Details

analyze249.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample1.3s (23%)

Results

1.0s	8256×	body	128	valid
46.0ms	398×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify282.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
806×	`fma-neg_binary64`
746×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	59	16
3	115	16
4	270	14
5	514	14
6	792	14
7	1191	14
8	1435	14
9	1716	14
10	2343	14
11	2639	14
12	2704	14
13	3251	14
14	3766	14
15	3977	14
16	4124	14
17	4234	14
18	4260	14
19	4085	14
20	4111	14
21	4149	14
22	4189	14
23	4189	14
24	4189	14
25	4871	14
26	4999	14
27	4907	14

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series274.0ms (4.7%)

Counts

2 → 60

Calls

2 calls:

193.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
81.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
7×	`associate-r_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64`
4×	`distribute-lft-out_binary64`

Counts

2 → 44

Calls

2 calls:

8.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
4.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-neg_binary64`
689×	`fma-def_binary64`
272×	`*-commutative_binary64`
264×	`sub-neg_binary64`
198×	`associate-+l+_binary64`

Counts

104 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	111	1600
1	334	1476
2	1274	1472
3	3013	1314
4	4563	1312
5	4938	1312

prune76.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y))) (cbrt.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)))) (cbrt.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y))))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	38.3b	(cbrt.f64 (pow.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)) 3))
	14.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
▶	0.1b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
	31.4b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	19.0b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3))) (+.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (-.f64 (.f64 (log.f64 z) (log.f64 z)) (*.f64 (-.f64 1 z) (log.f64 z))))))

Compiler

Compiled 1891 to 1022 computations (46% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 1/2 x y) (*.f64 y z))
✓	0.1b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
✓	0.3b	(*.f64 (log.f64 z) y)

series289.0ms (5%)

Counts

3 → 80

Calls

3 calls:

199.0ms	(*.f64 (log.f64 z) y)
83.0ms	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
7.0ms	(-.f64 (fma.f64 1/2 x y) (*.f64 y z))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
6×	`associate-+l+_binary64`

Counts

3 → 66

Calls

3 calls:

4.0ms	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
3.0ms	(*.f64 (log.f64 z) y)
2.0ms	(-.f64 (fma.f64 1/2 x y) (*.f64 y z))

simplify101.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

626×	`distribute-rgt-in_binary64`
604×	`distribute-lft-in_binary64`
577×	`fma-def_binary64`
473×	`associate-l_binary64`
362×	`fma-neg_binary64`

Counts

146 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1981
1	351	1879
2	1101	1709
3	4415	1709
4	4996	1709
5	4973	1709

prune139.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Error

0.0b

Counts

136 → 8

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y))) (cbrt.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y)))) (cbrt.f64 (fma.f64 1/2 x (fma.f64 y (-.f64 (log.f64 z) z) y))))
▶	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	14.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
	29.2b	(expm1.f64 (log1p.f64 (fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))))
	19.0b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3))) (+.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (-.f64 (.f64 (log.f64 z) (log.f64 z)) (*.f64 (-.f64 1 z) (log.f64 z))))))
	31.3b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (*.f64 (log.f64 z) (sqrt.f64 y)) (sqrt.f64 y)))
✓	0.1b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
	17.5b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (cbrt.f64 (.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (.f64 (log.f64 z) y))))

Compiler

Compiled 2816 to 1176 computations (58.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)

series595.0ms (10.3%)

Counts

4 → 72

Calls

4 calls:

303.0ms	(*.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))
228.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))))
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
30.0ms	(cbrt.f64 y)

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`pow1_binary64`
24×	`*-un-lft-identity_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 117

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))))
8.0ms	(*.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary64`
787×	`fma-def_binary64`
329×	`unswap-sqr_binary64`
297×	`exp-prod_binary64`
295×	`associate-l_binary64`

Counts

189 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	2502
1	422	2184
2	1780	2117
3	3532	2098
4	4868	2098
5	4963	2098

prune266.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	219	8	227

Error

0.0b

Counts

227 → 8

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (-.f64 (+.f64 (log.f64 z) 1) z)))
	17.5b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (cbrt.f64 (.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (.f64 (log.f64 z) y))))
	14.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
	29.2b	(expm1.f64 (log1p.f64 (fma.f64 y (-.f64 (log.f64 z) z) (fma.f64 1/2 x y))))
	1.0b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
✓	0.1b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
✓	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	31.3b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (*.f64 (log.f64 z) (sqrt.f64 y)) (sqrt.f64 y)))

Compiler

Compiled 5564 to 2669 computations (52% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series304.0ms (5.3%)

Counts

4 → 80

Calls

4 calls:

193.0ms	(*.f64 y (-.f64 (+.f64 (log.f64 z) 1) z))
86.0ms	(+.f64 (.f64 x 1/2) (.f64 y (-.f64 (+.f64 (log.f64 z) 1) z)))
19.0ms	(+.f64 (log.f64 z) 1)
5.0ms	(-.f64 (+.f64 (log.f64 z) 1) z)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64`
75×	`prod-diff_binary64`
60×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
40×	`associate-+r+_binary64`

Counts

4 → 184

Calls

4 calls:

8.0ms	(+.f64 (.f64 x 1/2) (.f64 y (-.f64 (+.f64 (log.f64 z) 1) z)))
8.0ms	(*.f64 y (-.f64 (+.f64 (log.f64 z) 1) z))
5.0ms	(-.f64 (+.f64 (log.f64 z) 1) z)
3.0ms	(+.f64 (log.f64 z) 1)

simplify152.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

338×	`*-commutative_binary64`
309×	`unsub-neg_binary64`
277×	`times-frac_binary64`
237×	`cancel-sign-sub-inv_binary64`
222×	`associate-+l+_binary64`

Counts

264 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	3693
1	490	3475
2	1645	3333
3	3577	3333
4	4972	3333
5	4901	3333

prune231.0ms (4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	237	7	244

Error

0.0b

Counts

244 → 7

Alt Table

Status	Error	Program
	1.0b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.1b	(fma.f64 y (-.f64 (+.f64 1 (log.f64 z)) z) (*.f64 1/2 x))
✓	0.1b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (log.f64 z) y))
	17.5b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (cbrt.f64 (.f64 (.f64 (.f64 (log.f64 z) y) (.f64 (log.f64 z) y)) (.f64 (log.f64 z) y))))
✓	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	14.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
	31.3b	(+.f64 (-.f64 (fma.f64 1/2 x y) (.f64 y z)) (.f64 (*.f64 (log.f64 z) (sqrt.f64 y)) (sqrt.f64 y)))

Compiler

Compiled 5374 to 2753 computations (48.8% saved)

regimes1.0s (18.1%)

Accuracy

Total 0.1b remaining (71.6%)

Threshold costs 0.1b (71.6%)

Counts

124 → 1

Compiler

Compiled 20498 to 13490 computations (34.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	21	16
3	23	16
4	24	16
5	23	16

end104.0ms (1.8%)

Compiler: Compiled 187 to 115 computations (38.5% saved)

Details

analyze249.0ms (4.3%)

sample1.3s (23%)

simplify282.0ms (4.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series274.0ms (4.7%)

rewrite14.0ms (0.3%)

simplify83.0ms (1.4%)

prune76.0ms (1.3%)

localize9.0ms (0.2%)

series289.0ms (5%)

rewrite13.0ms (0.2%)

simplify101.0ms (1.8%)

prune139.0ms (2.4%)

localize13.0ms (0.2%)

series595.0ms (10.3%)

rewrite31.0ms (0.5%)

simplify118.0ms (2%)

prune266.0ms (4.6%)

localize8.0ms (0.1%)

series304.0ms (5.3%)

rewrite41.0ms (0.7%)

simplify152.0ms (2.6%)

prune231.0ms (4%)

regimes1.0s (18.1%)

simplify2.0ms (0%)

end104.0ms (1.8%)

Profiling