Details

analyze2.4s (12.3%)

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
2.4%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample91.0ms (0.5%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
4.0ms	40×	body	128	nan
4.0ms	33×	body	128	invalid

Compiler

Compiled 51 to 37 computations (27.5% saved)

simplify329.0ms (1.7%)

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

prune7.0ms (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	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series440.0ms (2.2%)

Counts

3 → 128

Calls

3 calls:

379.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
39.0ms	(-.f64 1 (log.f64 t))
21.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite13.0ms (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:

7.0ms	(-.f64 1 (log.f64 t))
1.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
1.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify134.0ms (0.7%)

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

prune207.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	6	112

Error

0.0b

Counts

112 → 6

Alt Table

Status	Error	Program
	32.0b	(fma.f64 z (*.f64 (sqrt.f64 (-.f64 1 (log.f64 t))) (sqrt.f64 (-.f64 1 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 (.f64 z (log.f64 (/.f64 1 t))) (+.f64 z x)))) (*.f64 1/2 b))
	32.2b	(*.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)))))
	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	(fma.f64 z (-.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) (log.f64 (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 2531 to 1254 computations (50.5% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series451.0ms (2.3%)

Counts

4 → 60

Calls

4 calls:

402.0ms	(fma.f64 z (-.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) (log.f64 (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
18.0ms	(-.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) (log.f64 (sqrt.f64 t)))
15.0ms	(log.f64 (sqrt.f64 t))
15.0ms	(-.f64 1 (log.f64 (sqrt.f64 t)))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64`
78×	`prod-diff_binary64`
72×	`add-sqr-sqrt_binary64`
64×	`log-pow_binary64`
51×	`pow1_binary64`

Counts

4 → 187

Calls

4 calls:

19.0ms	(-.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) (log.f64 (sqrt.f64 t)))
8.0ms	(-.f64 1 (log.f64 (sqrt.f64 t)))
2.0ms	(log.f64 (sqrt.f64 t))
1.0ms	(fma.f64 z (-.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) (log.f64 (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

simplify244.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
416×	`associate-l_binary64`
359×	`exp-prod_binary64`
342×	`associate-r_binary64`
274×	`distribute-rgt-in_binary64`

Counts

247 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	5001
1	367	3786
2	1120	3246
3	4336	3246
4	5038	3246

prune506.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	250	6	256

Error

0.0b

Counts

256 → 6

Alt Table

Status	Error	Program
	32.2b	(*.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)))))
▶	0.1b	(fma.f64 z (log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	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	(fma.f64 z (-.f64 (-.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) (log.f64 (fabs.f64 (cbrt.f64 t)))) (log.f64 (sqrt.f64 (cbrt.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 (.f64 z (log.f64 (/.f64 1 t))) (+.f64 z x)))) (*.f64 1/2 b))
	0.1b	(fma.f64 z (-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 7518 to 3069 computations (59.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t)))
✓	0.1b	(fma.f64 z (log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.4b	(/.f64 (exp.f64 1) (sqrt.f64 t))
✓	0.4b	(/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))

series1.0s (5.2%)

Counts

4 → 84

Calls

4 calls:

769.0ms	(fma.f64 z (log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
246.0ms	(log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t)))
11.0ms	(/.f64 (exp.f64 1) (sqrt.f64 t))
8.0ms	(/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))

rewrite149.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

516×	`times-frac_binary64`
279×	`*-un-lft-identity_binary64`
279×	`add-sqr-sqrt_binary64`
279×	`add-cube-cbrt_binary64`
264×	`sqrt-prod_binary64`

Counts

4 → 378

Calls

4 calls:

23.0ms	(log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t)))
19.0ms	(/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))
7.0ms	(/.f64 (exp.f64 1) (sqrt.f64 t))
1.0ms	(fma.f64 z (log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

simplify541.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

558×	`log-div_binary64`
499×	`associate-/l/_binary64`
496×	`fma-def_binary64`
337×	`times-frac_binary64`
258×	`sub-neg_binary64`

Counts

462 → 480

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	398	12085
1	835	11025
2	1753	10216
3	4020	10128
4	4956	10128
5	5000	10128

prune1.2s (6.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	479	1	480
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	481	5	486

Error

0.0b

Counts

486 → 5

Alt Table

Status	Error	Program
	32.2b	(*.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)))))
✓	0.1b	(fma.f64 z (log.f64 (/.f64 (/.f64 (exp.f64 1) (sqrt.f64 t)) (sqrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 (.f64 z (log.f64 (/.f64 1 t))) (+.f64 z x)))) (*.f64 1/2 b))
	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	(fma.f64 z (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 14135 to 6638 computations (53% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (cbrt.f64 (E.f64)) t)
✓	0.1b	(fma.f64 z (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.4b	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t)))
✓	1.6b	(cbrt.f64 (E.f64))

series3.9s (19.8%)

Counts

4 → 96

Calls

4 calls:

2.4s	(fma.f64 z (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
1.2s	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t)))
272.0ms	(/.f64 (cbrt.f64 (E.f64)) t)
0.0ms	(cbrt.f64 (E.f64))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
36×	`times-frac_binary64`
34×	`log-prod_binary64`

Counts

4 → 113

Calls

4 calls:

15.0ms	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t)))
7.0ms	(/.f64 (cbrt.f64 (E.f64)) t)
1.0ms	(cbrt.f64 (E.f64))
1.0ms	(fma.f64 z (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

simplify205.0ms (1%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary64`
477×	`associate-+r+_binary64`
370×	`fma-neg_binary64`
295×	`distribute-rgt-in_binary64`
287×	`+-commutative_binary64`

Counts

209 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	4293
1	535	3675
2	1480	3476
3	4085	3476
4	4992	3476
5	4993	3476
6	5062	3476

prune227.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	217	4	221

Error

Counts

221 → 4

Alt Table

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

Compiler

Compiled 5818 to 2331 computations (59.9% saved)

regimes5.7s (28.9%)

Accuracy

Total 0.1b remaining (87.8%)

Threshold costs 0.1b (87.8%)

Counts

220 → 1

Compiler

Compiled 83319 to 56978 computations (31.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	36	35
2	44	35
3	48	35
4	51	35
5	52	35
6	51	35

end11.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 87 to 63 computations (27.6% saved)

sample1.7s (8.6%)

Algorithm

1×

intervals

Results

770.0ms	7998×	body	128	valid
147.0ms	1238×	body	128	invalid
95.0ms	1129×	body	128	nan
1.0ms	2×	body	1024	valid

Compiler

Compiled 194 to 133 computations (31.4% saved)

Details

analyze2.4s (12.3%)

sample91.0ms (0.5%)

simplify329.0ms (1.7%)

prune7.0ms (0%)

localize21.0ms (0.1%)

series440.0ms (2.2%)

rewrite13.0ms (0.1%)

simplify134.0ms (0.7%)

prune207.0ms (1%)

localize28.0ms (0.1%)

series451.0ms (2.3%)

rewrite56.0ms (0.3%)

simplify244.0ms (1.2%)

prune506.0ms (2.5%)

localize15.0ms (0.1%)

series1.0s (5.2%)

rewrite149.0ms (0.8%)

simplify541.0ms (2.7%)

prune1.2s (6.3%)

localize36.0ms (0.2%)

series3.9s (19.8%)

rewrite39.0ms (0.2%)

simplify205.0ms (1%)

prune227.0ms (1.1%)

regimes5.7s (28.9%)

simplify6.0ms (0%)

end11.0ms (0.1%)

sample1.7s (8.6%)

Profiling