Details

analyze67.0ms (2.4%)

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

Compiler

Compiled 10 to 9 computations (10% saved)

sample30.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms	237×	body	128	valid
2.0ms	5×	body	1024	valid
2.0ms	8×	body	512	valid
1.0ms	6×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify217.0ms (7.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4811	14
1	4811	14

prune2.0ms (0.1%)

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

Error

0.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_2806`
8×	`log-prod_binary64_2892`
6×	`add-log-exp_binary64_2845`
5×	`add-sqr-sqrt_binary64_2828` `add-cube-cbrt_binary64_2841`
4×	`add-exp-log_binary64_2844` `associate--l+_binary64_2743` `log-div_binary64_2893` `pow1_binary64_2867`
3×	`distribute-lft-out_binary64_2757` `add-cbrt-cube_binary64_2842` `flip-+_binary64_2780` `flip3-+_binary64_2809`
2×	`associate--l-_binary64_2744`
1×	`cancel-sign-sub-inv_binary64_2772` `flip3--_binary64_2810` `diff-log_binary64_2898` `rem-log-exp_binary64_2847` `sub-neg_binary64_2799` `sum-log_binary64_2897` `flip--_binary64_2781` `log-pow_binary64_2895` `+-commutative_binary64_2736`

Counts

3 → 45

Calls

3 calls:

6.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series92.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
41.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
6.0ms	(+.f64 1 (exp.f64 x))

simplify101.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4858	767
1	4858	767

prune50.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Error

0.2b

Counts

55 → 3

Compiler

Compiled 848 to 481 computations (43.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_2806`
14×	`log-prod_binary64_2892`
12×	`sqrt-prod_binary64_2822`
10×	`sqrt-div_binary64_2823` `add-sqr-sqrt_binary64_2828`
9×	`add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
8×	`log-div_binary64_2893`
7×	`add-log-exp_binary64_2845`
6×	`add-exp-log_binary64_2844` `log-pow_binary64_2895`
5×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
4×	`add-cbrt-cube_binary64_2842` `associate--l-_binary64_2744`
3×	`pow1/2_binary64_2886` `distribute-lft-out_binary64_2757` `sqrt-pow1_binary64_2824`
2×	`associate-+l-_binary64_2741` `diff-log_binary64_2898` `associate-+r-_binary64_2740` `rem-log-exp_binary64_2847`
1×	`cancel-sign-sub-inv_binary64_2772` `associate--l+_binary64_2743` `flip3--_binary64_2810` `sub-neg_binary64_2799` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `flip--_binary64_2781`

Counts

4 → 74

Calls

4 calls:

14.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series222.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (*.f64 x y))
70.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
59.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
21.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

simplify108.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4885	1378
1	4885	1378

prune102.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Error

0.2b

Counts

89 → 3

Compiler

Compiled 1903 to 1195 computations (37.2% saved)

localize14.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))
0.0b	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
5.6b	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_2806`
9×	`add-log-exp_binary64_2845`
8×	`log-prod_binary64_2892`
5×	`add-sqr-sqrt_binary64_2828` `add-cube-cbrt_binary64_2841`
4×	`add-exp-log_binary64_2844` `associate--l+_binary64_2743` `log-div_binary64_2893` `pow1_binary64_2867`
3×	`distribute-lft-out_binary64_2757` `add-cbrt-cube_binary64_2842` `flip-+_binary64_2780` `sum-log_binary64_2897` `flip3-+_binary64_2809`
2×	`associate--l-_binary64_2744`
1×	`cancel-sign-sub-inv_binary64_2772` `flip3--_binary64_2810` `associate-+r+_binary64_2738` `diff-log_binary64_2898` `rem-log-exp_binary64_2847` `sub-neg_binary64_2799` `flip--_binary64_2781` `log-pow_binary64_2895` `+-commutative_binary64_2736`

Counts

3 → 47

Calls

3 calls:

7.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
6.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))
5.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))

series69.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
20.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
12.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4958	1292
1	4958	1292

prune65.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	55	4	59

Error

0.2b

Counts

59 → 4

Compiler

Compiled 1323 to 844 computations (36.2% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.3b	(cbrt.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))))
5.6b	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
5.6b	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
5.6b	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_2806`
12×	`log-prod_binary64_2892`
8×	`add-sqr-sqrt_binary64_2828` `add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
7×	`add-exp-log_binary64_2844`
6×	`log-div_binary64_2893`
4×	`add-cbrt-cube_binary64_2842` `add-log-exp_binary64_2845` `cbrt-prod_binary64_2837` `log-pow_binary64_2895`
3×	`distribute-lft-out_binary64_2757` `rem-log-exp_binary64_2847` `flip-+_binary64_2780` `flip3-+_binary64_2809`
1×	`pow1/3_binary64_2888`

Counts

4 → 57

Calls

4 calls:

5.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
5.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
5.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
1.0ms	(cbrt.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))))

series148.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))))
19.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
17.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
17.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))

simplify79.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5049	1721

prune155.0ms (5.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	69	4	73

Error

0.2b

Counts

73 → 4

Compiler

Compiled 3296 to 2345 computations (28.9% saved)

regimes88.0ms (3.1%)

Accuracy

Total 0.3b remaining (55.8%)

Threshold costs 0.3b (55.8%)

Compiler

Compiled 955 to 756 computations (20.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	14
1	37	14

end0.0ms (0%)

sample1.0s (36.5%)

Algorithm

1×

intervals

Results

368.0ms	7349×	body	128	valid
86.0ms	217×	body	1024	valid
61.0ms	276×	body	512	valid
20.0ms	157×	body	256	valid
2.0ms	34×	body	128	invalid
2.0ms	1×	body	2048	valid
0.0ms	5×	body	128	overflowed

Compiler

Compiled 356 to 283 computations (20.5% saved)

Details

analyze67.0ms (2.4%)

sample30.0ms (1%)

simplify217.0ms (7.6%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite16.0ms (0.6%)

series92.0ms (3.2%)

simplify101.0ms (3.6%)

prune50.0ms (1.7%)

localize11.0ms (0.4%)

rewrite32.0ms (1.1%)

series222.0ms (7.8%)

simplify108.0ms (3.8%)

prune102.0ms (3.6%)

localize14.0ms (0.5%)

rewrite21.0ms (0.7%)

series69.0ms (2.4%)

simplify69.0ms (2.4%)

prune65.0ms (2.3%)

localize19.0ms (0.7%)

rewrite22.0ms (0.8%)

series148.0ms (5.2%)

simplify79.0ms (2.8%)

prune155.0ms (5.4%)

regimes88.0ms (3.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (36.5%)

Profiling