Details

analyze21.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample51.0ms (1.7%)

Algorithm

1×

intervals

Results

28.0ms	81×	body	1024	valid
7.0ms	40×	body	512	valid
3.0ms	7×	body	2048	valid
3.0ms	104×	body	128	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64` `+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	8	6
2	7	6

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

36.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	36.7b	(log.f64 (+.f64 1 x))

Compiler

Compiled 10 to 8 computations (20% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

3.1b	(log.f64 (+.f64 1 x))

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

36.7b

Rules

4×	`log-prod_binary64` `*-un-lft-identity_binary64`
2×	`pow1_binary64` `log-div_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `add-exp-log_binary64`
1×	`log-pow_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

1 → 15

Calls

1 calls:

4.0ms

(log.f64 (+.f64 1 x))

Compiler

Compiled 140 to 113 computations (19.3% saved)

series20.0ms (0.7%)

Error

0.1b

Counts

1 → 9

Calls

1 calls:

11.0ms

(log.f64 (+.f64 1 x))

Compiler

Compiled 224 to 180 computations (19.6% saved)

simplify80.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

550×	`sub-neg_binary64`
324×	`neg-mul-1_binary64`
300×	`distribute-rgt-neg-in_binary64`
291×	`neg-sub0_binary64`
282×	`associate-l_binary64`

Counts

24 → 20

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	308
1	144	276
2	313	270
3	868	267
4	3053	267
5	4390	267
6	5018	267

prune19.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	3	21

Error

0.0b

Counts

21 → 3

Alt Table

Status	Error	Program
	60.6b	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (log.f64 (-.f64 1 x)))
▶	24.1b	(+.f64 x (.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)))
✓	36.7b	(log.f64 (+.f64 1 x))

Compiler

Compiled 241 to 172 computations (28.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)
0.0b	(+.f64 1/3 (*.f64 x -1/4))
0.1b	(.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2))
0.2b	(.f64 x (+.f64 1/3 (.f64 x -1/4)))

rewrite86.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`associate-r_binary64`

Counts

4 → 69

Calls

4 calls:

11.0ms	(.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2))
6.0ms	(+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)
5.0ms	(.f64 x (+.f64 1/3 (.f64 x -1/4)))
3.0ms	(+.f64 1/3 (*.f64 x -1/4))

Compiler

Compiled 1602 to 1077 computations (32.8% saved)

series62.0ms (2.1%)

Error

0.0b

Counts

4 → 22

Calls

4 calls:

15.0ms	(.f64 x (+.f64 1/3 (.f64 x -1/4)))
11.0ms	(.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2))
9.0ms	(+.f64 1/3 (*.f64 x -1/4))
8.0ms	(+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)

Compiler

Compiled 675 to 468 computations (30.7% saved)

simplify81.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

675×	`distribute-rgt-in_binary64`
656×	`distribute-lft-in_binary64`
385×	`*-commutative_binary64`
286×	`unswap-sqr_binary64`
228×	`associate-l_binary64`

Counts

91 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1490
1	364	1349
2	1241	1313
3	3988	1313
4	4944	1313

prune47.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

0.0b

Counts

77 → 3

Alt Table

Status	Error	Program
▶	60.6b	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (log.f64 (-.f64 1 x)))
✓	24.1b	(+.f64 x (.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)))
✓	36.7b	(log.f64 (+.f64 1 x))

Compiler

Compiled 1198 to 811 computations (32.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (log.f64 (-.f64 1 x)))
1.2b	(log.f64 (-.f64 1 (*.f64 x x)))
3.1b	(log.f64 (-.f64 1 x))

rewrite60.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`log-prod_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`difference-of-squares_binary64`

Counts

3 → 68

Calls

3 calls:

9.0ms	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (log.f64 (-.f64 1 x)))
3.0ms	(log.f64 (-.f64 1 x))
2.0ms	(log.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 1178 to 802 computations (31.9% saved)

series55.0ms (1.8%)

Error

0.0b

Counts

3 → 22

Calls

3 calls:

15.0ms	(log.f64 (-.f64 1 (*.f64 x x)))
13.0ms	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (log.f64 (-.f64 1 x)))
10.0ms	(log.f64 (-.f64 1 x))

Compiler

Compiled 757 to 600 computations (20.7% saved)

simplify111.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

511×	`times-frac_binary64`
382×	`distribute-rgt-neg-in_binary64`
372×	`sub-neg_binary64`
350×	`distribute-lft-neg-in_binary64`
312×	`associate-l_binary64`

Counts

90 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	1459
1	389	1376
2	944	1361
3	2897	1353
4	4562	1353
5	5078	1353

prune37.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	49	4	53

Error

0.0b

Counts

53 → 4

Alt Table

Status	Error	Program
	62.7b	(/.f64 (-.f64 (pow.f64 (log.f64 (-.f64 1 (.f64 x x))) 3) (pow.f64 (log.f64 (-.f64 1 x)) 3)) (+.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 1 x))) 6) (.f64 (log.f64 (-.f64 1 (.f64 x x))) (+.f64 (log.f64 (-.f64 1 x)) (log.f64 (-.f64 1 (.f64 x x)))))))
▶	60.6b	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (pow.f64 (log.f64 (-.f64 1 x)) 3)))
✓	24.1b	(+.f64 x (.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)))
✓	36.7b	(log.f64 (+.f64 1 x))

Compiler

Compiled 861 to 592 computations (31.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (log.f64 (-.f64 1 x)) 3)
0.0b	(cbrt.f64 (pow.f64 (log.f64 (-.f64 1 x)) 3))
1.2b	(log.f64 (-.f64 1 (*.f64 x x)))
3.1b	(log.f64 (-.f64 1 x))

rewrite68.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
12×	`add-cube-cbrt_binary64`
11×	`pow1_binary64` `log-prod_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64`

Counts

4 → 81

Calls

4 calls:

3.0ms	(log.f64 (-.f64 1 x))
3.0ms	(pow.f64 (log.f64 (-.f64 1 x)) 3)
3.0ms	(log.f64 (-.f64 1 (*.f64 x x)))
2.0ms	(cbrt.f64 (pow.f64 (log.f64 (-.f64 1 x)) 3))

Compiler

Compiled 1353 to 1017 computations (24.8% saved)

series74.0ms (2.5%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

18.0ms	(pow.f64 (log.f64 (-.f64 1 x)) 3)
15.0ms	(log.f64 (-.f64 1 (*.f64 x x)))
11.0ms	(log.f64 (-.f64 1 x))
10.0ms	(cbrt.f64 (pow.f64 (log.f64 (-.f64 1 x)) 3))

Compiler

Compiled 1312 to 1047 computations (20.2% saved)

simplify109.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

376×	`times-frac_binary64`
265×	`sub-neg_binary64`
263×	`distribute-rgt-neg-in_binary64`
254×	`distribute-lft-neg-in_binary64`
208×	`log-prod_binary64`

Counts

108 → 78

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	174	1476
1	376	1340
2	1094	1314
3	2686	1307
4	4514	1304
5	5085	1304

prune40.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
	60.6b	(-.f64 (log.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (log.f64 (-.f64 1 x)) 3)) 3)))
	62.7b	(/.f64 (-.f64 (pow.f64 (log.f64 (-.f64 1 (.f64 x x))) 3) (pow.f64 (log.f64 (-.f64 1 x)) 3)) (+.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 1 x))) 6) (.f64 (log.f64 (-.f64 1 (.f64 x x))) (+.f64 (log.f64 (-.f64 1 x)) (log.f64 (-.f64 1 (.f64 x x)))))))
	24.1b	(+.f64 x (.f64 (.f64 x x) (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/4))) -1/2)))
	36.7b	(log.f64 (+.f64 1 x))

Compiler

Compiled 978 to 711 computations (27.3% saved)

regimes183.0ms (6.1%)

Accuracy

Total 0.1b remaining (85%)

Threshold costs 0.1b (85%)

Compiler

Compiled 1928 to 1432 computations (25.7% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	28	37
2	27	37

end1.0ms (0%)

Compiler: Compiled 26 to 19 computations (26.9% saved)

sample1.7s (57.5%)

Algorithm

1×

intervals

Results

901.0ms	2744×	body	1024	valid
211.0ms	1291×	body	512	valid
114.0ms	266×	body	2048	valid
98.0ms	3013×	body	128	valid
56.0ms	686×	body	256	valid

Compiler

Compiled 115 to 87 computations (24.3% saved)

Details

analyze21.0ms (0.7%)

sample51.0ms (1.7%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite20.0ms (0.7%)

series20.0ms (0.7%)

simplify80.0ms (2.7%)

prune19.0ms (0.6%)

localize9.0ms (0.3%)

rewrite86.0ms (2.9%)

series62.0ms (2.1%)

simplify81.0ms (2.7%)

prune47.0ms (1.6%)

localize9.0ms (0.3%)

rewrite60.0ms (2%)

series55.0ms (1.8%)

simplify111.0ms (3.7%)

prune37.0ms (1.2%)

localize10.0ms (0.3%)

rewrite68.0ms (2.3%)

series74.0ms (2.5%)

simplify109.0ms (3.6%)

prune40.0ms (1.3%)

regimes183.0ms (6.1%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (57.5%)

Profiling