Details

analyze456.0ms (5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
0%	31.2%	68.8%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	28.1%	71.9%	10
4.7%	21.8%	73.5%	11
4.7%	21.8%	73.5%	12
7%	19.5%	73.5%	13
8.2%	17.5%	74.3%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample2.6s (28.5%)

Results

1.1s	6006×	body	128	valid
527.0ms	675×	body	1024	valid
436.0ms	882×	body	512	valid
223.0ms	675×	body	256	valid
46.0ms	294×	body	128	invalid
19.0ms	18×	body	2048	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-neg_binary64`
326×	`fma-def_binary64`
173×	`distribute-rgt-in_binary64`
134×	`unsub-neg_binary64`
124×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	25	17
2	46	17
3	71	17
4	112	17
5	173	17
6	293	17
7	437	17
8	681	17
9	1080	17
10	1312	17
11	1523	17
12	1539	17
13	1539	17
14	1492	17

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (log1p.f64 (neg.f64 y)))
✓	0.0b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
✓	0.2b	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

series878.0ms (9.7%)

Counts

3 → 108

Calls

3 calls:

463.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))
253.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
162.0ms	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

6.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
2.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))
0.0ms	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

simplify154.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

368×	`distribute-neg-in_binary64`
341×	`distribute-rgt-in_binary64`
316×	`fma-neg_binary64`
292×	`times-frac_binary64`
259×	`sub-neg_binary64`

Counts

169 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3071
1	634	2835
2	2073	2748
3	4555	2748
4	4988	2748
5	4921	2748

prune142.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	5	170

Error

0.1b

Counts

170 → 5

Alt Table

Status	Error	Program
	0.7b	(+.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 (neg.f64 y)))) (.f64 (neg.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
	33.9b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 (neg.f64 y))))) (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))))) t)
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 (neg.f64 y))))) (cbrt.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 (neg.f64 y)))))) (cbrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))))) t)
	29.0b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) 3)) t)
▶	0.1b	(-.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)

Compiler

Compiled 3729 to 1337 computations (64.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
✓	0.0b	(.f64 1/2 (.f64 (pow.f64 y 2) z))
✓	0.3b	(*.f64 (log.f64 y) x)
✓	10.0b	(*.f64 (pow.f64 y 2) z)

series424.0ms (4.7%)

Counts

4 → 56

Calls

4 calls:

268.0ms	(*.f64 (log.f64 y) x)
137.0ms	(-.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
10.0ms	(.f64 1/2 (.f64 (pow.f64 y 2) z))
8.0ms	(*.f64 (pow.f64 y 2) z)

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-exp-log_binary64`
20×	`add-cube-cbrt_binary64`
15×	`associate-l_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(-.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
6.0ms	(.f64 1/2 (.f64 (pow.f64 y 2) z))
4.0ms	(*.f64 (pow.f64 y 2) z)
3.0ms	(*.f64 (log.f64 y) x)

simplify126.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

410×	`*-commutative_binary64`
375×	`exp-prod_binary64`
272×	`distribute-rgt-in_binary64`
264×	`distribute-lft-in_binary64`
248×	`fma-neg_binary64`

Counts

167 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	2856
1	486	2541
2	1511	2445
3	3661	2439
4	4814	2439
5	4841	2439

prune222.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	179	4	183
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	182	6	188

Error

0.0b

Counts

188 → 6

Alt Table

Status	Error	Program
	33.9b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (.f64 z (log1p.f64 (neg.f64 y))))) (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))))) t)
	0.7b	(+.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
	29.0b	(-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) 3)) t)
	33.6b	(-.f64 (-.f64 (.f64 (.f64 (log.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
▶	0.5b	(-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
	0.6b	(-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 y) x)) (cbrt.f64 (.f64 (log.f64 y) x))) (cbrt.f64 (.f64 (log.f64 y) x))) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)

Compiler

Compiled 5109 to 2399 computations (53% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (*.f64 (cbrt.f64 (log.f64 y)) x))
✓	0.5b	(cbrt.f64 (log.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))
	10.0b	(*.f64 (pow.f64 y 2) z)

series929.0ms (10.2%)

Counts

3 → 48

Calls

3 calls:

373.0ms	(cbrt.f64 (log.f64 y))
353.0ms	(*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))
203.0ms	(.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (*.f64 (cbrt.f64 (log.f64 y)) x))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
28×	`cbrt-prod_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 85

Calls

3 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (*.f64 (cbrt.f64 (log.f64 y)) x))
5.0ms	(*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))
1.0ms	(cbrt.f64 (log.f64 y))

simplify105.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

582×	`log-prod_binary64`
429×	`distribute-rgt-neg-out_binary64`
387×	`neg-mul-1_binary64`
357×	`distribute-lft-neg-out_binary64`
338×	`exp-prod_binary64`

Counts

133 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	99	1212
1	202	1025
2	654	975
3	1391	957
4	3802	877
5	4826	877
6	5104	877

prune220.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	186	8	194

Error

0.0b

Counts

194 → 8

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	33.6b	(-.f64 (-.f64 (.f64 (.f64 (log.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	0.6b	(-.f64 (-.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
✓	0.5b	(-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
	0.5b	(-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (cbrt.f64 (log.f64 y)))) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
	0.6b	(-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 y) x)) (cbrt.f64 (.f64 (log.f64 y) x))) (cbrt.f64 (.f64 (log.f64 y) x))) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
	0.5b	(-.f64 (-.f64 (.f64 (pow.f64 (pow.f64 (log.f64 y) 2) 1/3) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	0.7b	(+.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))

Compiler

Compiled 6406 to 2439 computations (61.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (pow.f64 (log.f64 y) 2))
✓	0.5b	(pow.f64 (log.f64 y) 2)
	0.5b	(cbrt.f64 (log.f64 y))
	10.0b	(*.f64 (pow.f64 y 2) z)

series352.0ms (3.9%)

Counts

2 → 20

Calls

2 calls:

330.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))
22.0ms	(pow.f64 (log.f64 y) 2)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
8×	`unpow-prod-down_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

2.0ms	(pow.f64 (log.f64 y) 2)
1.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1083×	`fma-neg_binary64`
522×	`log-prod_binary64`
421×	`exp-prod_binary64`
356×	`*-commutative_binary64`
352×	`cube-prod_binary64`

Counts

60 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	609
1	108	483
2	230	481
3	933	478
4	1794	478
5	3169	478
6	4639	478
7	4823	478

prune171.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	113	8	121

Error

0.0b

Counts

121 → 8

Alt Table

Status	Error	Program
	0.5b	(-.f64 (-.f64 (.f64 (pow.f64 (pow.f64 (log.f64 y) 2) 1/3) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	0.5b	(-.f64 (-.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)))) (cbrt.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	0.4b	(-.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (cbrt.f64 (log.f64 y)))) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	0.5b	(-.f64 (-.f64 (.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	33.6b	(-.f64 (-.f64 (.f64 (.f64 (log.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
✓	0.5b	(-.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) t)
	0.4b	(-.f64 (-.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (log.f64 y) 6))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (*.f64 y z))) t)
	0.7b	(+.f64 (-.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (.f64 y z))) (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))

Compiler

Compiled 3658 to 1897 computations (48.1% saved)

regimes1.8s (20%)

Accuracy

Total 0.1b remaining (28.1%)

Threshold costs 0.1b (28.1%)

Counts

199 → 1

Compiler

Compiled 29234 to 19659 computations (32.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
11×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	30	27
2	39	27
3	61	27
4	77	27
5	87	27
6	92	27
7	93	27
8	92	27

end222.0ms (2.4%)

Compiler: Compiled 305 to 203 computations (33.4% saved)

Details

analyze456.0ms (5%)

sample2.6s (28.5%)

simplify54.0ms (0.6%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series878.0ms (9.7%)

rewrite12.0ms (0.1%)

simplify154.0ms (1.7%)

prune142.0ms (1.6%)

localize14.0ms (0.2%)

series424.0ms (4.7%)

rewrite28.0ms (0.3%)

simplify126.0ms (1.4%)

prune222.0ms (2.4%)

localize15.0ms (0.2%)

series929.0ms (10.2%)

rewrite24.0ms (0.3%)

simplify105.0ms (1.2%)

prune220.0ms (2.4%)

localize18.0ms (0.2%)

series352.0ms (3.9%)

rewrite4.0ms (0%)

simplify83.0ms (0.9%)

prune171.0ms (1.9%)

regimes1.8s (20%)

simplify4.0ms (0%)

end222.0ms (2.4%)

Profiling