Details

analyze70.0ms (3.7%)

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
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

sample22.0ms (1.2%)

Algorithm

1×

intervals

Results

10.0ms	237×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	8×	body	160	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	80	invalid

simplify85.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5973	9

prune5.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.3b

Counts

2 → 1

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1.0 (exp.f64 x))) (*.f64 x y))
0.0b	(+.f64 1.0 (exp.f64 x))
0.3b	(log.f64 (+.f64 1.0 (exp.f64 x)))

rewrite15.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
8×	`log-prod_binary64`
6×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `log-div_binary64` `associate--l+_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
2×	`associate--l-_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `log-pow_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 44

Calls

3 calls:

7.0ms	(-.f64 (log.f64 (+.f64 1.0 (exp.f64 x))) (*.f64 x y))
4.0ms	(+.f64 1.0 (exp.f64 x))
4.0ms	(log.f64 (+.f64 1.0 (exp.f64 x)))

series28.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(-.f64 (log.f64 (+.f64 1.0 (exp.f64 x))) (*.f64 x y))
12.0ms	(log.f64 (+.f64 1.0 (exp.f64 x)))
2.0ms	(+.f64 1.0 (exp.f64 x))

simplify95.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4842	504
1	4842	504

prune70.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Merged error: 0.2b

Counts

54 → 3

localize16.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.3b	(log.f64 (+.f64 (pow.f64 1.0 3) (pow.f64 (exp.f64 x) 3)))
4.5b	(-.f64 (exp.f64 x) 1.0)
4.7b	(log.f64 (+.f64 (.f64 1.0 1.0) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1.0))))

rewrite29.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`log-prod_binary64` `add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
5×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
4×	`pow-pow_binary64` `log-div_binary64`
3×	`pow-unpow_binary64` `exp-prod_binary64`
2×	`flip3-+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sum-cubes_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 73

Calls

4 calls:

11.0ms	(log.f64 (+.f64 (pow.f64 1.0 3) (pow.f64 (exp.f64 x) 3)))
5.0ms	(log.f64 (+.f64 (.f64 1.0 1.0) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1.0))))
5.0ms	(-.f64 (exp.f64 x) 1.0)
4.0ms	(pow.f64 (exp.f64 x) 3)

series54.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(log.f64 (+.f64 (.f64 1.0 1.0) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1.0))))
20.0ms	(log.f64 (+.f64 (pow.f64 1.0 3) (pow.f64 (exp.f64 x) 3)))
6.0ms	(pow.f64 (exp.f64 x) 3)
2.0ms	(-.f64 (exp.f64 x) 1.0)

simplify58.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5002	829

prune132.0ms (7.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0.2b

Counts

88 → 3

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (exp.f64 x))
0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x)))) (*.f64 x y)))
1.0b	(log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x))))
1.0b	(log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x))))

rewrite29.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`log-prod_binary64`
25×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
12×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64` `associate-+r+_binary64`
7×	`distribute-lft-out_binary64` `log-pow_binary64` `associate-+l+_binary64` `associate--l+_binary64`
6×	`add-exp-log_binary64` `log-div_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-cbrt-cube_binary64`
3×	`sum-log_binary64`
2×	`pow1/2_binary64` `rem-log-exp_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `+-commutative_binary64`
1×	`sub-neg_binary64` `associate-+r-_binary64` `diff-log_binary64`

Counts

4 → 84

Calls

4 calls:

14.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x)))) (*.f64 x y)))
5.0ms	(log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x))))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x))))
4.0ms	(+.f64 1.0 (exp.f64 x))

series52.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x)))) (*.f64 x y)))
17.0ms	(log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x))))
15.0ms	(log.f64 (sqrt.f64 (+.f64 1.0 (exp.f64 x))))
2.0ms	(+.f64 1.0 (exp.f64 x))

simplify48.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4951	1004
1	4951	1004

prune129.0ms (6.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Merged error: 0.2b

Counts

99 → 3

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(-.f64 (log.f64 (+.f64 (.f64 (.f64 x x) 1/2) (+.f64 x 2.0))) (*.f64 x y))
6.8b	(log.f64 (+.f64 (.f64 (.f64 x x) 1/2) (+.f64 x 2.0)))

rewrite28.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64` `add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `log-prod_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `log-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `associate--l+_binary64`
2×	`flip3-+_binary64` `associate--l-_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `log-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

3 → 49

Calls

3 calls:

12.0ms	(-.f64 (log.f64 (+.f64 (.f64 (.f64 x x) 1/2) (+.f64 x 2.0))) (*.f64 x y))
10.0ms	(log.f64 (+.f64 (.f64 (.f64 x x) 1/2) (+.f64 x 2.0)))
6.0ms	(.f64 (.f64 x x) 1/2)

series20.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(-.f64 (log.f64 (+.f64 (.f64 (.f64 x x) 1/2) (+.f64 x 2.0))) (*.f64 x y))
5.0ms	(log.f64 (+.f64 (.f64 (.f64 x x) 1/2) (+.f64 x 2.0)))
4.0ms	(.f64 (.f64 x x) 1/2)

simplify54.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4937	746
1	4937	746

prune68.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	58	3	61

Merged error: 0.2b

Counts

61 → 3

regimes76.0ms (4.1%)

Accuracy

Total 0.3b remaining (56.4%)

Threshold costs 0.3b (56.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	26
1	63	26

end0.0ms (0%)

sample655.0ms (35.1%)

Algorithm

1×

intervals

Results

328.0ms	7376×	body	80	valid
70.0ms	224×	body	640	valid
61.0ms	104×	body	1280	valid
29.0ms	157×	body	320	valid
15.0ms	139×	body	160	valid
2.0ms	45×	body	80	invalid
0.0ms	10×	body	80	overflowed

Details

analyze70.0ms (3.7%)

sample22.0ms (1.2%)

simplify85.0ms (4.5%)

prune5.0ms (0.3%)

localize7.0ms (0.4%)

rewrite15.0ms (0.8%)

series28.0ms (1.5%)

simplify95.0ms (5.1%)

prune70.0ms (3.7%)

localize16.0ms (0.8%)

rewrite29.0ms (1.5%)

series54.0ms (2.9%)

simplify58.0ms (3.1%)

prune132.0ms (7.1%)

localize9.0ms (0.5%)

rewrite29.0ms (1.6%)

series52.0ms (2.8%)

simplify48.0ms (2.6%)

prune129.0ms (6.9%)

localize9.0ms (0.5%)

rewrite28.0ms (1.5%)

series20.0ms (1.1%)

simplify54.0ms (2.9%)

prune68.0ms (3.6%)

regimes76.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample655.0ms (35.1%)

Profiling