Details

analyze1.2s (11.4%)

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 (17.3%)

Symmetry

(sort x y)

Results

1.3s	8253×	body	128	valid
380.0ms	2399×	body	128	invalid
1.0ms	3×	body	512	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify281.0ms (2.7%)

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

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	(+.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 2 expressions with local error:

New	Error	Program
✓	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)))

series242.0ms (2.3%)

Counts

2 → 80

Calls

2 calls:

221.0ms	(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))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
12×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(-.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)))

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-neg_binary64`
596×	`exp-sum_binary64`
500×	`fma-def_binary64`
311×	`associate-+l+_binary64`
273×	`associate-l_binary64`

Counts

129 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2268
1	290	2158
2	870	1937
3	3022	1936
4	4102	1936
5	4929	1936

prune92.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Error

0.0b

Counts

87 → 5

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 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.3b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (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)))
	0.3b	(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)))

Compiler

Compiled 1939 to 938 computations (51.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (cbrt.f64 t))
✓	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)))
✓	0.3b	(-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t)))
✓	0.6b	(cbrt.f64 t)

series2.6s (24.9%)

Counts

4 → 108

Calls

4 calls:

1.4s	(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)))
606.0ms	(log.f64 (cbrt.f64 t))
571.0ms	(-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t)))
29.0ms	(cbrt.f64 t)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
12×	`log-prod_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t)))
1.0ms	(log.f64 (cbrt.f64 t))
1.0ms	(cbrt.f64 t)
0.0ms	(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)))

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

429×	`fma-neg_binary64`
375×	`exp-prod_binary64`
363×	`distribute-rgt-in_binary64`
337×	`distribute-lft-in_binary64`
336×	`cancel-sign-sub-inv_binary64`

Counts

201 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3755
1	415	3080
2	1456	2705
3	4208	2705
4	4961	2705

prune300.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	210	4	214

Error

0.0b

Counts

214 → 4

Alt Table

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

Compiler

Compiled 5612 to 2633 computations (53.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
✓	0.0b	(*.f64 (-.f64 a 1/2) b)
✓	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
✓	0.2b	(*.f64 z (log.f64 t))

series576.0ms (5.6%)

Counts

4 → 140

Calls

4 calls:

224.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
214.0ms	(*.f64 z (log.f64 t))
133.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
5.0ms	(*.f64 (-.f64 a 1/2) b)

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
27×	`add-log-exp_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`

Counts

4 → 116

Calls

4 calls:

11.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
7.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
4.0ms	(*.f64 (-.f64 a 1/2) b)
3.0ms	(*.f64 z (log.f64 t))

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

395×	`associate--l+_binary64`
356×	`fma-neg_binary64`
311×	`exp-sum_binary64`
252×	`cancel-sign-sub-inv_binary64`
193×	`associate--r+_binary64`

Counts

256 → 208

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	4510
1	661	4261
2	2495	4222
3	4593	4222
4	5122	4222

prune200.0ms (1.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	208	4	212

Error

Counts

212 → 4

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 (+.f64 x y) z) (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (*.f64 (-.f64 a 1/2) b))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 1/2 b) (.f64 3 (.f64 (log.f64 (pow.f64 t 1/3)) z))))
✓	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 5238 to 1876 computations (64.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 a 1/2) b)
✓	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (log.f64 (sqrt.f64 t)) z))
✓	0.1b	(-.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
✓	0.2b	(*.f64 (log.f64 (sqrt.f64 t)) z)

series533.0ms (5.2%)

Counts

3 → 72

Calls

3 calls:

233.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)
155.0ms	(-.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
145.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (log.f64 (sqrt.f64 t)) z))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-log-exp_binary64`
25×	`*-un-lft-identity_binary64`
13×	`prod-diff_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`associate--l+_binary64`

Counts

3 → 82

Calls

3 calls:

9.0ms	(-.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z))
6.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (log.f64 (sqrt.f64 t)) z))
3.0ms	(*.f64 (log.f64 (sqrt.f64 t)) z)

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-neg_binary64`
540×	`distribute-rgt-in_binary64`
538×	`fma-def_binary64`
503×	`distribute-lft-in_binary64`
386×	`associate-l_binary64`

Counts

154 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2781
1	318	2525
2	938	2327
3	4719	2327
4	5269	2327

prune194.0ms (1.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	221	4	225

Error

Counts

225 → 4

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 (+.f64 x y) z) (.f64 (log.f64 (sqrt.f64 t)) z)) (.f64 (log.f64 (sqrt.f64 t)) z)) (*.f64 (-.f64 a 1/2) b))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 1/2 b) (.f64 3 (.f64 (log.f64 (pow.f64 t 1/3)) z))))
✓	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 6519 to 1782 computations (72.7% saved)

regimes1.7s (16.7%)

Accuracy

Total 0.0b remaining (69.8%)

Threshold costs 0.0b (69.8%)

Counts

127 → 1

Compiler

Compiled 37557 to 25546 computations (32% 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

end84.0ms (0.8%)

Remove: (sort x y)
Compiler: Compiled 184 to 125 computations (32.1% saved)

Details

analyze1.2s (11.4%)

sample1.8s (17.3%)

simplify281.0ms (2.7%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series242.0ms (2.3%)

rewrite6.0ms (0.1%)

simplify93.0ms (0.9%)

prune92.0ms (0.9%)

localize15.0ms (0.2%)

series2.6s (24.9%)

rewrite13.0ms (0.1%)

simplify109.0ms (1.1%)

prune300.0ms (2.9%)

localize13.0ms (0.1%)

series576.0ms (5.6%)

rewrite31.0ms (0.3%)

simplify134.0ms (1.3%)

prune200.0ms (1.9%)

localize13.0ms (0.1%)

series533.0ms (5.2%)

rewrite23.0ms (0.2%)

simplify96.0ms (0.9%)

prune194.0ms (1.9%)

regimes1.7s (16.7%)

simplify2.0ms (0%)

end84.0ms (0.8%)

Profiling