Details

analyze1.4s (14.4%)

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)

sample56.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
4.0ms	48×	body	128	invalid
3.0ms	43×	body	128	nan

Compiler

Compiled 51 to 37 computations (27.5% saved)

simplify295.0ms (3%)

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

0.0b

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)

localize11.0ms (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)))

rewrite11.0ms (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))
0.0ms	(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))

series759.0ms (7.8%)

Counts

3 → 128

Calls

3 calls:

537.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
193.0ms	(-.f64 1 (log.f64 t))
28.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify141.0ms (1.5%)

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 → 339

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

prune124.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	334	5	339
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	336	5	341

Error

0.0b

Counts

341 → 5

Alt Table

Status	Error	Program
	32.0b	(fma.f64 z (+.f64 1 (*.f64 (neg.f64 (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.3b	(fma.f64 z (log.f64 (/.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)))))
▶	0.1b	(+.f64 (-.f64 z (*.f64 z (log.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 2524 to 1234 computations (51.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 78

Calls

3 calls:

4.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
3.0ms	(*.f64 z (log.f64 t))
3.0ms	(-.f64 z (*.f64 z (log.f64 t)))

series1.5s (15.3%)

Counts

3 → 100

Calls

3 calls:

509.0ms	(-.f64 z (*.f64 z (log.f64 t)))
492.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
483.0ms	(*.f64 z (log.f64 t))

simplify127.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

505×	`distribute-rgt-in_binary64`
477×	`distribute-lft-in_binary64`
290×	`associate--l+_binary64`
285×	`fma-neg_binary64`
196×	`cancel-sign-sub-inv_binary64`

Counts

178 → 329

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2995
1	428	2851
2	1358	2795
3	4581	2793
4	4960	2793

prune169.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	434	2	436
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	436	5	441

Error

Counts

441 → 5

Alt Table

Status	Error	Program
	32.0b	(fma.f64 z (+.f64 1 (*.f64 (neg.f64 (sqrt.f64 (log.f64 t))) (sqrt.f64 (log.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)))
	0.3b	(fma.f64 z (log.f64 (/.f64 E.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 z (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.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)))

Compiler

Compiled 3863 to 1503 computations (61.1% saved)

localize230.0ms (2.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
✓	0.3b	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))
	0.3b	(*.f64 (log.f64 (sqrt.f64 t)) z)
✓	0.3b	(*.f64 (log.f64 (sqrt.f64 t)) z)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`prod-diff_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 73

Calls

3 calls:

6.0ms	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
3.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)
3.0ms	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))

series1.0s (10.6%)

Counts

3 → 24

Calls

3 calls:

363.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)
339.0ms	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
327.0ms	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-neg_binary64`
543×	`cancel-sign-sub-inv_binary64`
431×	`associate-l_binary64`
392×	`associate-r_binary64`
334×	`fma-def_binary64`

Counts

97 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1521
1	245	1297
2	631	1229
3	2700	1222
4	4898	1222
5	4878	1222

prune143.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
	0.3b	(fma.f64 z (log.f64 (/.f64 E.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 z (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.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)))
▶	0.1b	(+.f64 (-.f64 (.f64 (-.f64 1 (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 3970 to 1180 computations (70.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (sqrt.f64 t))
✓	0.2b	(-.f64 (.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) z) (.f64 (log.f64 (sqrt.f64 t)) z))
✓	0.3b	(*.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) z)
	0.3b	(*.f64 (log.f64 (sqrt.f64 t)) z)

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
8×	`pow1_binary64`
7×	`associate-l_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

35.0ms	(*.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) z)
6.0ms	(-.f64 (.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) z) (.f64 (log.f64 (sqrt.f64 t)) z))
1.0ms	(log.f64 (sqrt.f64 t))

series685.0ms (7.1%)

Counts

3 → 12

Calls

3 calls:

349.0ms	(-.f64 (.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) z) (.f64 (log.f64 (sqrt.f64 t)) z))
329.0ms	(*.f64 (-.f64 1 (log.f64 (sqrt.f64 t))) z)
6.0ms	(log.f64 (sqrt.f64 t))

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-+l+_binary64`
337×	`associate-l_binary64`
267×	`associate-+r+_binary64`
265×	`associate-r_binary64`
257×	`fma-def_binary64`

Counts

74 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	1186
1	227	1070
2	642	933
3	1879	925
4	4737	923
5	5003	923

prune125.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	189	4	193

Error

Counts

193 → 4

Alt Table

Status	Error	Program
	0.3b	(fma.f64 z (log.f64 (/.f64 E.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 z (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.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)))
✓	0.1b	(+.f64 (-.f64 (.f64 (-.f64 1 (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 3334 to 1408 computations (57.8% saved)

regimes1.2s (12.2%)

Accuracy

Total 0.1b remaining (75.9%)

Threshold costs 0.1b (75.9%)

Compiler

Compiled 21764 to 14713 computations (32.4% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	34	34
2	45	34
3	51	34
4	55	34
5	56	34
6	54	34

end7.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 84 to 54 computations (35.7% saved)

sample1.4s (14.6%)

Algorithm

1×

intervals

Results

695.0ms	7996×	body	128	valid
86.0ms	1171×	body	128	invalid
74.0ms	1126×	body	128	nan
0.0ms	3×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 156 to 105 computations (32.7% saved)

Details

analyze1.4s (14.4%)

sample56.0ms (0.6%)

simplify295.0ms (3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite11.0ms (0.1%)

series759.0ms (7.8%)

simplify141.0ms (1.5%)

prune124.0ms (1.3%)

localize13.0ms (0.1%)

rewrite15.0ms (0.2%)

series1.5s (15.3%)

simplify127.0ms (1.3%)

prune169.0ms (1.7%)

localize230.0ms (2.4%)

rewrite17.0ms (0.2%)

series1.0s (10.6%)

simplify110.0ms (1.1%)

prune143.0ms (1.5%)

localize15.0ms (0.2%)

rewrite45.0ms (0.5%)

series685.0ms (7.1%)

simplify93.0ms (1%)

prune125.0ms (1.3%)

regimes1.2s (12.2%)

simplify7.0ms (0.1%)

end7.0ms (0.1%)

sample1.4s (14.6%)

Profiling