Details

analyze1.2s (14.1%)

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
0%	56.1%	43.9%	13
0%	56.1%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample3.2s (36.2%)

Symmetry

(sort x y)

Results

1.8s	8254×	body	128	valid
1.0s	623×	body	8192	exit
323.0ms	1829×	body	128	invalid
1.0ms	2×	body	1024	valid

Compiler

Compiled 45 to 31 computations (31.1% saved)

simplify285.0ms (3.2%)

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))
▶	0.0b	(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)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series245.0ms (2.8%)

Counts

2 → 120

Calls

2 calls:

234.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
11.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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))

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

688×	`associate--l+_binary64`
559×	`exp-diff_binary64`
446×	`associate-+l-_binary64`
320×	`associate-l_binary64`
296×	`associate-r_binary64`

Counts

140 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	2481
1	211	2304
2	554	2131
3	2029	2131
4	4532	2131
5	5214	2131

prune59.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Error

0.0b

Counts

69 → 4

Alt Table

Status	Error	Program
	13.5b	(-.f64 (+.f64 (.f64 a b) (+.f64 y 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	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 1329 to 690 computations (48.1% saved)

localize13.0ms (0.2%)

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))

series611.0ms (6.9%)

Counts

4 → 140

Calls

4 calls:

229.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
223.0ms	(*.f64 z (log.f64 t))
152.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
6.0ms	(*.f64 (-.f64 a 1/2) b)

rewrite35.0ms (0.4%)

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)))
5.0ms	(*.f64 (-.f64 a 1/2) b)
4.0ms	(*.f64 z (log.f64 t))

simplify148.0ms (1.7%)

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

prune242.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	204	4	208
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	206	6	212

Error

0.0b

Counts

212 → 6

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 z (log.f64 t) (*.f64 b (-.f64 1/2 a))))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	13.5b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (log.f64 t)))) (.f64 (-.f64 a 1/2) b))
	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))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 5351 to 1946 computations (63.6% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series387.0ms (4.4%)

Counts

3 → 132

Calls

3 calls:

233.0ms	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 z (log.f64 t) (*.f64 b (-.f64 1/2 a))))
149.0ms	(fma.f64 z (log.f64 t) (*.f64 b (-.f64 1/2 a)))
5.0ms	(*.f64 b (-.f64 1/2 a))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
33×	`prod-diff_binary64`
29×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out_binary64`

Counts

3 → 104

Calls

3 calls:

9.0ms	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 z (log.f64 t) (*.f64 b (-.f64 1/2 a))))
6.0ms	(*.f64 b (-.f64 1/2 a))
0.0ms	(fma.f64 z (log.f64 t) (*.f64 b (-.f64 1/2 a)))

simplify134.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

430×	`associate-+r+_binary64`
345×	`exp-sum_binary64`
304×	`*-commutative_binary64`
299×	`associate--l+_binary64`
273×	`exp-prod_binary64`

Counts

236 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	4547
1	487	4140
2	1709	3857
3	4028	3857
4	4868	3857

prune177.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	163	6	169

Error

Counts

169 → 6

Alt Table

Status	Error	Program
	13.5b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
▶	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 b (-.f64 1/2 a) (*.f64 z (log.f64 t))))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (log.f64 t)))) (.f64 (-.f64 a 1/2) b))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	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))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 4438 to 1887 computations (57.5% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series367.0ms (4.2%)

Counts

2 → 120

Calls

2 calls:

224.0ms	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 b (-.f64 1/2 a) (*.f64 z (log.f64 t))))
142.0ms	(fma.f64 b (-.f64 1/2 a) (*.f64 z (log.f64 t)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
15×	`distribute-lft-out_binary64`
15×	`prod-diff_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

9.0ms	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 b (-.f64 1/2 a) (*.f64 z (log.f64 t))))
0.0ms	(fma.f64 b (-.f64 1/2 a) (*.f64 z (log.f64 t)))

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

615×	`distribute-rgt-in_binary64`
615×	`fma-def_binary64`
597×	`distribute-lft-in_binary64`
444×	`associate-l_binary64`
362×	`fma-neg_binary64`

Counts

174 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	3917
1	348	3577
2	1177	3181
3	4621	3181
4	4919	3181

prune239.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
	0.3b	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 b (-.f64 1/2 a) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (log.f64 t) (cbrt.f64 z)))))
✓	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 b (-.f64 1/2 a) (*.f64 z (log.f64 t))))
	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (fma.f64 b (-.f64 1/2 a) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))))
	13.5b	(fma.f64 b -1/2 (fma.f64 a b (+.f64 y x)))
	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))
✓	0.0b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 3365 to 1292 computations (61.6% saved)

regimes1.0s (11.7%)

Accuracy

Total 0.1b remaining (74.9%)

Threshold costs 0.1b (74.9%)

Counts

82 → 1

Compiler

Compiled 21229 to 14484 computations (31.8% saved)

simplify3.0ms (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

end106.0ms (1.2%)

Remove: (sort x y)
Compiler: Compiled 223 to 147 computations (34.1% saved)

Details

analyze1.2s (14.1%)

sample3.2s (36.2%)

simplify285.0ms (3.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series245.0ms (2.8%)

rewrite2.0ms (0%)

simplify95.0ms (1.1%)

prune59.0ms (0.7%)

localize13.0ms (0.2%)

series611.0ms (6.9%)

rewrite35.0ms (0.4%)

simplify148.0ms (1.7%)

prune242.0ms (2.7%)

localize13.0ms (0.1%)

series387.0ms (4.4%)

rewrite26.0ms (0.3%)

simplify134.0ms (1.5%)

prune177.0ms (2%)

localize13.0ms (0.1%)

series367.0ms (4.2%)

rewrite15.0ms (0.2%)

simplify121.0ms (1.4%)

prune239.0ms (2.7%)

regimes1.0s (11.7%)

simplify3.0ms (0%)

end106.0ms (1.2%)

Profiling