Details

analyze1.2s (18.4%)

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
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.8s (28.3%)

Symmetry

(sort x y)

Results

1.3s	8254×	body	128	valid
364.0ms	2337×	body	128	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify283.0ms (4.4%)

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 (0.1%)

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
▶	0.0b	(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)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series220.0ms (3.4%)

Counts

1 → 72

Calls

1 calls:

220.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
694×	`associate--l+_binary64`
549×	`exp-diff_binary64`
441×	`associate-+l-_binary64`
298×	`associate-+l+_binary64`

Counts

82 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1752
1	183	1708
2	506	1547
3	1783	1535
4	4632	1535
5	5329	1535

prune39.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

0.0b

Counts

44 → 4

Alt Table

Status	Error	Program
✓	0.0b	(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)))))
	52.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y))) (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (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)))

Compiler

Compiled 944 to 496 computations (47.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 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)))
✓	0.2b	(-.f64 z (*.f64 z (log.f64 t)))
✓	0.3b	(*.f64 z (log.f64 t))

series629.0ms (9.8%)

Counts

3 → 100

Calls

3 calls:

210.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
210.0ms	(*.f64 z (log.f64 t))
208.0ms	(-.f64 z (*.f64 z (log.f64 t)))

rewrite14.0ms (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 z (log.f64 t))
4.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
3.0ms	(-.f64 z (*.f64 z (log.f64 t)))

simplify100.0ms (1.6%)

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 → 149

Iterations

Useful iterations: 3 (0.0ms)

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

prune126.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	150	3	153

Error

Counts

153 → 3

Alt Table

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

Compiler

Compiled 3171 to 1212 computations (61.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series959.0ms (15%)

Counts

4 → 84

Calls

4 calls:

259.0ms	(+.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)))
237.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)
233.0ms	(-.f64 (-.f64 z (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
230.0ms	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
20×	`*-un-lft-identity_binary64`
17×	`prod-diff_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 105

Calls

4 calls:

7.0ms	(+.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)))
7.0ms	(-.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)
2.0ms	(-.f64 z (*.f64 (log.f64 (sqrt.f64 t)) z))

simplify118.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
776×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
428×	`distribute-lft-in_binary64`
241×	`cancel-sign-sub-inv_binary64`

Counts

189 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	3829
1	427	3516
2	1277	3400
3	4716	3304
4	5220	3304

prune150.0ms (2.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	207	3	210

Error

Counts

210 → 3

Alt Table

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

Compiler

Compiled 5881 to 1683 computations (71.4% saved)

regimes558.0ms (8.7%)

Accuracy

Total 0.0b remaining (40.5%)

Threshold costs 0.0b (40.5%)

Counts

43 → 1

Compiler

Compiled 11155 to 7604 computations (31.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	23	20
2	28	20
3	30	20
4	31	20
5	29	20

end75.0ms (1.2%)

Remove: (sort x y)
Compiler: Compiled 149 to 100 computations (32.9% saved)

Details

analyze1.2s (18.4%)

sample1.8s (28.3%)

simplify283.0ms (4.4%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series220.0ms (3.4%)

rewrite2.0ms (0%)

simplify73.0ms (1.1%)

prune39.0ms (0.6%)

localize11.0ms (0.2%)

series629.0ms (9.8%)

rewrite14.0ms (0.2%)

simplify100.0ms (1.6%)

prune126.0ms (2%)

localize13.0ms (0.2%)

series959.0ms (15%)

rewrite25.0ms (0.4%)

simplify118.0ms (1.8%)

prune150.0ms (2.3%)

regimes558.0ms (8.7%)

simplify2.0ms (0%)

end75.0ms (1.2%)

Profiling