Details

analyze1.6s (15.2%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample34.0ms (0.3%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
5.0ms	80×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series55.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

33.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
11.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
11.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`*-un-lft-identity_binary64`
121×	`add-sqr-sqrt_binary64`
118×	`times-frac_binary64`
116×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

3 → 215

Calls

3 calls:

18.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
12.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
6.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify177.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
501×	`distribute-rgt-in_binary64`
470×	`distribute-lft-in_binary64`
329×	`fma-neg_binary64`
178×	`cancel-sign-sub-inv_binary64`

Counts

311 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	8725
1	750	5951
2	1752	4992
3	4889	4992
4	4828	4992

prune314.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	266	4	270
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	267	5	272

Error

0.0b

Counts

272 → 5

Alt Table

Status	Error	Program
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
	25.9b	(+.f64 (/.f64 x y) (cbrt.f64 (pow.f64 (+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) 3)))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))

Compiler

Compiled 10122 to 7096 computations (29.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series35.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

35.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-def_binary64`
492×	`associate-l_binary64`
423×	`associate-+l+_binary64`
379×	`associate-r_binary64`
267×	`associate-*l/_binary64`

Counts

58 → 29

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	1177
1	83	1126
2	164	1126
3	357	1126
4	1233	1009
5	4295	1009
6	5040	1009

prune173.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	164	5	169

Error

0.0b

Counts

169 → 5

Alt Table

Status	Error	Program
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
	25.9b	(+.f64 (/.f64 x y) (cbrt.f64 (pow.f64 (+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) 3)))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))

Compiler

Compiled 5530 to 4086 computations (26.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.5b	(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

series909.0ms (8.6%)

Counts

3 → 72

Calls

3 calls:

477.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

369.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

63.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite69.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-prod_binary64`
114×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 181

Calls

3 calls:

23.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

17.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

5.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

simplify234.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
506×	`times-frac_binary64`
279×	`associate-r_binary64`
275×	`cancel-sign-sub-inv_binary64`
272×	`associate-l_binary64`

Counts

253 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	323	7739
1	734	7358
2	2319	6759
3	4761	6652
4	4989	6652
5	4963	6652

prune654.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	517	1	518
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	517	6	523

Error

Counts

523 → 6

Alt Table

Status	Error	Program
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
	25.9b	(+.f64 (/.f64 x y) (cbrt.f64 (pow.f64 (+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) 3)))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
▶	0.9b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) 4)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))

Compiler

Compiled 22239 to 16390 computations (26.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
✓	0.5b	(cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))
✓	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) 4)

series2.8s (26.8%)

Counts

3 → 72

Calls

3 calls:

996.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))

922.0ms

(cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

907.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) 4)

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 83

Calls

3 calls:

13.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))

9.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) 4)

6.0ms

(cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

simplify171.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

475×	`cancel-sign-sub-inv_binary64`
431×	`times-frac_binary64`
297×	`associate-r_binary64`
286×	`fma-neg_binary64`
218×	`associate-l_binary64`

Counts

155 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	367	5571
1	879	5312
2	2563	5148
3	4518	4751
4	4926	4751

prune721.0ms (6.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	415	0	415
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	415	6	421

Error

Counts

421 → 6

Alt Table

Status	Error	Program
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
	25.9b	(+.f64 (/.f64 x y) (cbrt.f64 (pow.f64 (+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) 3)))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.9b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) 4)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))

Compiler

Compiled 24960 to 19289 computations (22.7% saved)

regimes958.0ms (9.1%)

Accuracy

Total 0.1b remaining (77.8%)

Threshold costs 0.1b (77.8%)

Counts

126 → 1

Compiler

Compiled 19199 to 14754 computations (23.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	18	22
2	27	22
3	39	22
4	44	22
5	46	22
6	45	22

end1.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample1.3s (12.3%)

Algorithm

1×

intervals

Results

646.0ms	8000×	body	128	valid
140.0ms	2209×	body	128	invalid

Compiler

Compiled 218 to 169 computations (22.5% saved)

Details

analyze1.6s (15.2%)

sample34.0ms (0.3%)

simplify103.0ms (1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series55.0ms (0.5%)

rewrite58.0ms (0.5%)

simplify177.0ms (1.7%)

prune314.0ms (3%)

localize9.0ms (0.1%)

series35.0ms (0.3%)

rewrite1.0ms (0%)

simplify71.0ms (0.7%)

prune173.0ms (1.6%)

localize12.0ms (0.1%)

series909.0ms (8.6%)

rewrite69.0ms (0.7%)

simplify234.0ms (2.2%)

prune654.0ms (6.2%)

localize18.0ms (0.2%)

series2.8s (26.8%)

rewrite35.0ms (0.3%)

simplify171.0ms (1.6%)

prune721.0ms (6.8%)

regimes958.0ms (9.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.3s (12.3%)

Profiling