Details

analyze481.0ms (3.2%)

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)

sample26.0ms (0.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify288.0ms (1.9%)

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 1 z) (log.f64 z))
✓	0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
✓	0.1b	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

series419.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

242.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
164.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
13.0ms	(+.f64 (-.f64 1 z) (log.f64 z))

rewrite53.0ms (0.4%)

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:

16.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
15.0ms	(+.f64 (-.f64 1 z) (log.f64 z))
11.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

simplify184.0ms (1.2%)

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

prune277.0ms (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

0.0b

Counts

150 → 6

Alt Table

Status	Error	Program
	17.0b	(+.f64 (.f64 x 1/2) (.f64 y (cbrt.f64 (pow.f64 (-.f64 (+.f64 (log.f64 z) 1) z) 3))))
	19.0b	(+.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 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))))
	33.5b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.8b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) (cbrt.f64 y))))
▶	0.1b	(fma.f64 y (-.f64 (+.f64 (log.f64 z) 1) z) (*.f64 1/2 x))

Compiler

Compiled 3097 to 1816 computations (41.4% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series401.0ms (2.7%)

Counts

3 → 60

Calls

3 calls:

256.0ms	(+.f64 (log.f64 z) 1)
140.0ms	(fma.f64 y (-.f64 (+.f64 (log.f64 z) 1) z) (*.f64 1/2 x))
5.0ms	(-.f64 (+.f64 (log.f64 z) 1) z)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`prod-diff_binary64`
15×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (log.f64 z) 1) z)
3.0ms	(+.f64 (log.f64 z) 1)
1.0ms	(fma.f64 y (-.f64 (+.f64 (log.f64 z) 1) z) (*.f64 1/2 x))

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
672×	`fma-def_binary64`
390×	`associate-l_binary64`
337×	`distribute-rgt-in_binary64`
311×	`distribute-lft-in_binary64`

Counts

134 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1666
1	307	1492
2	953	1442
3	4304	1442
4	4913	1442

prune102.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Error

0.0b

Counts

108 → 6

Alt Table

Status	Error	Program
	17.0b	(fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (+.f64 (log.f64 z) 1) z) 3)) (*.f64 1/2 x))
	19.0b	(+.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 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))))
	33.5b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.8b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) (cbrt.f64 y))))
✓	0.1b	(fma.f64 y (-.f64 (+.f64 (log.f64 z) 1) z) (*.f64 1/2 x))

Compiler

Compiled 2058 to 1134 computations (44.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
✓	0.1b	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series3.4s (22.4%)

Counts

4 → 60

Calls

4 calls:

2.8s	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))))
517.0ms	(+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)

rewrite119.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`*-un-lft-identity_binary64`
58×	`distribute-lft-out_binary64`
57×	`pow1_binary64`
34×	`log-pow_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

4 → 139

Calls

4 calls:

40.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))))
35.0ms	(+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
14.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
2.0ms	(cbrt.f64 z)

simplify300.0ms (2%)

Algorithm

1×	egg-herbie

Rules

528×	`associate-+r+_binary64`
388×	`log-prod_binary64`
361×	`*-commutative_binary64`
320×	`cancel-sign-sub-inv_binary64`
242×	`exp-prod_binary64`

Counts

199 → 179

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	179	3021
1	448	2002
2	1729	1918
3	3743	1900
4	4938	1900
5	4824	1897
6	4912	1897

prune463.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	215	6	221

Error

Counts

221 → 6

Alt Table

Status	Error	Program
	17.0b	(fma.f64 y (cbrt.f64 (pow.f64 (-.f64 (+.f64 (log.f64 z) 1) z) 3)) (*.f64 1/2 x))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 y (.f64 (cbrt.f64 (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))) (cbrt.f64 (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))))) (cbrt.f64 (+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))))))
	9.7b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 (-.f64 (+.f64 1 (log.f64 z)) z) (.f64 y (+.f64 (log.f64 (cbrt.f64 z)) (-.f64 1 z)))) (-.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))))
▶	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y) (.f64 (log.f64 (cbrt.f64 z)) y)))
	0.8b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) (cbrt.f64 y))))
✓	0.1b	(fma.f64 y (-.f64 (+.f64 (log.f64 z) 1) z) (*.f64 1/2 x))

Compiler

Compiled 5698 to 2817 computations (50.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y)
✓	0.2b	(*.f64 (log.f64 (cbrt.f64 z)) y)
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)

series2.8s (18.6%)

Counts

2 → 48

Calls

2 calls:

1.6s	(.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y)
1.2s	(*.f64 (log.f64 (cbrt.f64 z)) y)

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`
13×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

2 → 50

Calls

2 calls:

29.0ms	(.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y)
11.0ms	(*.f64 (log.f64 (cbrt.f64 z)) y)

simplify166.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

547×	`distribute-rgt-in_binary64`
520×	`distribute-lft-in_binary64`
473×	`fma-neg_binary64`
260×	`*-commutative_binary64`
247×	`fma-def_binary64`

Counts

98 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1491
1	286	1222
2	870	1209
3	3073	1206
4	4338	1198
5	4971	1198
6	4920	1198

prune478.0ms (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	196	6	202

Error

Counts

202 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y) (.f64 1/3 (*.f64 (log.f64 z) y))))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 y (.f64 (cbrt.f64 (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))) (cbrt.f64 (+.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))))) (cbrt.f64 (+.f64 (+.f64 (-.f64 1 z) (log.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))))))
✓	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y) (.f64 (log.f64 (cbrt.f64 z)) y)))
	0.2b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 (+.f64 (-.f64 1 z) (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) y) (.f64 (.f64 (log.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))))
	0.7b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 (.f64 (-.f64 (fma.f64 2/3 (log.f64 z) 1) z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (*.f64 (log.f64 (cbrt.f64 z)) y)))
✓	0.1b	(fma.f64 y (-.f64 (+.f64 (log.f64 z) 1) z) (*.f64 1/2 x))

Compiler

Compiled 5498 to 2473 computations (55% saved)

regimes3.2s (21.2%)

Accuracy

Total 0.1b remaining (82.7%)

Threshold costs 0.1b (82.7%)

Counts

156 → 1

Compiler

Compiled 28067 to 19683 computations (29.9% saved)

simplify6.0ms (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	11	16
1	17	16
2	21	16
3	23	16
4	24	16
5	23	16

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample1.7s (11.4%)

Algorithm

1×

intervals

Results

921.0ms	8000×	body	128	valid
33.0ms	310×	body	128	invalid
6.0ms	67×	body	128	nan

Compiler

Compiled 215 to 135 computations (37.2% saved)

Details

analyze481.0ms (3.2%)

sample26.0ms (0.2%)

simplify288.0ms (1.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series419.0ms (2.8%)

rewrite53.0ms (0.4%)

simplify184.0ms (1.2%)

prune277.0ms (1.8%)

localize17.0ms (0.1%)

series401.0ms (2.7%)

rewrite13.0ms (0.1%)

simplify86.0ms (0.6%)

prune102.0ms (0.7%)

localize16.0ms (0.1%)

series3.4s (22.4%)

rewrite119.0ms (0.8%)

simplify300.0ms (2%)

prune463.0ms (3.1%)

localize17.0ms (0.1%)

series2.8s (18.6%)

rewrite46.0ms (0.3%)

simplify166.0ms (1.1%)

prune478.0ms (3.2%)

regimes3.2s (21.2%)

simplify6.0ms (0%)

end1.0ms (0%)

sample1.7s (11.4%)

Profiling