Details

analyze1.3s (10.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	74.8%	25.2%	5
0%	74.8%	25.2%	6
0%	74.8%	25.2%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	62.3%	37.7%	10
0%	56.1%	43.9%	11
0%	56.1%	43.9%	12
1.6%	54.5%	43.9%	13
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample2.0s (15.8%)

Symmetry

(sort x y)

Results

1.5s	8251×	body	128	valid
417.0ms	2485×	body	128	invalid
2.0ms	3×	body	1024	valid
1.0ms	2×	body	512	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify293.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

5327×	`fma-def_binary64`
866×	`fma-neg_binary64`
705×	`sub-neg_binary64`
654×	`unsub-neg_binary64`
445×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	101	22
3	269	21
4	805	20
5	2079	20
6	2787	20
7	3848	20
8	4164	20
9	4306	20
10	4090	20
11	4094	20
12	4190	20
13	4488	20
14	4581	20
15	4587	20
16	4587	20
17	4593	20
18	4599	20
19	4599	20
20	4617	20
21	4601	20
22	4601	20
23	9364	20

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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series269.0ms (2.2%)

Counts

3 → 128

Calls

3 calls:

237.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
21.0ms	(-.f64 1 (log.f64 t))
10.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(-.f64 1 (log.f64 t))
2.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
593×	`exp-sum_binary64`
523×	`fma-def_binary64`
300×	`associate-+l+_binary64`
285×	`sub-neg_binary64`

Counts

187 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2997
1	318	2754
2	918	2521
3	3268	2521
4	4379	2521
5	5221	2521

prune119.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	7	112

Error

0.0b

Counts

112 → 7

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y))))) (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
▶	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.2b	(fma.f64 z (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	14.0b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	35.5b	(*.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))

Compiler

Compiled 2523 to 1248 computations (50.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.2b	(*.f64 z (log.f64 t))
✓	0.3b	(-.f64 z (*.f64 z (log.f64 t)))

series439.0ms (3.5%)

Counts

2 → 28

Calls

2 calls:

229.0ms	(-.f64 z (*.f64 z (log.f64 t)))
209.0ms	(*.f64 z (log.f64 t))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
6×	`distribute-lft-in_binary64`

Counts

2 → 53

Calls

2 calls:

13.0ms	(*.f64 z (log.f64 t))
3.0ms	(-.f64 z (*.f64 z (log.f64 t)))

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-neg_binary64`
355×	`unsub-neg_binary64`
270×	`fma-def_binary64`
267×	`times-frac_binary64`
252×	`sub-neg_binary64`

Counts

81 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	948
1	220	821
2	634	776
3	1726	774
4	3513	774
5	4916	774
6	4967	774
7	4791	774

prune139.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	117	5	122

Error

Counts

122 → 5

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	14.0b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	0.1b	(+.f64 (-.f64 z (+.f64 (.f64 z (.f64 (log.f64 (cbrt.f64 t)) 2)) (*.f64 z (log.f64 (cbrt.f64 t))))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(+.f64 (-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 z (log.f64 (cbrt.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 2598 to 1048 computations (59.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (log.f64 (cbrt.f64 t)))
✓	0.3b	(-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 z (log.f64 (cbrt.f64 t))))
✓	0.3b	(fma.f64 z (*.f64 (log.f64 (cbrt.f64 t)) -2) z)
✓	0.6b	(cbrt.f64 t)

series4.8s (38.6%)

Counts

4 → 84

Calls

4 calls:

2.5s	(-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 z (log.f64 (cbrt.f64 t))))
1.2s	(*.f64 z (log.f64 (cbrt.f64 t)))
1.1s	(fma.f64 z (*.f64 (log.f64 (cbrt.f64 t)) -2) z)
32.0ms	(cbrt.f64 t)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`log-prod_binary64`
19×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`cbrt-prod_binary64`

Counts

4 → 90

Calls

4 calls:

4.0ms	(*.f64 z (log.f64 (cbrt.f64 t)))
3.0ms	(-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 z (log.f64 (cbrt.f64 t))))
1.0ms	(cbrt.f64 t)
0.0ms	(fma.f64 z (*.f64 (log.f64 (cbrt.f64 t)) -2) z)

simplify139.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-neg_binary64`
551×	`fma-def_binary64`
304×	`exp-prod_binary64`
298×	`log-prod_binary64`
248×	`*-commutative_binary64`

Counts

174 → 160

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	162	2782
1	361	2311
2	1081	2065
3	3126	2060
4	4367	2044
5	4743	2024
6	4778	2024

prune224.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	178	5	183

Error

Counts

183 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (*.f64 z (-.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	14.0b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	0.1b	(+.f64 (-.f64 z (+.f64 (.f64 z (.f64 (log.f64 (cbrt.f64 t)) 2)) (*.f64 z (log.f64 (cbrt.f64 t))))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.1b	(+.f64 (-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 z (log.f64 (cbrt.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 5382 to 2276 computations (57.7% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
	0.0b	(-.f64 1 (log.f64 t))
✓	0.3b	(*.f64 z (-.f64 1 (log.f64 t)))

series244.0ms (2%)

Counts

1 → 24

Calls

1 calls:

244.0ms

(*.f64 z (-.f64 1 (log.f64 t)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
17×	`distribute-lft-in_binary64`

Counts

1 → 60

Calls

1 calls:

7.0ms

(*.f64 z (-.f64 1 (log.f64 t)))

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
641×	`fma-neg_binary64`
476×	`associate-+l+_binary64`
455×	`associate-+r+_binary64`
302×	`distribute-rgt-neg-out_binary64`

Counts

84 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1157
1	172	1023
2	564	899
3	1294	824
4	3119	824
5	4632	824
6	4928	824
7	4745	824

prune161.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	136	5	141

Error

Counts

141 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (*.f64 z (-.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	14.0b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	0.1b	(+.f64 (-.f64 z (+.f64 (.f64 z (.f64 (log.f64 (cbrt.f64 t)) 2)) (*.f64 z (log.f64 (cbrt.f64 t))))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.1b	(+.f64 (-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 z (log.f64 (cbrt.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 3507 to 1607 computations (54.2% saved)

regimes1.8s (14.6%)

Accuracy

Total 0.1b remaining (78.5%)

Threshold costs 0.1b (78.5%)

Counts

125 → 1

Compiler

Compiled 38483 to 25243 computations (34.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	26	22
2	31	22
3	33	22
4	34	22
5	32	22

end96.0ms (0.8%)

Remove: (sort x y)
Compiler: Compiled 209 to 140 computations (33% saved)

Details

analyze1.3s (10.3%)

sample2.0s (15.8%)

simplify293.0ms (2.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series269.0ms (2.2%)

rewrite8.0ms (0.1%)

simplify122.0ms (1%)

prune119.0ms (1%)

localize12.0ms (0.1%)

series439.0ms (3.5%)

rewrite19.0ms (0.2%)

simplify122.0ms (1%)

prune139.0ms (1.1%)

localize19.0ms (0.2%)

series4.8s (38.6%)

rewrite13.0ms (0.1%)

simplify139.0ms (1.1%)

prune224.0ms (1.8%)

localize13.0ms (0.1%)

series244.0ms (2%)

rewrite11.0ms (0.1%)

simplify107.0ms (0.9%)

prune161.0ms (1.3%)

regimes1.8s (14.6%)

simplify3.0ms (0%)

end96.0ms (0.8%)

Profiling