Details

analyze1.3s (11.8%)

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)

sample2.0s (17.9%)

Symmetry

(sort x y)

Results

1.5s	8254×	body	128	valid
423.0ms	2474×	body	128	invalid
1.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify279.0ms (2.5%)

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

0.1b

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)))

series245.0ms (2.2%)

Counts

2 → 80

Calls

2 calls:

225.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
20.0ms	(-.f64 1 (log.f64 t))

rewrite8.0ms (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:

6.0ms	(-.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)))

simplify97.0ms (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

prune89.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Error

0.0b

Counts

87 → 6

Alt Table

Status	Error	Program
	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)))))
	0.4b	(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	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(fma.f64 z (log.f64 (/.f64 (E.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)))
	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)))))

Compiler

Compiled 2077 to 1022 computations (50.8% saved)

localize44.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (log.f64 (/.f64 (E.f64) t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.4b	(/.f64 (E.f64) t)

series476.0ms (4.2%)

Counts

2 → 76

Calls

2 calls:

474.0ms	(fma.f64 z (log.f64 (/.f64 (E.f64) t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
2.0ms	(/.f64 (E.f64) t)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-exp-log_binary64`

Counts

2 → 40

Calls

2 calls:

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

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
743×	`fma-neg_binary64`
432×	`+-commutative_binary64`
373×	`exp-diff_binary64`
372×	`associate--l+_binary64`

Counts

116 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	2101
1	261	1974
2	612	1856
3	1716	1854
4	3705	1854
5	4956	1854

prune98.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	76	6	82

Error

0.0b

Counts

82 → 6

Alt Table

Status	Error	Program
	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)))))
	0.4b	(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 (log.f64 (.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.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)))
	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)))))

Compiler

Compiled 1735 to 852 computations (50.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (log.f64 (.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.f64)) t))
✓	1.0b	(*.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64)))
✓	1.6b	(cbrt.f64 (E.f64))

series494.0ms (4.4%)

Counts

4 → 84

Calls

4 calls:

491.0ms	(fma.f64 z (log.f64 (.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
3.0ms	(.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.f64)) t))
0.0ms	(cbrt.f64 (E.f64))
0.0ms	(*.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
29×	`cbrt-prod_binary64`
28×	`associate-r_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 112

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.f64)) t))
4.0ms	(*.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64)))
1.0ms	(cbrt.f64 (E.f64))
0.0ms	(fma.f64 z (log.f64 (.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (/.f64 (cbrt.f64 (E.f64)) t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

simplify353.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-/l*_binary64`
400×	`fma-def_binary64`
371×	`associate-*l/_binary64`
359×	`associate-*r/_binary64`
346×	`times-frac_binary64`

Counts

196 → 191

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	3296
1	437	2991
2	1522	2866
3	4431	2825
4	4982	2825
5	4980	2825

prune340.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	221	6	227

Error

0.0b

Counts

227 → 6

Alt Table

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

Compiler

Compiled 5812 to 2093 computations (64% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2))
✓	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 (23.2%)

Counts

4 → 108

Calls

4 calls:

1.3s	(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)))
650.0ms	(-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2))
647.0ms	(-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t)))
32.0ms	(cbrt.f64 t)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
20×	`add-cube-cbrt_binary64`
9×	`log-pow_binary64`

Counts

4 → 95

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2)) (log.f64 (cbrt.f64 t)))
2.0ms	(-.f64 1 (*.f64 (log.f64 (cbrt.f64 t)) 2))
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)))

simplify132.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-neg_binary64`
417×	`distribute-rgt-in_binary64`
404×	`cancel-sign-sub-inv_binary64`
362×	`distribute-lft-in_binary64`
180×	`distribute-rgt-neg-in_binary64`

Counts

203 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	3991
1	478	3219
2	1681	2848
3	4535	2846
4	4762	2846

prune269.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	195	5	200

Error

0.0b

Counts

200 → 5

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (fma.f64 a b (+.f64 y x)) z) (fma.f64 3 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 t)) (cbrt.f64 -1))) z) (*.f64 b 1/2)))
	0.1b	(fma.f64 z (log.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64)))) (log.f64 (/.f64 (cbrt.f64 (E.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)))
	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)))))

Compiler

Compiled 5294 to 2566 computations (51.5% saved)

regimes2.1s (18.3%)

Accuracy

Total 0.1b remaining (77.7%)

Threshold costs 0.1b (77.7%)

Counts

134 → 1

Compiler

Compiled 38905 to 27468 computations (29.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	30
1	27	30
2	30	30
3	28	30

end121.0ms (1.1%)

Remove: (sort x y)
Compiler: Compiled 244 to 172 computations (29.5% saved)

Details

analyze1.3s (11.8%)

sample2.0s (17.9%)

simplify279.0ms (2.5%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series245.0ms (2.2%)

rewrite8.0ms (0.1%)

simplify97.0ms (0.9%)

prune89.0ms (0.8%)

localize44.0ms (0.4%)

series476.0ms (4.2%)

rewrite4.0ms (0%)

simplify90.0ms (0.8%)

prune98.0ms (0.9%)

localize16.0ms (0.1%)

series494.0ms (4.4%)

rewrite23.0ms (0.2%)

simplify353.0ms (3.1%)

prune340.0ms (3%)

localize16.0ms (0.1%)

series2.6s (23.2%)

rewrite16.0ms (0.1%)

simplify132.0ms (1.2%)

prune269.0ms (2.4%)

regimes2.1s (18.3%)

simplify2.0ms (0%)

end121.0ms (1.1%)

Profiling