306

prune364.0ms (6.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	532	1	533
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	534	4	538

Error

0.0b

Counts

538 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	7.7b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	3.0b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 13374 to 6440 computations (51.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z a))
✓	3.0b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)

series58.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
18.0ms	(/.f64 y (-.f64 z a))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

5.0ms	(/.f64 y (-.f64 z a))
0.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
706×	`fma-def_binary64`
452×	`fma-neg_binary64`
347×	`cancel-sign-sub-inv_binary64`
187×	`associate-/l/_binary64`

Counts

133 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3219
1	538	3160
2	1818	2505
3	4711	2505
4	5035	2505

prune81.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	115	5	120

Error

0.0b

Counts

120 → 5

Alt Table

Status	Error	Program
	17.1b	(fma.f64 (cbrt.f64 (.f64 (.f64 (/.f64 y (-.f64 z a)) (/.f64 y (-.f64 z a))) (/.f64 y (-.f64 z a)))) (-.f64 z t) x)
✓	2.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	7.7b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	3.0b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 2578 to 826 computations (68% saved)

regimes826.0ms (15.4%)

Accuracy

Total 0.5b remaining (97%)

Threshold costs 0.5b (97%)

Counts

89 → 3

Compiler

Compiled 12287 to 7352 computations (40.2% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	80
1	28	80
2	36	80
3	40	80
4	42	80
5	42	80

end80.0ms (1.5%)

Compiler: Compiled 216 to 92 computations (57.4% saved)

Details

analyze1.2s (22.7%)

sample1.2s (21.8%)

simplify115.0ms (2.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series66.0ms (1.2%)

rewrite10.0ms (0.2%)

simplify97.0ms (1.8%)

prune126.0ms (2.4%)

localize10.0ms (0.2%)

series93.0ms (1.7%)

rewrite39.0ms (0.7%)

simplify213.0ms (4%)

prune246.0ms (4.6%)

localize13.0ms (0.2%)

series74.0ms (1.4%)

rewrite83.0ms (1.5%)

simplify249.0ms (4.6%)

prune364.0ms (6.8%)

localize8.0ms (0.1%)

series58.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify102.0ms (1.9%)

prune81.0ms (1.5%)

regimes826.0ms (15.4%)

bsearch6.0ms (0.1%)

simplify4.0ms (0.1%)

end80.0ms (1.5%)

Profiling