Details

analyze66.0ms (2.2%)

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)

sample25.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	230×	body	128	valid
3.0ms	8×	body	1024	valid
3.0ms	13×	body	512	valid
1.0ms	5×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify227.0ms (7.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4811	14
1	4811	14

prune3.0ms (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

Merged error: 0.3b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.3b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_2806`
4×	`add-log-exp_binary64_2845` `log-prod_binary64_2892`
3×	`add-sqr-sqrt_binary64_2828` `add-exp-log_binary64_2844` `add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
2×	`distribute-lft-out_binary64_2757` `add-cbrt-cube_binary64_2842` `log-div_binary64_2893` `flip-+_binary64_2780` `flip3-+_binary64_2809`
1×	`rem-log-exp_binary64_2847` `sum-log_binary64_2897` `log-pow_binary64_2895` `+-commutative_binary64_2736`

Counts

2 → 27

Calls

2 calls:

5.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series54.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
6.0ms	(+.f64 1 (exp.f64 x))

simplify82.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4941	373
1	4941	373

prune34.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	2	34

Merged error: 0.2b

Counts

34 → 2

Compiler

Compiled 476 to 278 computations (41.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2)
0.3b	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
4.7b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.7b	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_2806`
16×	`add-sqr-sqrt_binary64_2828`
10×	`add-cube-cbrt_binary64_2841`
9×	`log-prod_binary64_2892`
7×	`pow1_binary64_2867`
6×	`add-exp-log_binary64_2844` `add-log-exp_binary64_2845`
4×	`add-cbrt-cube_binary64_2842` `log-div_binary64_2893` `pow-pow_binary64_2878` `unpow-prod-down_binary64_2885` `difference-of-squares_binary64_2775`
3×	`cancel-sign-sub-inv_binary64_2772` `distribute-lft-out_binary64_2757` `exp-prod_binary64_2858` `pow-unpow_binary64_2883` `unpow2_binary64_2871`
2×	`distribute-lft-out--_binary64_2758` `rem-log-exp_binary64_2847` `flip-+_binary64_2780` `flip3-+_binary64_2809` `sqr-pow_binary64_2778` `log-pow_binary64_2895`
1×	`pow-exp_binary64_2874` `distribute-rgt-out--_binary64_2760` `flip3--_binary64_2810` `diff-log_binary64_2898` `sub-neg_binary64_2799` `pow-to-exp_binary64_2875` `flip--_binary64_2781`

Counts

4 → 72

Calls

4 calls:

9.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
6.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
4.0ms	(pow.f64 (exp.f64 x) 2)

series228.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
77.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
22.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
12.0ms	(pow.f64 (exp.f64 x) 2)

simplify87.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4924	1223
1	4924	1223

prune112.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	2	86

Merged error: 0.2b

Counts

86 → 2

Compiler

Compiled 2252 to 1357 computations (39.7% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
0.0b	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))
6.8b	(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))
5.0ms	(+.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 (2.3%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
21.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
10.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4958	1292
1	4958	1292

prune62.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	55	3	58

Merged error: 0.2b

Counts

58 → 3

Compiler

Compiled 1268 to 809 computations (36.2% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 2 x) (+.f64 (+.f64 (/.f64 2 (.f64 x x)) (log.f64 1/2)) (.f64 2 (log.f64 x))))
0.0b	(+.f64 (/.f64 2 (*.f64 x x)) (log.f64 1/2))
0.0b	(+.f64 (+.f64 (/.f64 2 (.f64 x x)) (log.f64 1/2)) (.f64 2 (log.f64 x)))
0.2b	(/.f64 2 (*.f64 x x))

rewrite51.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-log-exp_binary64_2845`
14×	`*-un-lft-identity_binary64_2806`
10×	`associate-+r+_binary64_2738` `sum-log_binary64_2897`
9×	`add-sqr-sqrt_binary64_2828` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-cube-cbrt_binary64_2841` `log-prod_binary64_2892`
5×	`pow1_binary64_2867`
4×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
3×	`times-frac_binary64_2812` `distribute-lft-out_binary64_2757` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `associate-/l*_binary64_2751` `+-commutative_binary64_2736`
2×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-add_binary64_2814`
1×	`div-inv_binary64_2803` `associate-/r*_binary64_2750` `associate-+l+_binary64_2739` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `clear-num_binary64_2805` `log-pow_binary64_2895` `frac-2neg_binary64_2817`

Counts

4 → 73

Calls

4 calls:

17.0ms	(+.f64 (/.f64 2 x) (+.f64 (+.f64 (/.f64 2 (.f64 x x)) (log.f64 1/2)) (.f64 2 (log.f64 x))))
12.0ms	(+.f64 (+.f64 (/.f64 2 (.f64 x x)) (log.f64 1/2)) (.f64 2 (log.f64 x)))
11.0ms	(+.f64 (/.f64 2 (*.f64 x x)) (log.f64 1/2))
5.0ms	(/.f64 2 (*.f64 x x))

series334.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(+.f64 (+.f64 (/.f64 2 (.f64 x x)) (log.f64 1/2)) (.f64 2 (log.f64 x)))
93.0ms	(+.f64 (/.f64 2 (*.f64 x x)) (log.f64 1/2))
26.0ms	(+.f64 (/.f64 2 x) (+.f64 (+.f64 (/.f64 2 (.f64 x x)) (log.f64 1/2)) (.f64 2 (log.f64 x))))
16.0ms	(/.f64 2 (*.f64 x x))

simplify86.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4961	1723
1	4961	1723

prune111.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	85	3	88

Merged error: 0.2b

Counts

88 → 3

Compiler

Compiled 2269 to 1485 computations (34.6% saved)

regimes96.0ms (3.2%)

Compiler: Compiled 928 to 759 computations (18.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	35
1	62	35

end0.0ms (0%)

sample1.1s (36%)

Algorithm

1×

intervals

Results

352.0ms	7383×	body	128	valid
96.0ms	247×	body	1024	valid
50.0ms	216×	body	512	valid
19.0ms	153×	body	256	valid
3.0ms	56×	body	128	invalid
1.0ms	1×	body	2048	valid
0.0ms	7×	body	128	overflowed

Compiler

Compiled 360 to 293 computations (18.6% saved)

Details

analyze66.0ms (2.2%)

sample25.0ms (0.8%)

simplify227.0ms (7.6%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

rewrite11.0ms (0.4%)

series54.0ms (1.8%)

simplify82.0ms (2.8%)

prune34.0ms (1.2%)

localize14.0ms (0.5%)

rewrite32.0ms (1.1%)

series228.0ms (7.7%)

simplify87.0ms (2.9%)

prune112.0ms (3.8%)

localize9.0ms (0.3%)

rewrite21.0ms (0.7%)

series69.0ms (2.3%)

simplify65.0ms (2.2%)

prune62.0ms (2.1%)

localize14.0ms (0.5%)

rewrite51.0ms (1.7%)

series334.0ms (11.2%)

simplify86.0ms (2.9%)

prune111.0ms (3.7%)

regimes96.0ms (3.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (36%)

Profiling