Details

analyze448.0ms (1.5%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (3.7%)

Results

861.0ms	8256×	body	128	valid
77.0ms	731×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify40.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

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

5.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series10.0ms (0%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64`

Counts

1 → 52

Calls

1 calls:

6.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

simplify94.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

412×	`unsub-neg_binary64`
396×	`exp-prod_binary64`
359×	`distribute-rgt-in_binary64`
334×	`distribute-lft-in_binary64`
331×	`fma-def_binary64`

Counts

88 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1249
1	225	1167
2	784	1113
3	2358	1057
4	3941	1057
5	4982	1057
6	4909	1057

prune58.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Error

0.0b

Counts

76 → 6

Alt Table

Status	Error	Program
	6.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
▶	0.9b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
	33.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	21.6b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 1613 to 765 computations (52.6% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.6b	(.f64 y (.f64 z x))

series28.0ms (0.1%)

Counts

3 → 60

Calls

3 calls:

10.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
10.0ms	(+.f64 (.f64 y (.f64 z x)) x)
8.0ms	(.f64 y (.f64 z x))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
4.0ms	(+.f64 (.f64 y (.f64 z x)) x)
4.0ms	(.f64 y (.f64 z x))

simplify94.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
502×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
279×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

116 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1397
1	285	1233
2	896	1196
3	2752	1195
4	4487	1195
5	4963	1195

prune80.0ms (0.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	33.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	32.1b	(.f64 (-.f64 (.f64 y x) x) z)
▶	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.9b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	21.6b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	26.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) x) (.f64 z x))

Compiler

Compiled 1949 to 555 computations (71.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.6b	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
✓	5.0b	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))

series794.0ms (2.6%)

Counts

4 → 120

Calls

4 calls:

662.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
86.0ms	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
34.0ms	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))
12.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

rewrite61.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
38×	`cbrt-prod_binary64`

Counts

4 → 158

Calls

4 calls:

18.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
10.0ms	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
9.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
2.0ms	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))

simplify304.0ms (1%)

Algorithm

1×	egg-herbie

Rules

975×	`fma-def_binary64`
704×	`times-frac_binary64`
347×	`*-commutative_binary64`
234×	`+-commutative_binary64`
149×	`associate-+r+_binary64`

Counts

278 → 394

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	950	16210
1	3205	15465
2	4983	15465
3	4978	15465

prune840.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	543	1	544
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	543	8	551

Error

Counts

551 → 8

Alt Table

Status	Error	Program
	33.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	32.1b	(.f64 (-.f64 (.f64 y x) x) z)
✓	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.9b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	21.6b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	26.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) x) (.f64 z x))
▶	20.0b	(.f64 (/.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))))) (.f64 (cbrt.f64 (+.f64 (fma.f64 y z 1) z)) (cbrt.f64 (+.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 33862 to 22558 computations (33.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(/.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))))) (*.f64 (cbrt.f64 (+.f64 (fma.f64 y z 1) z)) (cbrt.f64 (+.f64 (fma.f64 y z 1) z))))
✓	6.2b	(-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))
✓	7.8b	(.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z)))))
✓	17.8b	(cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z)))

series22.7s (74%)

Counts

4 → 120

Calls

4 calls:

20.6s	(/.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))))) (*.f64 (cbrt.f64 (+.f64 (fma.f64 y z 1) z)) (cbrt.f64 (+.f64 (fma.f64 y z 1) z))))
2.0s	(.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z)))))
50.0ms	(cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z)))
8.0ms	(-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))

rewrite55.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`cbrt-div_binary64`
30×	`add-exp-log_binary64`
22×	`associate-*r/_binary64`
18×	`add-cbrt-cube_binary64`
14×	`flip--_binary64`

Counts

4 → 107

Calls

4 calls:

17.0ms	(/.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))))) (*.f64 (cbrt.f64 (+.f64 (fma.f64 y z 1) z)) (cbrt.f64 (+.f64 (fma.f64 y z 1) z))))
10.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z)))))
6.0ms	(-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))
3.0ms	(cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z)))

simplify989.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1021×	`fma-def_binary64`
570×	`times-frac_binary64`
23×	`unpow1/3_binary64`
13×	`exp-prod_binary64`
8×	`unpow2_binary64`

Counts

227 → 275

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3406	72857
1	5337	72857

prune2.4s (7.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	377	8	385

Error

Counts

385 → 8

Alt Table

Status	Error	Program
	33.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	32.1b	(.f64 (-.f64 (.f64 y x) x) z)
✓	5.5b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.9b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	21.6b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	26.1b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (.f64 z x)))) x) (.f64 z x))
✓	20.0b	(.f64 (/.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))) (cbrt.f64 (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (.f64 z z))))) (.f64 (cbrt.f64 (+.f64 (fma.f64 y z 1) z)) (cbrt.f64 (+.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 109481 to 80164 computations (26.8% saved)

regimes387.0ms (1.3%)

Accuracy

Total 1.7b remaining (99.4%)

Threshold costs 0b (0%)

Counts

49 → 1

Compiler

Compiled 9186 to 5605 computations (39% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	13	14
2	23	14
3	29	14
4	33	14
5	34	14
6	34	14

end125.0ms (0.4%)

Compiler: Compiled 209 to 118 computations (43.5% saved)

Details

analyze448.0ms (1.5%)

sample1.1s (3.7%)

simplify40.0ms (0.1%)

prune4.0ms (0%)

localize5.0ms (0%)

series10.0ms (0%)

rewrite9.0ms (0%)

simplify94.0ms (0.3%)

prune58.0ms (0.2%)

localize8.0ms (0%)

series28.0ms (0.1%)

rewrite16.0ms (0.1%)

simplify94.0ms (0.3%)

prune80.0ms (0.3%)

localize10.0ms (0%)

series794.0ms (2.6%)

rewrite61.0ms (0.2%)

simplify304.0ms (1%)

prune840.0ms (2.7%)

localize18.0ms (0.1%)

series22.7s (74%)

rewrite55.0ms (0.2%)

simplify989.0ms (3.2%)

prune2.4s (7.7%)

regimes387.0ms (1.3%)

simplify3.0ms (0%)

end125.0ms (0.4%)

Profiling