Details

analyze1.1s (23.3%)

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
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.3%	66.5%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample73.0ms (1.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	27×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify114.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune4.0ms (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

0.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series58.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

38.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
20.0ms	(/.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)

simplify93.0ms (1.9%)

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

prune105.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	5	136

Error

0.0b

Counts

136 → 5

Alt Table

Status	Error	Program
	6.1b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	1.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)
▶	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	26.4b	(fma.f64 (/.f64 y a) t x)

Compiler

Compiled 3342 to 1087 computations (67.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series81.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

37.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
25.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
19.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite43.0ms (0.9%)

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:

12.0ms	(/.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)

simplify185.0ms (3.7%)

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

prune240.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	337	4	341

Error

0.0b

Counts

341 → 4

Alt Table

Status	Error	Program
	6.1b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	1.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	1.1b	(fma.f64 y (/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))) x)

Compiler

Compiled 8561 to 2748 computations (67.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.2b	(*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))
✓	0.3b	(/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t))))
✓	0.9b	(fma.f64 y (/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))) x)

series94.0ms (1.9%)

Counts

4 → 156

Calls

4 calls:

37.0ms	(fma.f64 y (/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))) x)
31.0ms	(*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))
17.0ms	(/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t))))
8.0ms	(/.f64 1 (-.f64 z t))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-exp-log_binary64`
49×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 151

Calls

4 calls:

11.0ms	(/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t))))
11.0ms	(*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))
4.0ms	(/.f64 1 (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))) x)

simplify138.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

721×	`cancel-sign-sub-inv_binary64`
533×	`sub-neg_binary64`
245×	`fma-neg_binary64`
242×	`+-commutative_binary64`
225×	`times-frac_binary64`

Counts

307 → 319

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	6781
1	996	6306
2	3733	5865
3	5455	5865

prune223.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	319	4	323

Error

0.0b

Counts

323 → 4

Alt Table

Status	Error	Program
	6.1b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	1.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	1.1b	(fma.f64 y (/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))) x)

Compiler

Compiled 7674 to 3133 computations (59.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
✓	0.5b	(cbrt.f64 (-.f64 z t))
✓	0.9b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)

series134.0ms (2.7%)

Counts

4 → 144

Calls

4 calls:

44.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)
37.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
32.0ms	(cbrt.f64 (-.f64 z t))
21.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
59×	`cbrt-prod_binary64`
54×	`associate-r_binary64`
42×	`times-frac_binary64`

Counts

4 → 172

Calls

4 calls:

19.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a)))
10.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
2.0ms	(cbrt.f64 (-.f64 z t))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)

simplify194.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-l_binary64`
459×	`associate-r_binary64`
279×	`fma-neg_binary64`
237×	`associate-/l*_binary64`
179×	`times-frac_binary64`

Counts

316 → 339

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	549	8705
1	1445	8358
2	4973	8358
3	5177	8358

prune334.0ms (6.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	439	0	439
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	439	4	443

Error

0.0b

Counts

443 → 4

Alt Table

Status	Error	Program
	6.1b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	1.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	1.1b	(fma.f64 y (/.f64 1 (*.f64 (-.f64 z a) (/.f64 1 (-.f64 z t)))) x)

Compiler

Compiled 14807 to 4843 computations (67.3% saved)

regimes661.0ms (13.4%)

Accuracy

Total 1.2b remaining (97.7%)

Threshold costs 0b (0%)

Counts

78 → 1

Compiler

Compiled 11472 to 7010 computations (38.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`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	10	14
1	14	14
2	22	14
3	26	14
4	28	14
5	28	14

end0.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

sample871.0ms (17.7%)

Algorithm

1×

intervals

Results

380.0ms	7998×	body	128	valid
40.0ms	709×	body	128	invalid
0.0ms	2×	body	512	valid

Compiler

Compiled 118 to 70 computations (40.7% saved)

Details

analyze1.1s (23.3%)

sample73.0ms (1.5%)

simplify114.0ms (2.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series58.0ms (1.2%)

rewrite10.0ms (0.2%)

simplify93.0ms (1.9%)

prune105.0ms (2.1%)

localize8.0ms (0.2%)

series81.0ms (1.6%)

rewrite43.0ms (0.9%)

simplify185.0ms (3.7%)

prune240.0ms (4.9%)

localize10.0ms (0.2%)

series94.0ms (1.9%)

rewrite37.0ms (0.8%)

simplify138.0ms (2.8%)

prune223.0ms (4.5%)

localize11.0ms (0.2%)

series134.0ms (2.7%)

rewrite50.0ms (1%)

simplify194.0ms (3.9%)

prune334.0ms (6.8%)

regimes661.0ms (13.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample871.0ms (17.7%)

Profiling