Details

analyze888.0ms (12%)

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)

sample1.1s (15%)

Results

936.0ms	8256×	body	128	valid
81.0ms	712×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify97.0ms (1.3%)

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

5.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	7.4b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 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)
✓	5.9b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series57.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

34.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
15.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
7.0ms	(/.f64 2 (-.f64 y t))

rewrite52.0ms (0.7%)

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:

16.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
7.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
3.0ms	(/.f64 2 (-.f64 y t))

simplify214.0ms (2.9%)

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

prune313.0ms (4.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	340	11	351
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	341	12	353

Error

Counts

353 → 12

Alt Table

Status	Error	Program
	5.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	6.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	35.6b	(.f64 (.f64 x (/.f64 1 (sqrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	6.6b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
	5.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	5.0b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	46.2b	(.f64 (.f64 x (/.f64 2 (-.f64 (pow.f64 y 3) (pow.f64 t 3)))) (/.f64 (+.f64 (.f64 y y) (+.f64 (.f64 t t) (*.f64 y t))) z))
	4.4b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) 1)) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
▶	4.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
	48.7b	(*.f64 x (/.f64 (/.f64 (/.f64 2 (+.f64 (sqrt.f64 y) (sqrt.f64 t))) (-.f64 (sqrt.f64 y) (sqrt.f64 t))) z))
✓	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))

Compiler

Compiled 7786 to 3684 computations (52.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z)
✓	0.6b	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
✓	0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
✓	3.7b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))

series466.0ms (6.3%)

Counts

4 → 132

Calls

4 calls:

286.0ms	(/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z)
102.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
44.0ms	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
33.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))

rewrite122.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

342×	`times-frac_binary64`
276×	`cbrt-prod_binary64`
273×	`add-sqr-sqrt_binary64`
267×	`*-un-lft-identity_binary64`
177×	`add-cube-cbrt_binary64`

Counts

4 → 365

Calls

4 calls:

32.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
21.0ms	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
10.0ms	(/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z)
3.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))

simplify424.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

518×	`*-commutative_binary64`
380×	`associate-/l*_binary64`
306×	`associate-*r/_binary64`
286×	`fma-def_binary64`
217×	`associate-*l/_binary64`

Counts

497 → 551

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	722	15970
1	1823	15424
2	4854	15321
3	4997	15321
4	4978	15321

prune769.0ms (10.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	686	1	687
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	687	12	699

Error

Counts

699 → 12

Alt Table

Status	Error	Program
	21.6b	(.f64 (.f64 x (cbrt.f64 (/.f64 (/.f64 4 (-.f64 y t)) (-.f64 y t)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
	5.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	6.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	35.6b	(.f64 (.f64 x (/.f64 1 (sqrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	6.6b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
	5.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	5.0b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	46.2b	(.f64 (.f64 x (/.f64 2 (-.f64 (pow.f64 y 3) (pow.f64 t 3)))) (/.f64 (+.f64 (.f64 y y) (+.f64 (.f64 t t) (*.f64 y t))) z))
▶	4.4b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) 1)) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
✓	4.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
✓	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))

Compiler

Compiled 27028 to 16157 computations (40.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 2 (cbrt.f64 (-.f64 y t)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
✓	0.6b	(cbrt.f64 (-.f64 y t))
✓	3.7b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) 1)) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

series118.0ms (1.6%)

Counts

4 → 120

Calls

4 calls:

37.0ms	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) 1)) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
33.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))
26.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
21.0ms	(cbrt.f64 (-.f64 y t))

rewrite110.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

248×	`add-exp-log_binary64`
186×	`times-frac_binary64`
150×	`add-sqr-sqrt_binary64`
148×	`*-un-lft-identity_binary64`
115×	`div-exp_binary64`

Counts

4 → 299

Calls

4 calls:

35.0ms	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) 1)) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
4.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))
2.0ms	(cbrt.f64 (-.f64 y t))

simplify205.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-*l/_binary64`
385×	`associate-/l*_binary64`
282×	`associate-/r*_binary64`
260×	`fma-def_binary64`
252×	`times-frac_binary64`

Counts

419 → 483

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	695	13388
1	1920	10649
2	5118	10649

prune570.0ms (7.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	582	1	583
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	585	10	595

Error

Counts

595 → 10

Alt Table

Status	Error	Program
	5.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	6.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	5.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	5.0b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	46.2b	(.f64 (.f64 x (/.f64 2 (-.f64 (pow.f64 y 3) (pow.f64 t 3)))) (/.f64 (+.f64 (.f64 y y) (+.f64 (.f64 t t) (*.f64 y t))) z))
	6.6b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	4.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
▶	4.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
✓	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))

Compiler

Compiled 22139 to 10317 computations (53.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series71.0ms (1%)

Counts

3 → 96

Calls

3 calls:

37.0ms	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
18.0ms	(/.f64 x (-.f64 y t))
16.0ms	(*.f64 2 (/.f64 x (-.f64 y t)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 107

Calls

3 calls:

7.0ms	(*.f64 2 (/.f64 x (-.f64 y t)))
6.0ms	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
4.0ms	(/.f64 x (-.f64 y t))

simplify105.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
546×	`associate-/l/_binary64`
185×	`associate-/l*_binary64`
161×	`distribute-rgt-in_binary64`
147×	`times-frac_binary64`

Counts

203 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	255	4141
1	687	3859
2	2331	3543
3	4991	3543

prune153.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	169	9	178

Error

Counts

178 → 9

Alt Table

Status	Error	Program
	5.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	6.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	5.0b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.0b	(/.f64 2 (/.f64 z (/.f64 x (-.f64 y t))))
	6.6b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	4.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
	4.9b	(/.f64 (*.f64 2 (/.f64 1 (/.f64 (-.f64 y t) x))) z)
✓	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))

Compiler

Compiled 3171 to 1382 computations (56.4% saved)

regimes1.4s (18.3%)

Accuracy

Total 1.8b remaining (98.9%)

Threshold costs 0b (0%)

Counts

187 → 1

Compiler

Compiled 30472 to 19510 computations (36% saved)

simplify3.0ms (0%)

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	16	49
1	20	49
2	25	49
3	27	49
4	28	49
5	28	49

end120.0ms (1.6%)

Compiler: Compiled 236 to 152 computations (35.6% saved)

Details

analyze888.0ms (12%)

sample1.1s (15%)

simplify97.0ms (1.3%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series57.0ms (0.8%)

rewrite52.0ms (0.7%)

simplify214.0ms (2.9%)

prune313.0ms (4.2%)

localize10.0ms (0.1%)

series466.0ms (6.3%)

rewrite122.0ms (1.7%)

simplify424.0ms (5.7%)

prune769.0ms (10.4%)

localize13.0ms (0.2%)

series118.0ms (1.6%)

rewrite110.0ms (1.5%)

simplify205.0ms (2.8%)

prune570.0ms (7.7%)

localize6.0ms (0.1%)

series71.0ms (1%)

rewrite24.0ms (0.3%)

simplify105.0ms (1.4%)

prune153.0ms (2.1%)

regimes1.4s (18.3%)

simplify3.0ms (0%)

end120.0ms (1.6%)

Profiling