Details

analyze2.4s (21.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample3.2s (28.5%)

Symmetry

(sort x y)

(sort z t)

Results

1.5s	7494×	body	128	invalid
1.5s	8256×	body	128	valid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify223.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1133×	`distribute-rgt-in_binary64`
1066×	`distribute-lft-in_binary64`
969×	`unsub-neg_binary64`
583×	`fma-def_binary64`
461×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	97	24
3	277	24
4	797	24
5	1809	24
6	2532	24
7	2783	24
8	3128	24
9	3409	24
10	3319	24
11	3327	24
12	3331	24
13	3461	24
14	3620	24
15	3621	24
16	3623	24
17	3623	24
18	5071	24

prune4.0ms (0%)

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

6.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 94 to 57 computations (39.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	9.5b	(.f64 (.f64 c (fma.f64 b c a)) i)

series118.0ms (1.1%)

Counts

4 → 228

Calls

4 calls:

74.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
21.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
12.0ms	(*.f64 c (fma.f64 b c a))
10.0ms	(fma.f64 x y (*.f64 z t))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
3.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
3.0ms	(*.f64 c (fma.f64 b c a))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify125.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
563×	`distribute-rgt-in_binary64`
556×	`distribute-lft-in_binary64`
505×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

301 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	4992
1	327	4027
2	1091	3988
3	4531	3988
4	4933	3988

prune213.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	148	12	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	12	161

Error

0.2b

Counts

161 → 12

Alt Table

Status	Error	Program
	33.8b	(.f64 2 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 y x)) 3)) (.f64 (.f64 c (fma.f64 b c a)) i)))
▶	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
	5.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	20.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 c (fma.f64 b c a)) i) (.f64 (.f64 c (fma.f64 b c a)) i)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
	8.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	13.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i a))))
	12.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	35.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (fma.f64 b c a))) i)))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))
	31.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)))))

Compiler

Compiled 4411 to 1317 computations (70.1% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 t z (*.f64 y x))
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
✓	1.0b	(*.f64 i (fma.f64 c b a))
✓	4.6b	(.f64 c (.f64 i (fma.f64 c b a)))

series107.0ms (1%)

Counts

4 → 240

Calls

4 calls:

65.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
21.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
11.0ms	(*.f64 i (fma.f64 c b a))
9.0ms	(fma.f64 t z (*.f64 y x))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`fma-udef_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
4.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
3.0ms	(*.f64 i (fma.f64 c b a))
0.0ms	(fma.f64 t z (*.f64 y x))

simplify157.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
606×	`distribute-lft-in_binary64`
552×	`fma-def_binary64`
290×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

321 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	5146
1	339	4265
2	1166	4226
3	4533	4226
4	4990	4226
5	4926	4226

prune188.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	158	9	167

Error

0.0b

Counts

167 → 9

Alt Table

Status	Error	Program
	8.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	8.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	33.8b	(.f64 2 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 y x)) 3)) (.f64 (.f64 c (fma.f64 b c a)) i)))
✓	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	5.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 i (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a))))))
▶	2.2b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	35.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 4037 to 1113 computations (72.4% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 t z (*.f64 y x))
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
✓	6.3b	(.f64 (.f64 c i) (fma.f64 c b a))

series88.0ms (0.8%)

Counts

2 → 144

Calls

2 calls:

60.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
27.0ms	(.f64 (.f64 c i) (fma.f64 c b a))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`fma-udef_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(.f64 (.f64 c i) (fma.f64 c b a))
3.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))

simplify124.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
516×	`fma-def_binary64`
445×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
295×	`*-commutative_binary64`

Counts

189 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	3996
1	308	3155
2	1033	3116
3	3628	3108
4	4843	3108
5	4797	3108

prune114.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	121	9	130

Error

0.0b

Counts

130 → 9

Alt Table

Status	Error	Program
	8.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	8.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	33.8b	(.f64 2 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 y x)) 3)) (.f64 (.f64 c (fma.f64 b c a)) i)))
✓	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
▶	5.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 i (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a))))))
✓	2.2b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	35.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 3277 to 924 computations (71.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 i (*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))
✓	1.5b	(cbrt.f64 (fma.f64 c b a))
✓	4.6b	(.f64 c (.f64 (.f64 i (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a))))

series145.0ms (1.3%)

Counts

4 → 168

Calls

4 calls:

60.0ms	(*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))
46.0ms	(cbrt.f64 (fma.f64 c b a))
22.0ms	(.f64 c (.f64 (.f64 i (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a))))
16.0ms	(.f64 (.f64 i (*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
29×	`add-exp-log_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
18×	`pow-prod-down_binary64`

Counts

4 → 107

Calls

4 calls:

10.0ms	(.f64 (.f64 i (*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))
8.0ms	(.f64 c (.f64 (.f64 i (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a))))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))
1.0ms	(cbrt.f64 (fma.f64 c b a))

simplify153.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
524×	`associate-r_binary64`
410×	`associate-l_binary64`
266×	`times-frac_binary64`
251×	`associate-/r*_binary64`

Counts

275 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	416	6967
1	1285	6198
2	4742	6188
3	5400	6188

prune471.0ms (4.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	377	9	386

Error

0.0b

Counts

386 → 9

Alt Table

Status	Error	Program
	8.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	8.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	33.8b	(.f64 2 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 y x)) 3)) (.f64 (.f64 c (fma.f64 b c a)) i)))
✓	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	5.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 i (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a))))))
✓	2.2b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	35.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 19315 to 8035 computations (58.4% saved)

regimes3.0s (27.1%)

Accuracy

Total 0.7b remaining (96.8%)

Threshold costs 0.7b (96.8%)

Counts

130 → 3

Compiler

Compiled 56653 to 36330 computations (35.9% saved)

bsearch5.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	112
1	64	112
2	86	112
3	104	112
4	130	112
5	146	112
6	154	112
7	158	112
8	159	112
9	158	112

end189.0ms (1.7%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 793 to 384 computations (51.6% saved)

Iter	Nodes	Cost
0	38	112
1	64	112
2	86	112
3	104	112
4	130	112
5	146	112
6	154	112
7	158	112
8	159	112
9	158	112

Iter	Nodes	Cost
0	38	112
1	64	112
2	86	112
3	104	112
4	130	112
5	146	112
6	154	112
7	158	112
8	159	112
9	158	112

Details

analyze2.4s (21.2%)

sample3.2s (28.5%)

simplify223.0ms (2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series118.0ms (1.1%)

rewrite16.0ms (0.1%)

simplify125.0ms (1.1%)

prune213.0ms (1.9%)

localize35.0ms (0.3%)

series107.0ms (1%)

rewrite16.0ms (0.1%)

simplify157.0ms (1.4%)

prune188.0ms (1.7%)

localize12.0ms (0.1%)

series88.0ms (0.8%)

rewrite11.0ms (0.1%)

simplify124.0ms (1.1%)

prune114.0ms (1%)

localize25.0ms (0.2%)

series145.0ms (1.3%)

rewrite31.0ms (0.3%)

simplify153.0ms (1.4%)

prune471.0ms (4.2%)

regimes3.0s (27.1%)

bsearch5.0ms (0%)

simplify7.0ms (0.1%)

end189.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	38	112
1	64	112
2	86	112
3	104	112
4	130	112
5	146	112
6	154	112
7	158	112
8	159	112
9	158	112