Details

analyze1.2s (15.3%)

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
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.8s (23.3%)

Symmetry

(sort x y)

Results

1.3s	8253×	body	128	valid
361.0ms	2380×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify280.0ms (3.7%)

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	(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 2 expressions with local error:

New	Error	Program
✓	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)))

series218.0ms (2.9%)

Counts

2 → 120

Calls

2 calls:

208.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
10.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite1.0ms (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))

simplify89.0ms (1.2%)

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

prune61.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Error

0.0b

Counts

69 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x) (fma.f64 b (-.f64 a 1/2) y))
	13.7b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	32.8b	(*.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	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 1315 to 686 computations (47.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series330.0ms (4.3%)

Counts

3 → 144

Calls

3 calls:

224.0ms	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x) (fma.f64 b (-.f64 a 1/2) y))
99.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) x)
6.0ms	(fma.f64 b (-.f64 a 1/2) y)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`fma-udef_binary64`

Counts

3 → 39

Calls

3 calls:

2.0ms	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x) (fma.f64 b (-.f64 a 1/2) y))
0.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) x)
0.0ms	(fma.f64 b (-.f64 a 1/2) y)

simplify124.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
405×	`associate-+l+_binary64`
394×	`sub-neg_binary64`
370×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`

Counts

183 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	2966
1	293	2734
2	785	2605
3	3751	2601
4	4885	2601
5	5026	2601

prune79.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

0.0b

Counts

87 → 5

Alt Table

Status	Error	Program
	0.1b	(+.f64 (fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x)) y)
	13.7b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
	47.3b	(/.f64 (-.f64 (.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x) (fma.f64 z (-.f64 1 (log.f64 t)) x)) (.f64 (fma.f64 b (-.f64 a 1/2) y) (fma.f64 b (-.f64 a 1/2) y))) (-.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x) (fma.f64 b (-.f64 a 1/2) y)))
▶	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	43.3b	(+.f64 (*.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x)) (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) x))) (fma.f64 b (-.f64 a 1/2) y))

Compiler

Compiled 1792 to 981 computations (45.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series628.0ms (8.3%)

Counts

3 → 100

Calls

3 calls:

212.0ms	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
211.0ms	(*.f64 z (log.f64 t))
204.0ms	(-.f64 z (*.f64 z (log.f64 t)))

rewrite13.0ms (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)))

simplify105.0ms (1.4%)

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

prune189.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	174	5	179

Error

0.0b

Counts

179 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x)) y)
	14.5b	(+.f64 (/.f64 (.f64 z (-.f64 z (.f64 z (*.f64 (log.f64 t) (log.f64 t))))) (fma.f64 z (log.f64 t) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	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)))

Compiler

Compiled 3815 to 1494 computations (60.8% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series372.0ms (4.9%)

Counts

2 → 132

Calls

2 calls:

200.0ms	(+.f64 (fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x)) y)
172.0ms	(fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x)) y)
0.0ms	(fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x))

simplify111.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

767×	`exp-sum_binary64`
399×	`associate-+l+_binary64`
364×	`sub-neg_binary64`
351×	`fma-neg_binary64`
309×	`associate--l+_binary64`

Counts

160 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	3244
1	302	3006
2	779	2878
3	3370	2878
4	4535	2878
5	5480	2878

prune92.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Error

0.0b

Counts

101 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 b (-.f64 a 1/2) (fma.f64 z (-.f64 1 (log.f64 t)) x)) y)
	14.5b	(+.f64 (/.f64 (.f64 z (-.f64 z (.f64 z (*.f64 (log.f64 t) (log.f64 t))))) (fma.f64 z (log.f64 t) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (-.f64 z (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	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)))

Compiler

Compiled 1922 to 1014 computations (47.2% saved)

regimes1.7s (22.3%)

Accuracy

Total 0.1b remaining (76.6%)

Threshold costs 0.1b (76.6%)

Counts

139 → 1

Compiler

Compiled 36075 to 25008 computations (30.7% 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

end219.0ms (2.9%)

Compiler: Compiled 214 to 139 computations (35% saved)

Details

analyze1.2s (15.3%)

sample1.8s (23.3%)

simplify280.0ms (3.7%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series218.0ms (2.9%)

rewrite1.0ms (0%)

simplify89.0ms (1.2%)

prune61.0ms (0.8%)

localize11.0ms (0.1%)

series330.0ms (4.3%)

rewrite4.0ms (0.1%)

simplify124.0ms (1.6%)

prune79.0ms (1%)

localize11.0ms (0.1%)

series628.0ms (8.3%)

rewrite13.0ms (0.2%)

simplify105.0ms (1.4%)

prune189.0ms (2.5%)

localize12.0ms (0.2%)

series372.0ms (4.9%)

rewrite4.0ms (0%)

simplify111.0ms (1.5%)

prune92.0ms (1.2%)

regimes1.7s (22.3%)

simplify2.0ms (0%)

end219.0ms (2.9%)

Profiling