Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample849.0ms (36.2%)

Results

799.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify25.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
257×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
55×	`sub-neg_binary64`
32×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	54	11
3	122	11
4	222	9
5	361	9
6	423	9
7	587	9
8	645	9
9	664	9
10	593	9

prune6.0ms (0.3%)

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	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x -3/25 -253/1000)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
1.0ms	(fma.f64 x -3/25 -253/1000)

rewrite1.0ms (0.1%)

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 x (fma.f64 x -3/25 -253/1000) 1)
0.0ms	(fma.f64 x -3/25 -253/1000)

simplify74.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

549×	`associate-l_binary64`
533×	`fma-neg_binary64`
477×	`associate-r_binary64`
446×	`unsub-neg_binary64`
418×	`times-frac_binary64`

Counts

44 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	455
1	77	344
2	166	341
3	592	341
4	2915	341
5	4504	341
6	5515	341

prune37.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

0.0b

Counts

39 → 5

Alt Table

Status	Error	Program
	6.9b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 x -3/25 -253/1000) (fma.f64 x -3/25 -253/1000)) (fma.f64 x -3/25 -253/1000))) 1)
	22.8b	(exp.f64 (log1p.f64 (*.f64 x (fma.f64 x -3/25 -253/1000))))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	53.1b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)

Compiler

Compiled 487 to 376 computations (22.8% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.0b	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
✓	0.1b	(*.f64 253/1000 x)
✓	0.2b	(*.f64 3/25 (pow.f64 x 2))

series14.0ms (0.6%)

Counts

4 → 9

Calls

4 calls:

7.0ms	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
2.0ms	(*.f64 3/25 (pow.f64 x 2))
1.0ms	(*.f64 253/1000 x)

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
11×	`associate-r_binary64`
11×	`add-log-exp_binary64`

Counts

4 → 96

Calls

4 calls:

5.0ms	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
4.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
3.0ms	(*.f64 253/1000 x)

simplify105.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
611×	`fma-def_binary64`
367×	`cancel-sign-sub-inv_binary64`
261×	`*-commutative_binary64`
257×	`distribute-rgt-neg-in_binary64`

Counts

105 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	154	1581
1	332	1362
2	982	1151
3	2910	1087
4	4383	1074
5	4965	1074
6	4825	1074

prune238.0ms (10.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	147	6	153

Error

0.0b

Counts

153 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)) (.f64 (cbrt.f64 3/25) (pow.f64 x 2))) (.f64 253/1000 x)))
▶	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.5b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))) (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))))) (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))))
	53.1b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)

Compiler

Compiled 3119 to 2532 computations (18.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
	0.1b	(*.f64 253/1000 x)
✓	0.1b	(*.f64 x (sqrt.f64 3/25))
✓	0.4b	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))

series18.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))
6.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
3.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64`
18×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x))
6.0ms	(*.f64 x (sqrt.f64 3/25))
6.0ms	(.f64 (.f64 x (sqrt.f64 3/25)) (*.f64 x (sqrt.f64 3/25)))

simplify83.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-neg_binary64`
341×	`distribute-lft-out_binary64`
340×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
315×	`unswap-sqr_binary64`

Counts

110 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	981
1	223	899
2	797	829
3	2066	829
4	4718	829
5	5053	829

prune188.0ms (8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	152	6	158

Error

0.0b

Counts

158 → 6

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)) (.f64 (cbrt.f64 3/25) (pow.f64 x 2))) (.f64 253/1000 x)))
✓	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.5b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))) (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))))) (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))))
	53.1b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)

Compiler

Compiled 3166 to 2514 computations (20.6% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 253/1000 x)
✓	0.2b	(.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)) (*.f64 (cbrt.f64 3/25) (pow.f64 x 2)))
✓	0.3b	(*.f64 (cbrt.f64 3/25) (pow.f64 x 2))
✓	1.0b	(*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))

series20.0ms (0.9%)

Counts

3 → 12

Calls

3 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)) (*.f64 (cbrt.f64 3/25) (pow.f64 x 2)))
6.0ms	(*.f64 (cbrt.f64 3/25) (pow.f64 x 2))
0.0ms	(*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
34×	`add-exp-log_binary64`
23×	`cbrt-prod_binary64`
22×	`prod-exp_binary64`
15×	`associate-r_binary64`

Counts

3 → 104

Calls

3 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)) (*.f64 (cbrt.f64 3/25) (pow.f64 x 2)))
5.0ms	(*.f64 (cbrt.f64 3/25) (pow.f64 x 2))
4.0ms	(*.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))

simplify100.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
618×	`unswap-sqr_binary64`
301×	`*-commutative_binary64`
269×	`log-prod_binary64`
265×	`exp-prod_binary64`

Counts

116 → 136

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1366
1	201	1177
2	627	1158
3	1114	1103
4	2564	1027
5	4571	1027
6	4943	1027

prune209.0ms (8.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	158	6	164

Error

0.0b

Counts

164 → 6

Alt Table

Status	Error	Program
✓	0.4b	(-.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25)) (.f64 (cbrt.f64 3/25) (pow.f64 x 2))) (.f64 253/1000 x)))
✓	0.2b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.5b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))) (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))))) (cbrt.f64 (-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))))
	53.1b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)

Compiler

Compiled 3742 to 3269 computations (12.6% saved)

regimes158.0ms (6.7%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

43 → 1

Compiler

Compiled 1774 to 1449 computations (18.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	26	16
3	46	16
4	61	16
5	67	16
6	69	16
7	66	16

end112.0ms (4.8%)

Compiler: Compiled 133 to 109 computations (18% saved)

Details

analyze4.0ms (0.2%)

sample849.0ms (36.2%)

simplify25.0ms (1.1%)

prune6.0ms (0.3%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify74.0ms (3.2%)

prune37.0ms (1.6%)

localize7.0ms (0.3%)

series14.0ms (0.6%)

rewrite21.0ms (0.9%)

simplify105.0ms (4.5%)

prune238.0ms (10.1%)

localize8.0ms (0.3%)

series18.0ms (0.8%)

rewrite21.0ms (0.9%)

simplify83.0ms (3.5%)

prune188.0ms (8%)

localize14.0ms (0.6%)

series20.0ms (0.9%)

rewrite23.0ms (1%)

simplify100.0ms (4.3%)

prune209.0ms (8.9%)

regimes158.0ms (6.7%)

simplify3.0ms (0.1%)

end112.0ms (4.8%)

Profiling