Details

analyze1.2s (19.9%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (18.7%)

Results

1.0s	8252×	body	128	valid
95.0ms	763×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	2×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 58 to 31 computations (46.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	0.5b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series104.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

50.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
34.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
20.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 122

Calls

3 calls:

11.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
2.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
498×	`sub-neg_binary64`
213×	`associate--l+_binary64`
201×	`fma-neg_binary64`
200×	`+-commutative_binary64`

Counts

266 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	6584
1	983	6188
2	3712	6122
3	5248	6122

prune200.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	234	8	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	234	9	243

Error

Counts

243 → 9

Alt Table

Status	Error	Program
	42.8b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))))))
	52.0b	(+.f64 x (.f64 (.f64 y (/.f64 (sqrt.f64 (-.f64 z t)) (+.f64 (sqrt.f64 z) (sqrt.f64 a)))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))))
	10.6b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
	23.0b	(+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
	31.3b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))))
✓	0.4b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	7.2b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
	18.5b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
▶	0.5b	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))

Compiler

Compiled 6619 to 2011 computations (69.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	0.5b	(*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))))

series122.0ms (2%)

Counts

4 → 180

Calls

4 calls:

48.0ms	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))
33.0ms	(*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))))
20.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
20.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite87.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
337×	`add-sqr-sqrt_binary64`
325×	`*-un-lft-identity_binary64`
159×	`add-cube-cbrt_binary64`
98×	`associate-r_binary64`

Counts

4 → 349

Calls

4 calls:

23.0ms	(*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))))
10.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
3.0ms	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))

simplify246.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

295×	`fma-neg_binary64`
284×	`associate--l+_binary64`
262×	`associate--r+_binary64`
241×	`associate-/l*_binary64`
202×	`sub-neg_binary64`

Counts

529 → 556

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	490	12377
1	1312	11592
2	4811	11592
3	5074	11592

prune469.0ms (7.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	553	3	556
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	557	8	565

Error

Counts

565 → 8

Alt Table

Status	Error	Program
	23.0b	(+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
▶	0.4b	(+.f64 x (.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))))
	4.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.4b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	52.0b	(+.f64 x (.f64 (.f64 y (/.f64 (sqrt.f64 (-.f64 z t)) (+.f64 (sqrt.f64 z) (sqrt.f64 a)))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))))
	7.2b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
	0.5b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	18.5b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))

Compiler

Compiled 15279 to 5057 computations (66.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))))
✓	0.0b	(/.f64 1 (-.f64 z a))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))
✓	0.5b	(.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)))

series108.0ms (1.7%)

Counts

4 → 168

Calls

4 calls:

46.0ms	(+.f64 x (.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))))
33.0ms	(.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)))
20.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))
8.0ms	(/.f64 1 (-.f64 z a))

rewrite64.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-sqr-sqrt_binary64`
117×	`distribute-lft-in_binary64`
117×	`distribute-rgt-in_binary64`
113×	`*-un-lft-identity_binary64`
96×	`add-cube-cbrt_binary64`

Counts

4 → 269

Calls

4 calls:

11.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))
10.0ms	(.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t)))
6.0ms	(+.f64 x (.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))))
4.0ms	(/.f64 1 (-.f64 z a))

simplify194.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

504×	`sub-neg_binary64`
364×	`associate-r_binary64`
336×	`associate-l_binary64`
274×	`+-commutative_binary64`
272×	`fma-neg_binary64`

Counts

437 → 474

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	542	10280
1	1160	8887
2	4284	8815
3	5186	8815

prune411.0ms (6.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	474	8	482

Error

Counts

482 → 8

Alt Table

Status	Error	Program
	23.0b	(+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
✓	0.4b	(+.f64 x (.f64 y (.f64 (/.f64 1 (-.f64 z a)) (-.f64 z t))))
	4.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.4b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	52.0b	(+.f64 x (.f64 (.f64 y (/.f64 (sqrt.f64 (-.f64 z t)) (+.f64 (sqrt.f64 z) (sqrt.f64 a)))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 (sqrt.f64 z) (sqrt.f64 a)))))
	7.2b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
▶	0.5b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	18.5b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))

Compiler

Compiled 13612 to 4850 computations (64.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.6b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

series89.0ms (1.4%)

Counts

2 → 108

Calls

2 calls:

49.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
40.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`times-frac_binary64`
161×	`*-un-lft-identity_binary64`
159×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

2 → 161

Calls

2 calls:

22.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
9.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

simplify148.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

927×	`times-frac_binary64`
242×	`associate-/r/_binary64`
200×	`associate-/l/_binary64`
174×	`associate-*l/_binary64`
173×	`*-commutative_binary64`

Counts

269 → 279

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	404	7649
1	1020	7254
2	3700	7212
3	5018	7212

prune274.0ms (4.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	360	2	362
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	363	7	370

Error

Counts

370 → 7

Alt Table

Status	Error	Program
	23.0b	(+.f64 x (cbrt.f64 (.f64 (.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
	0.5b	(+.f64 x (/.f64 1 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y)))
	4.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	50.0b	(+.f64 x (*.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 a))) (/.f64 y (/.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 a)) (-.f64 z t)))))
✓	0.4b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.5b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	18.5b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))

Compiler

Compiled 9447 to 2444 computations (74.1% saved)

regimes879.0ms (14.1%)

Accuracy

Total 1.3b remaining (99.1%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 20312 to 11968 computations (41.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	25	16
3	29	16
4	31	16
5	31	16

end84.0ms (1.4%)

Compiler: Compiled 187 to 103 computations (44.9% saved)

Details

analyze1.2s (19.9%)

sample1.2s (18.7%)

simplify112.0ms (1.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series104.0ms (1.7%)

rewrite30.0ms (0.5%)

simplify125.0ms (2%)

prune200.0ms (3.2%)

localize8.0ms (0.1%)

series122.0ms (2%)

rewrite87.0ms (1.4%)

simplify246.0ms (3.9%)

prune469.0ms (7.5%)

localize8.0ms (0.1%)

series108.0ms (1.7%)

rewrite64.0ms (1%)

simplify194.0ms (3.1%)

prune411.0ms (6.6%)

localize7.0ms (0.1%)

series89.0ms (1.4%)

rewrite51.0ms (0.8%)

simplify148.0ms (2.4%)

prune274.0ms (4.4%)

regimes879.0ms (14.1%)

simplify3.0ms (0%)

end84.0ms (1.4%)

Profiling