Details

analyze1.3s (17.1%)

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
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (19.1%)

Results

929.0ms	7014×	body	128	valid
164.0ms	392×	body	1024	valid
140.0ms	440×	body	512	valid
107.0ms	790×	body	128	invalid
75.0ms	351×	body	256	valid
27.0ms	59×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify129.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune4.0ms (0%)

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

10.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.9b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	3.1b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series60.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (0.1%)

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

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune122.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Error

0.0b

Counts

139 → 7

Alt Table

Status	Error	Program
	27.2b	(fma.f64 y (-.f64 (/.f64 t a) (*.f64 (+.f64 (/.f64 t a) 1) (/.f64 z a))) (+.f64 x y))
	27.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
✓	12.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	15.3b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
▶	12.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
	30.6b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.5b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 3649 to 1220 computations (66.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
✓	3.1b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
✓	3.2b	(cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))

series830.0ms (10.5%)

Counts

4 → 168

Calls

4 calls:

523.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
225.0ms	(cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))
52.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
29.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))

rewrite128.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

303×	`*-un-lft-identity_binary64`
248×	`cbrt-prod_binary64`
247×	`add-sqr-sqrt_binary64`
205×	`times-frac_binary64`
96×	`distribute-lft-out--_binary64`

Counts

4 → 284

Calls

4 calls:

29.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
26.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
5.0ms	(cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))

simplify259.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

657×	`*-commutative_binary64`
239×	`fma-def_binary64`
233×	`associate-+r+_binary64`
223×	`associate-r_binary64`
172×	`associate-/l*_binary64`

Counts

452 → 497

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1683	24862
1	5103	24862

prune917.0ms (11.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	711	0	711
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	711	7	718

Error

0.0b

Counts

718 → 7

Alt Table

Status	Error	Program
	27.2b	(fma.f64 y (-.f64 (/.f64 t a) (*.f64 (+.f64 (/.f64 t a) 1) (/.f64 z a))) (+.f64 x y))
	27.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
✓	12.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
▶	15.3b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
✓	12.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
	30.6b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.5b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 53131 to 22442 computations (57.8% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.4b	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
✓	4.8b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	10.0b	(/.f64 (*.f64 y t) (-.f64 a t))

series73.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

33.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
22.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
18.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`associate-/r*_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
5.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
5.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
491×	`associate-/l/_binary64`
302×	`distribute-rgt-in_binary64`
222×	`distribute-lft-in_binary64`
193×	`cancel-sign-sub-inv_binary64`

Counts

156 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	3210
1	652	3051
2	2336	2584
3	5067	2584

prune144.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	159	5	164

Error

0.0b

Counts

164 → 5

Alt Table

Status	Error	Program
✓	12.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	24.4b	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
▶	13.9b	(-.f64 (+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)) (/.f64 y (/.f64 (-.f64 a t) z)))
	30.6b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.5b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 4432 to 1102 computations (75.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) z)
	2.4b	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
✓	3.7b	(/.f64 y (/.f64 (-.f64 a t) z))
	10.0b	(/.f64 (*.f64 y t) (-.f64 a t))

series37.0ms (0.5%)

Counts

2 → 76

Calls

2 calls:

28.0ms	(/.f64 y (/.f64 (-.f64 a t) z))
9.0ms	(/.f64 (-.f64 a t) z)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
100×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 136

Calls

2 calls:

8.0ms	(/.f64 y (/.f64 (-.f64 a t) z))
4.0ms	(/.f64 (-.f64 a t) z)

simplify129.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

781×	`times-frac_binary64`
618×	`associate-/r/_binary64`
545×	`associate-/r*_binary64`
334×	`fma-def_binary64`
255×	`fma-neg_binary64`

Counts

212 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	3977
1	651	3859
2	2024	3694
3	4853	3694
4	5069	3694

prune184.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	299	6	305

Error

Counts

305 → 6

Alt Table

Status	Error	Program
	23.3b	(-.f64 (-.f64 x (/.f64 (*.f64 y a) t)) (/.f64 y (/.f64 (-.f64 a t) z)))
	24.4b	(-.f64 (-.f64 x (/.f64 (.f64 a y) t)) (/.f64 (.f64 y z) (-.f64 a t)))
✓	12.0b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
✓	13.9b	(-.f64 (+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)) (/.f64 y (/.f64 (-.f64 a t) z)))
	30.6b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.5b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

Compiler

Compiled 8531 to 1691 computations (80.2% saved)

regimes1.5s (18.6%)

Accuracy

Total 7.9b remaining (99.5%)

Threshold costs 0b (0%)

Counts

113 → 6

Compiler

Compiled 14952 to 8604 computations (42.5% saved)

bsearch147.0ms (1.9%)

Steps

Iters	Range		Point
9	1.6404224127148872e+49	9.408477575184421e+55	7.886165021559944e+50
4	2.488457280765803e-270	9.857087376262201e-267	1.1785256264895896e-269
10	-9.928958438862481e-116	-4.983762078791565e-130	-4.3030892615262975e-119
8	-4.829209728513151e-105	-7.729905841669531e-110	-3.405149008362116e-109
10	-9.233587392154741e-22	-6.920857839660166e-36	-1.6426802885300486e-35

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
17×	`sub-neg_binary64`
12×	`*-commutative_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	155
1	60	155
2	85	155
3	110	155
4	123	155
5	128	155
6	129	155
7	129	155

end100.0ms (1.3%)

Compiler: Compiled 347 to 153 computations (55.9% saved)

Details

analyze1.3s (17.1%)

sample1.5s (19.1%)

simplify129.0ms (1.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series60.0ms (0.8%)

rewrite11.0ms (0.1%)

simplify120.0ms (1.5%)

prune122.0ms (1.5%)

localize13.0ms (0.2%)

series830.0ms (10.5%)

rewrite128.0ms (1.6%)

simplify259.0ms (3.3%)

prune917.0ms (11.6%)

localize15.0ms (0.2%)

series73.0ms (0.9%)

rewrite22.0ms (0.3%)

simplify79.0ms (1%)

prune144.0ms (1.8%)

localize11.0ms (0.1%)

series37.0ms (0.5%)

rewrite24.0ms (0.3%)

simplify129.0ms (1.6%)

prune184.0ms (2.3%)

regimes1.5s (18.6%)

bsearch147.0ms (1.9%)

simplify7.0ms (0.1%)

end100.0ms (1.3%)

Profiling