Details

analyze1.8s (22.1%)

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
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.7s (21.1%)

Symmetry

(sort x y)

(sort t a)

Results

1.2s	8256×	body	128	valid
429.0ms	3124×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1034×	`fma-def_binary64`
336×	`fma-neg_binary64`
138×	`distribute-rgt-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
128×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	26	21
2	52	21
3	87	21
4	128	21
5	161	21
6	203	21
7	247	21
8	464	21
9	822	21
10	1234	21
11	1169	21
12	1237	21
13	1311	21
14	1375	21
15	1375	21
16	1282	21

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

25.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	4.7b	(.f64 (.f64 x y) z)
✓	10.8b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	25.3b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series207.0ms (2.5%)

Counts

4 → 136

Calls

4 calls:

163.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
26.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
9.0ms	(-.f64 (.f64 z z) (.f64 t a))
8.0ms	(.f64 (.f64 x y) z)

rewrite106.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
260×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Counts

4 → 260

Calls

4 calls:

98.0ms	(-.f64 (.f64 z z) (.f64 t a))
98.0ms	(.f64 (.f64 x y) z)
98.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
98.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	283	50
2	3754	50
3	5413	50
0	0	0
1	0	0

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-def_binary64`
513×	`associate-*l/_binary64`
330×	`associate-/r/_binary64`
224×	`times-frac_binary64`
204×	`associate-r_binary64`

Counts

396 → 313

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2730
1	570	2726
2	2444	2703
3	5590	2703

prune242.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	304	9	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	9	314

Error

3.2b

Counts

314 → 9

Alt Table

Status	Error	Program
▶	22.7b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	44.4b	(.f64 y (.f64 (sqrt.f64 (/.f64 -1 (.f64 a t))) (.f64 z x)))
	22.7b	(.f64 (/.f64 (.f64 x y) 1) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	25.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (fma.f64 z z (neg.f64 (*.f64 t a)))))
	26.1b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	36.1b	(neg.f64 (*.f64 y x))
	37.9b	(*.f64 y x)
	26.2b	(.f64 x (.f64 (.f64 z y) (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2)))
	36.4b	(/.f64 (.f64 (.f64 x y) z) (neg.f64 z))

Compiler

Compiled 9357 to 2908 computations (68.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.4b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	25.3b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series219.0ms (2.7%)

Counts

2 → 64

Calls

2 calls:

161.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
58.0ms	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))

rewrite76.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

868×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Counts

2 → 71

Calls

2 calls:

75.0ms	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
75.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	325	36
2	4097	36
3	5722	36
0	0	0
1	0	0

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
297×	`times-frac_binary64`
223×	`fma-neg_binary64`
215×	`associate-r_binary64`
201×	`associate-/r*_binary64`

Counts

135 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	2413
1	608	2399
2	2908	2374
3	4922	2372
4	4992	2372
5	4959	2372

prune256.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	339	2	341
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	342	8	350

Error

3.2b

Counts

350 → 8

Alt Table

Status	Error	Program
	25.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (fma.f64 z z (neg.f64 (*.f64 t a)))))
	26.1b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	36.1b	(neg.f64 (*.f64 y x))
	37.9b	(*.f64 y x)
✓	22.7b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	36.4b	(/.f64 (.f64 (.f64 x y) z) (neg.f64 z))
	23.6b	(/.f64 y (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x))
▶	23.2b	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))

Compiler

Compiled 10716 to 4103 computations (61.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	1.3b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y)
✓	2.0b	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))
	25.3b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series229.0ms (2.8%)

Counts

2 → 76

Calls

2 calls:

167.0ms	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))
62.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y)

rewrite87.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

904×	`prod-diff_binary64`
153×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`
143×	`add-log-exp_binary64`

Counts

2 → 86

Calls

2 calls:

85.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y)
85.0ms	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	295	39
2	4161	39
3	5910	39
0	0	0
1	0	0

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-def_binary64`
364×	`associate-/r/_binary64`
244×	`times-frac_binary64`
215×	`associate-r_binary64`
169×	`associate-/l/_binary64`

Counts

162 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2607
1	604	2555
2	2649	2520
3	5211	2520

prune295.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	357	0	357
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	357	8	365

Error

3.2b

Counts

365 → 8

Alt Table

Status	Error	Program
	25.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (fma.f64 z z (neg.f64 (*.f64 t a)))))
	26.1b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	36.1b	(neg.f64 (*.f64 y x))
	37.9b	(*.f64 y x)
✓	22.7b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	36.4b	(/.f64 (.f64 (.f64 x y) z) (neg.f64 z))
▶	23.6b	(/.f64 y (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x))
✓	23.2b	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))

Compiler

Compiled 10431 to 3693 computations (64.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	1.5b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x)
✓	2.3b	(/.f64 y (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x))
	25.3b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series214.0ms (2.6%)

Counts

2 → 76

Calls

2 calls:

155.0ms	(/.f64 y (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x))
59.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x)

rewrite81.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

904×	`prod-diff_binary64`
153×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`
143×	`add-log-exp_binary64`

Counts

2 → 86

Calls

2 calls:

78.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x)
78.0ms	(/.f64 y (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	295	39
2	4161	39
3	5910	39
0	0	0
1	0	0

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-def_binary64`
358×	`associate-/r/_binary64`
259×	`times-frac_binary64`
215×	`associate-r_binary64`
163×	`associate-/r*_binary64`

Counts

162 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2607
1	607	2557
2	2674	2520
3	5183	2520

prune286.0ms (3.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	356	1	357
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	356	9	365

Error

3.2b

Counts

365 → 9

Alt Table

Status	Error	Program
✓	23.6b	(/.f64 y (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) x))
	36.1b	(/.f64 y (/.f64 -1 x))
	25.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (fma.f64 z z (neg.f64 (*.f64 t a)))))
	26.1b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	36.1b	(neg.f64 (*.f64 y x))
	37.9b	(*.f64 y x)
✓	22.7b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	36.4b	(/.f64 (.f64 (.f64 x y) z) (neg.f64 z))
✓	23.2b	(/.f64 x (/.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z) y))

Compiler

Compiled 10354 to 3641 computations (64.8% saved)

regimes1.5s (18.8%)

Accuracy

Total 2.6b remaining (43.6%)

Threshold costs 0b (0%)

Counts

72 → 5

Compiler

Compiled 13411 to 8761 computations (34.7% saved)

bsearch94.0ms (1.1%)

Steps

Iters	Range		Point
1	7.117950652165511e+139	3.3941090306412616e+146	1.55751804684065e+143
6	3.1020319062174382e-207	1.9525707860654897e-206	1.8773682071337756e-206
6	-1.548476653252807e-214	-1.0731371878635678e-215	-1.5207850390489686e-214
3	-2.0654440825124184e+110	-1.6177088015078025e+100	-1.0184175095225266e+104

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	96
1	58	96
2	73	96
3	83	96
4	87	96
5	87	96

end291.0ms (3.5%)

Remove: (sort t a)
Compiler: Compiled 689 to 364 computations (47.2% saved)

Details

analyze1.8s (22.1%)

sample1.7s (21.1%)

simplify59.0ms (0.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series207.0ms (2.5%)

rewrite106.0ms (1.3%)

simplify81.0ms (1%)

prune242.0ms (2.9%)

localize12.0ms (0.1%)

series219.0ms (2.7%)

rewrite76.0ms (0.9%)

simplify109.0ms (1.3%)

prune256.0ms (3.1%)

localize10.0ms (0.1%)

series229.0ms (2.8%)

rewrite87.0ms (1.1%)

simplify66.0ms (0.8%)

prune295.0ms (3.6%)

localize11.0ms (0.1%)

series214.0ms (2.6%)

rewrite81.0ms (1%)

simplify69.0ms (0.8%)

prune286.0ms (3.5%)

regimes1.5s (18.8%)

bsearch94.0ms (1.1%)

simplify13.0ms (0.2%)

end291.0ms (3.5%)

Profiling