Details

analyze2.9s (23.7%)

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
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)

sample3.1s (25.5%)

Symmetry

(sort x y)

(sort t a)

Results

2.2s	8256×	body	128	valid
794.0ms	3257×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify80.0ms (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

prune3.0ms (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

21.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	21.8b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	5.2b	(.f64 (.f64 x y) z)
✓	7.4b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series491.0ms (4%)

Counts

4 → 136

Calls

4 calls:

384.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
73.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
18.0ms	(.f64 (.f64 x y) z)
15.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite173.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 256

Calls

4 calls:

158.0ms	(-.f64 (.f64 z z) (.f64 t a))
158.0ms	(.f64 (.f64 x y) z)
158.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
158.0ms	(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

simplify148.0ms (1.2%)

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

392 → 309

Iterations

Useful iterations: 2 (0.0ms)

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

prune414.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	302	7	309
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	303	7	310

Error

2.8b

Counts

310 → 7

Alt Table

Status	Error	Program
	22.9b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
	37.8b	(neg.f64 (*.f64 y x))
	35.8b	(*.f64 y x)
▶	20.8b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	22.7b	(.f64 x (.f64 (.f64 z y) (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2)))
	22.6b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	39.6b	(fma.f64 1/2 (/.f64 (.f64 a (.f64 t (.f64 y x))) (.f64 z z)) (*.f64 y x))

Compiler

Compiled 9241 to 2861 computations (69% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	3.3b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
	23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series303.0ms (2.5%)

Counts

2 → 64

Calls

2 calls:

235.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
68.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)

rewrite80.0ms (0.7%)

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 → 62

Calls

2 calls:

79.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
79.0ms	(.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	36
1	325	36
2	4097	36
3	5722	36
0	0	0
1	0	0

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

513×	`fma-def_binary64`
497×	`associate-*l/_binary64`
329×	`associate-/r/_binary64`
225×	`times-frac_binary64`
204×	`associate-r_binary64`

Counts

126 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	2203
1	563	2193
2	2434	2166
3	5534	2166

prune417.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	330	6	336

Error

2.8b

Counts

336 → 6

Alt Table

Status	Error	Program
	22.9b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
	37.8b	(neg.f64 (*.f64 y x))
	35.8b	(*.f64 y x)
	22.7b	(.f64 x (.f64 (.f64 z y) (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2)))
▶	20.8b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	22.6b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 10255 to 3855 computations (62.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	3.3b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series367.0ms (3%)

Counts

1 → 44

Calls

1 calls:

367.0ms

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

rewrite95.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
139×	`add-log-exp_binary64`

Counts

1 → 55

Calls

1 calls:

92.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	289	21
2	3995	21
3	5724	21
0	0	0
1	0	0

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-*r/_binary64`
433×	`associate-*l/_binary64`
419×	`fma-def_binary64`
280×	`associate-/r/_binary64`
198×	`times-frac_binary64`

Counts

99 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1625
1	454	1621
2	2031	1608
3	5330	1608

prune327.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	355	0	355
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	355	6	361

Error

2.8b

Counts

361 → 6

Alt Table

Status	Error	Program
	22.9b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
	37.8b	(neg.f64 (*.f64 y x))
	35.8b	(*.f64 y x)
	22.7b	(.f64 x (.f64 (.f64 z y) (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2)))
✓	20.8b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
▶	22.6b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 10279 to 3374 computations (67.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	6.7b	(.f64 y (.f64 z x))
✓	7.4b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series394.0ms (3.2%)

Counts

2 → 44

Calls

2 calls:

376.0ms	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
18.0ms	(.f64 y (.f64 z x))

rewrite96.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
145×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
135×	`add-log-exp_binary64`

Counts

2 → 62

Calls

2 calls:

91.0ms	(.f64 y (.f64 z x))
91.0ms	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	283	28
2	3767	28
3	5426	28
0	0	0
1	0	0

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-*r/_binary64`
433×	`associate-*l/_binary64`
419×	`fma-def_binary64`
280×	`associate-/r/_binary64`
198×	`times-frac_binary64`

Counts

106 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1625
1	454	1621
2	2031	1608
3	5330	1608

prune360.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	307	7	314

Error

2.8b

Counts

314 → 7

Alt Table

Status	Error	Program
	22.9b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
	37.8b	(neg.f64 (*.f64 y x))
	35.8b	(*.f64 y x)
	22.7b	(.f64 x (.f64 (.f64 z y) (pow.f64 (-.f64 (.f64 z z) (*.f64 t a)) -1/2)))
✓	20.8b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
✓	22.6b	(/.f64 (.f64 y (.f64 z x)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	37.7b	(/.f64 (.f64 y (.f64 z x)) (neg.f64 z))

Compiler

Compiled 9100 to 2783 computations (69.4% saved)

regimes1.6s (12.8%)

Accuracy

Total 2.7b remaining (42.8%)

Threshold costs 0b (0%)

Counts

52 → 3

Compiler

Compiled 8186 to 5409 computations (33.9% saved)

bsearch52.0ms (0.4%)

Steps

Iters	Range		Point
6	2.956768345402315e+142	8.487210617174824e+143	4.257216888057887e+142
1	-9.849348287214884e+143	-4.3441659668286355e+140	-2.0742634033648369e+142

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-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	22	43
1	39	43
2	55	43
3	66	43
4	72	43
5	73	43
6	73	43

end480.0ms (3.9%)

Remove: (sort t a)
Compiler: Compiled 379 to 231 computations (39.1% saved)

Details

analyze2.9s (23.7%)

sample3.1s (25.5%)

simplify80.0ms (0.7%)

prune3.0ms (0%)

localize21.0ms (0.2%)

series491.0ms (4%)

rewrite173.0ms (1.4%)

simplify148.0ms (1.2%)

prune414.0ms (3.4%)

localize20.0ms (0.2%)

series303.0ms (2.5%)

rewrite80.0ms (0.7%)

simplify104.0ms (0.8%)

prune417.0ms (3.4%)

localize19.0ms (0.2%)

series367.0ms (3%)

rewrite95.0ms (0.8%)

simplify95.0ms (0.8%)

prune327.0ms (2.7%)

localize18.0ms (0.1%)

series394.0ms (3.2%)

rewrite96.0ms (0.8%)

simplify91.0ms (0.7%)

prune360.0ms (2.9%)

regimes1.6s (12.8%)

bsearch52.0ms (0.4%)

simplify7.0ms (0.1%)

end480.0ms (3.9%)

Profiling