Details

analyze217.0ms (2.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample265.0ms (2.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid
0.0ms	1×	body	128	nan

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify282.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
806×	`fma-neg_binary64`
746×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	59	16
3	115	16
4	270	14
5	514	14
6	792	14
7	1191	14
8	1435	14
9	1716	14
10	2343	14
11	2639	14
12	2704	14
13	3251	14
14	3766	14
15	3977	14
16	4124	14
17	4234	14
18	4260	14
19	4085	14
20	4111	14
21	4149	14
22	4189	14
23	4189	14
24	4189	14
25	4871	14
26	4999	14
27	4907	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

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
✓	0.0b	(+.f64 (-.f64 1 z) (log.f64 z))
✓	0.2b	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

series291.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

201.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
85.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
5.0ms	(+.f64 (-.f64 1 z) (log.f64 z))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`
9×	`prod-diff_binary64`

Counts

3 → 85

Calls

3 calls:

8.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
7.0ms	(+.f64 (-.f64 1 z) (log.f64 z))
6.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Rules

353×	`times-frac_binary64`
345×	`associate-+l+_binary64`
335×	`*-commutative_binary64`
284×	`cancel-sign-sub-inv_binary64`
270×	`associate-+r+_binary64`

Counts

157 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2280
1	446	2015
2	1697	1951
3	3681	1950
4	4939	1950
5	4823	1950

prune191.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	6	150

Error

Counts

150 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))))
	14.3b	(+.f64 (.f64 x 1/2) (.f64 y (cbrt.f64 (pow.f64 (-.f64 (+.f64 (log.f64 z) 1) z) 3))))
	0.8b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	16.3b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3))) (+.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (-.f64 (.f64 (log.f64 z) (log.f64 z)) (*.f64 (-.f64 1 z) (log.f64 z))))))
	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 (-.f64 1 z) y) (*.f64 (log.f64 z) y)))
	24.7b	(+.f64 (.f64 x 1/2) (.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))

Compiler

Compiled 3095 to 1816 computations (41.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2))
✓	0.2b	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
✓	0.2b	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
✓	0.5b	(cbrt.f64 z)

series1.3s (12.4%)

Counts

4 → 60

Calls

4 calls:

699.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
439.0ms	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
114.0ms	(+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2))
30.0ms	(cbrt.f64 z)

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-log-exp_binary64`
14×	`associate-+l+_binary64`

Counts

4 → 101

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
9.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
6.0ms	(+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2))
1.0ms	(cbrt.f64 z)

simplify145.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-+l+_binary64`
387×	`*-commutative_binary64`
334×	`fma-neg_binary64`
315×	`associate-+r+_binary64`
285×	`times-frac_binary64`

Counts

161 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2833
1	483	1965
2	1763	1828
3	3854	1826
4	4934	1826
5	4981	1826
6	4823	1826

prune206.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	201	5	206

Error

Counts

206 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z)) (*.f64 y (log.f64 (cbrt.f64 z)))))
	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (-.f64 (+.f64 1 (*.f64 3 (log.f64 (pow.f64 z 1/3)))) z)))
✓	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))))
	16.3b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3))) (+.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (-.f64 (.f64 (log.f64 z) (log.f64 z)) (*.f64 (-.f64 1 z) (log.f64 z))))))
	24.7b	(+.f64 (.f64 x 1/2) (.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))

Compiler

Compiled 5205 to 2918 computations (43.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z)) (.f64 y (log.f64 (cbrt.f64 z))))
✓	0.1b	(*.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z))
✓	0.3b	(*.f64 y (log.f64 (cbrt.f64 z)))
	0.5b	(cbrt.f64 z)

series3.2s (30.7%)

Counts

3 → 72

Calls

3 calls:

1.3s	(+.f64 (.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z)) (.f64 y (log.f64 (cbrt.f64 z))))
1.2s	(*.f64 y (log.f64 (cbrt.f64 z)))
659.0ms	(*.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
40×	`distribute-lft-in_binary64`
40×	`distribute-rgt-in_binary64`

Counts

3 → 141

Calls

3 calls:

8.0ms	(*.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z))
8.0ms	(+.f64 (.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z)) (.f64 y (log.f64 (cbrt.f64 z))))
4.0ms	(*.f64 y (log.f64 (cbrt.f64 z)))

simplify152.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

386×	`fma-neg_binary64`
298×	`exp-prod_binary64`
275×	`sub-neg_binary64`
223×	`associate-+l+_binary64`
219×	`associate-l_binary64`

Counts

213 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	263	3383
1	532	3159
2	1797	3015
3	4087	3003
4	4759	3003
5	4952	3003

prune237.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	254	4	258

Error

Counts

258 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (-.f64 (+.f64 1 (*.f64 3 (log.f64 (pow.f64 z 1/3)))) z)))
✓	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))))
▶	0.1b	(+.f64 (.f64 x 1/2) (fma.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z) (.f64 y (log.f64 (cbrt.f64 z)))))
	24.7b	(+.f64 (.f64 x 1/2) (.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))

Compiler

Compiled 7613 to 3494 computations (54.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (log.f64 (cbrt.f64 z)) 2 1)
✓	0.1b	(fma.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z) (*.f64 y (log.f64 (cbrt.f64 z))))
	0.3b	(*.f64 y (log.f64 (cbrt.f64 z)))
	0.5b	(cbrt.f64 z)

series1.9s (18.6%)

Counts

2 → 36

Calls

2 calls:

1.3s	(fma.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z) (*.f64 y (log.f64 (cbrt.f64 z))))
586.0ms	(fma.f64 (log.f64 (cbrt.f64 z)) 2 1)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z) (*.f64 y (log.f64 (cbrt.f64 z))))
0.0ms	(fma.f64 (log.f64 (cbrt.f64 z)) 2 1)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
531×	`distribute-rgt-in_binary64`
498×	`distribute-lft-in_binary64`
380×	`fma-neg_binary64`
319×	`unsub-neg_binary64`

Counts

56 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	998
1	152	879
2	389	755
3	1083	702
4	3846	701
5	4924	701
6	4835	701

prune118.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (-.f64 (+.f64 1 (*.f64 3 (log.f64 (pow.f64 z 1/3)))) z)))
✓	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))))
✓	0.1b	(+.f64 (.f64 x 1/2) (fma.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z) (.f64 y (log.f64 (cbrt.f64 z)))))
	24.7b	(+.f64 (.f64 x 1/2) (.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))

Compiler

Compiled 3185 to 1597 computations (49.9% saved)

regimes593.0ms (5.7%)

Accuracy

Total 0.1b remaining (68.6%)

Threshold costs 0.1b (68.6%)

Counts

83 → 1

Compiler

Compiled 10844 to 7759 computations (28.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-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	13	18
1	21	18
2	25	18
3	27	18
4	28	18
5	27	18

end1.0ms (0%)

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

sample945.0ms (9.1%)

Algorithm

1×

intervals

Results

589.0ms	8000×	body	128	valid
16.0ms	289×	body	128	invalid
3.0ms	59×	body	128	nan

Compiler

Compiled 113 to 82 computations (27.4% saved)

Details

analyze217.0ms (2.1%)

sample265.0ms (2.6%)

simplify282.0ms (2.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series291.0ms (2.8%)

rewrite25.0ms (0.2%)

simplify106.0ms (1%)

prune191.0ms (1.8%)

localize12.0ms (0.1%)

series1.3s (12.4%)

rewrite31.0ms (0.3%)

simplify145.0ms (1.4%)

prune206.0ms (2%)

localize14.0ms (0.1%)

series3.2s (30.7%)

rewrite32.0ms (0.3%)

simplify152.0ms (1.5%)

prune237.0ms (2.3%)

localize12.0ms (0.1%)

series1.9s (18.6%)

rewrite1.0ms (0%)

simplify77.0ms (0.7%)

prune118.0ms (1.1%)

regimes593.0ms (5.7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample945.0ms (9.1%)

Profiling