Details

analyze1.9s (18.5%)

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)

sample1.8s (17.5%)

Symmetry

(sort x y)

(sort t a)

Results

1.2s	8256×	body	128	valid
450.0ms	3221×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify61.0ms (0.6%)

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

25.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.4b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (.f64 z z) (.f64 t a))
✓	5.9b	(.f64 (.f64 x y) z)
✓	8.9b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	26.0b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series202.0ms (2%)

Counts

4 → 136

Calls

4 calls:

159.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
27.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
8.0ms	(.f64 (.f64 x y) z)
8.0ms	(-.f64 (.f64 z z) (.f64 t a))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

6.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(.f64 (.f64 x y) z)
3.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
379×	`times-frac_binary64`
318×	`associate-r_binary64`
293×	`associate-l_binary64`
277×	`associate-/l*_binary64`

Counts

222 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4463
1	842	4196
2	3899	4138
3	4961	4138
4	4976	4138

prune154.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	179	11	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	11	191

Error

4.8b

Counts

191 → 11

Alt Table

Status	Error	Program
	25.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
▶	23.5b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
	29.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) (cbrt.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z)))) (cbrt.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	28.6b	(/.f64 (.f64 (.f64 x y) z) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	24.9b	(.f64 (/.f64 (.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))) (/.f64 z (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z))))
	37.7b	(neg.f64 (*.f64 y x))
	39.7b	(*.f64 y x)
	27.0b	(.f64 (.f64 y (.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (.f64 a t)))))
	26.5b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	42.2b	(exp.f64 (log.f64 (/.f64 (.f64 y (.f64 z x)) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
	40.9b	(/.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))

Compiler

Compiled 5182 to 1597 computations (69.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
✓	3.6b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
✓	17.0b	(sqrt.f64 (neg.f64 (*.f64 a t)))

series438.0ms (4.3%)

Counts

3 → 52

Calls

3 calls:

333.0ms	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
93.0ms	(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
11.0ms	(sqrt.f64 (neg.f64 (*.f64 a t)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`times-frac_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 95

Calls

3 calls:

5.0ms	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a t))) z) z))
2.0ms	(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 a t)))

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/r/_binary64`
607×	`associate-*r/_binary64`
266×	`fma-def_binary64`
200×	`cancel-sign-sub-inv_binary64`
157×	`associate-/l*_binary64`

Counts

147 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	4134
1	654	3630
2	2402	3587
3	5206	3587

prune117.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	179	7	186

Error

1.4b

Counts

186 → 7

Alt Table

Status	Error	Program
▶	24.8b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))
	37.7b	(neg.f64 (*.f64 y x))
	39.7b	(*.f64 y x)
	27.0b	(.f64 (.f64 y (.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (.f64 a t)))))
	25.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	26.5b	(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	40.9b	(/.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))

Compiler

Compiled 4629 to 1241 computations (73.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)
✓	0.2b	(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))
✓	3.6b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))

series426.0ms (4.2%)

Counts

3 → 52

Calls

3 calls:

314.0ms	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))
99.0ms	(/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)
12.0ms	(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 117

Calls

3 calls:

6.0ms	(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))
5.0ms	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))
2.0ms	(/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)

simplify170.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-def_binary64`
217×	`associate-r_binary64`
216×	`associate-l_binary64`
205×	`cancel-sign-sub-inv_binary64`
185×	`fma-neg_binary64`

Counts

169 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	329	4800
1	849	4428
2	3029	4227
3	4590	4225
4	4980	4225
5	4931	4225

prune176.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	225	7	232
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	229	10	239

Error

Counts

239 → 10

Alt Table

Status	Error	Program
	26.9b	(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))
	29.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)) (cbrt.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))) (/.f64 y (/.f64 (cbrt.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)) z)))
	41.7b	(.f64 (/.f64 (.f64 y (*.f64 z x)) (sqrt.f64 (neg.f64 t))) (sqrt.f64 (/.f64 1 a)))
	39.7b	(*.f64 y x)
	29.0b	(.f64 (.f64 (/.f64 x (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)) y) z)
▶	24.7b	(.f64 (.f64 x y) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))
	37.7b	(neg.f64 (*.f64 y x))
	24.8b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (.f64 (sqrt.f64 (cbrt.f64 a)) (sqrt.f64 (neg.f64 t)))) z) z))
	25.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	29.5b	(/.f64 x (/.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z) (.f64 z y)))

Compiler

Compiled 6445 to 1844 computations (71.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z))
✓	0.2b	(*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a))
✓	3.6b	(.f64 (.f64 x y) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))

series448.0ms (4.4%)

Counts

3 → 52

Calls

3 calls:

318.0ms	(.f64 (.f64 x y) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))
118.0ms	(/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z))
12.0ms	(*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 104

Calls

3 calls:

7.0ms	(.f64 (.f64 x y) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))
6.0ms	(*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a))
2.0ms	(/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z))

simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
320×	`associate-l_binary64`
291×	`associate-r_binary64`
259×	`cancel-sign-sub-inv_binary64`
249×	`fma-neg_binary64`

Counts

156 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	4251
1	793	3886
2	2930	3694
3	4544	3694
4	4931	3694

prune122.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	176	10	186

Error

Counts

186 → 10

Alt Table

Status	Error	Program
	26.9b	(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))
	29.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)) (cbrt.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))) (/.f64 y (/.f64 (cbrt.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)) z)))
✓	24.7b	(.f64 (.f64 x y) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)))
	28.5b	(/.f64 (.f64 y (.f64 z x)) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z))
	41.7b	(.f64 (/.f64 (.f64 y (*.f64 z x)) (sqrt.f64 (neg.f64 t))) (sqrt.f64 (/.f64 1 a)))
	39.7b	(*.f64 y x)
	29.0b	(.f64 (.f64 (/.f64 x (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 t)) (sqrt.f64 a)) z)) y) z)
	37.7b	(neg.f64 (*.f64 y x))
	24.8b	(/.f64 (.f64 x y) (/.f64 (hypot.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (.f64 (sqrt.f64 (cbrt.f64 a)) (sqrt.f64 (neg.f64 t)))) z) z))
	25.4b	(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 4925 to 1587 computations (67.8% saved)

regimes3.2s (31.4%)

Accuracy

Total 3.9b remaining (98%)

Threshold costs 0b (0%)

Counts

125 → 5

Compiler

Compiled 26743 to 15795 computations (40.9% saved)

bsearch132.0ms (1.3%)

Steps

Iters	Range		Point
9	1.1869224238885904e+53	5.16106278097033e+59	7.57008347475156e+58
5	7.458391318088252e-115	2.89314209234144e-114	7.581764408590992e-115
9	-5.507983832535132e-158	-5.0904519005896404e-164	-5.158443679629766e-164
1	-1.42737910576664e+156	-1.3811132325521838e+152	-1.3347213958553576e+154

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

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	45	129
1	64	129
2	81	129
3	91	129
4	96	129
5	97	129
6	96	129

end427.0ms (4.2%)

Compiler: Compiled 726 to 364 computations (49.9% saved)

Details

analyze1.9s (18.5%)

sample1.8s (17.5%)

simplify61.0ms (0.6%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series202.0ms (2%)

rewrite22.0ms (0.2%)

simplify131.0ms (1.3%)

prune154.0ms (1.5%)

localize9.0ms (0.1%)

series438.0ms (4.3%)

rewrite14.0ms (0.1%)

simplify91.0ms (0.9%)

prune117.0ms (1.1%)

localize10.0ms (0.1%)

series426.0ms (4.2%)

rewrite22.0ms (0.2%)

simplify170.0ms (1.7%)

prune176.0ms (1.7%)

localize10.0ms (0.1%)

series448.0ms (4.4%)

rewrite22.0ms (0.2%)

simplify121.0ms (1.2%)

prune122.0ms (1.2%)

regimes3.2s (31.4%)

bsearch132.0ms (1.3%)

simplify6.0ms (0.1%)

end427.0ms (4.2%)

Profiling