Details

analyze881.0ms (12.9%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (18.1%)

Results

1.0s	8256×	body	128	valid
107.0ms	720×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

prune3.0ms (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

5.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	5.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	5.6b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series73.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

41.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
22.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
10.0ms	(/.f64 2 (-.f64 y t))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 234

Calls

3 calls:

17.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
7.0ms	(/.f64 2 (-.f64 y t))
6.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)

simplify194.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
216×	`times-frac_binary64`
212×	`*-commutative_binary64`

Counts

342 → 351

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	7256
1	1123	6896
2	3980	6860
3	4623	6847
4	4989	6847

prune278.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	344	7	351
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	344	9	353

Error

0.0b

Counts

353 → 9

Alt Table

Status	Error	Program
	7.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	6.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	25.0b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	5.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.0b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
▶	2.1b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	30.5b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	6.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 7632 to 3582 computations (53.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (-.f64 y t))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	1.6b	(/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))))

series1.5s (21.7%)

Counts

4 → 96

Calls

4 calls:

1.3s	(/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))))
91.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
31.0ms	(cbrt.f64 z)
28.0ms	(cbrt.f64 (-.f64 y t))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`cbrt-prod_binary64`
24×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 109

Calls

4 calls:

16.0ms	(/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
2.0ms	(cbrt.f64 (-.f64 y t))
1.0ms	(cbrt.f64 z)

simplify125.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

441×	`associate-r_binary64`
416×	`associate-l_binary64`
316×	`associate-/r*_binary64`
291×	`*-commutative_binary64`
218×	`fma-def_binary64`

Counts

205 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	451	5674
1	1228	4896
2	4641	4712
3	4972	4712

prune417.0ms (6.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	371	10	381

Error

Counts

381 → 10

Alt Table

Status	Error	Program
	7.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	6.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	25.0b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	5.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.0b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
▶	1.5b	(.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
✓	2.1b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	30.5b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	6.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 15633 to 6752 computations (56.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (-.f64 y t))
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 z)

series36.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

36.0ms

(cbrt.f64 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 x)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
374×	`log-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
287×	`*-commutative_binary64`

Counts

25 → 18

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	141
1	38	137
2	86	137
3	208	137
4	626	133
5	1904	133
6	2565	133
7	3552	133
8	4861	133

prune280.0ms (4.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	313	0	313
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	313	10	323

Error

Counts

323 → 10

Alt Table

Status	Error	Program
	7.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	6.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	25.0b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	5.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.0b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
✓	1.5b	(.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
✓	2.1b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	30.5b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	6.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
▶	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 14229 to 4571 computations (67.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(*.f64 x (/.f64 2 (-.f64 y t)))
✓	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

series64.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

43.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
21.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 68

Calls

2 calls:

7.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
6.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
583×	`associate-/r/_binary64`
230×	`associate-/l*_binary64`
215×	`times-frac_binary64`
133×	`associate-/r*_binary64`

Counts

152 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	3100
1	611	2837
2	2636	2627
3	5071	2627

prune153.0ms (2.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	2	4	6
Picked	0	1	1
Done	1	2	3
Total	182	8	190

Error

Counts

190 → 8

Alt Table

Status	Error	Program
	7.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	25.0b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
	5.1b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 2 (-.f64 y t)))))
✓	2.1b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
✓	5.7b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	30.5b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	6.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
✓	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 3323 to 1695 computations (49% saved)

regimes1.1s (15.6%)

Accuracy

Total 2.3b remaining (98.5%)

Threshold costs 0b (0%)

Counts

129 → 3

Compiler

Compiled 18367 to 12006 computations (34.6% saved)

bsearch37.0ms (0.5%)

Steps

Iters	Range		Point
9	5.491980664829274e-36	2.3156697815252118e-27	8.706980749572951e-32
7	-2.3596056895766246e-92	-1.1913584738584556e-93	-2.127933069782768e-92

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	57
1	23	57
2	28	57
3	30	57
4	31	57
5	31	57

end103.0ms (1.5%)

Compiler: Compiled 239 to 149 computations (37.7% saved)

Details

analyze881.0ms (12.9%)

sample1.2s (18.1%)

simplify93.0ms (1.4%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series73.0ms (1.1%)

rewrite54.0ms (0.8%)

simplify194.0ms (2.8%)

prune278.0ms (4.1%)

localize16.0ms (0.2%)

series1.5s (21.7%)

rewrite32.0ms (0.5%)

simplify125.0ms (1.8%)

prune417.0ms (6.1%)

localize16.0ms (0.2%)

series36.0ms (0.5%)

rewrite1.0ms (0%)

simplify66.0ms (1%)

prune280.0ms (4.1%)

localize6.0ms (0.1%)

series64.0ms (0.9%)

rewrite21.0ms (0.3%)

simplify80.0ms (1.2%)

prune153.0ms (2.2%)

regimes1.1s (15.6%)

bsearch37.0ms (0.5%)

simplify4.0ms (0.1%)

end103.0ms (1.5%)

Profiling