Details

analyze504.0ms (13.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Symmetry

Compiler

Compiled 10 to 8 computations (20% saved)

sample54.0ms (1.4%)

Algorithm

1×

intervals

Results

17.0ms	110×	body	2048	nan
11.0ms	256×	body	128	valid
8.0ms	62×	body	1024	nan
3.0ms	34×	body	512	nan
1.0ms	14×	body	256	nan
1.0ms	18×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify147.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	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

32.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
30.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite64.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

10×	`*-un-lft-identity_binary64_2806`
7×	`add-sqr-sqrt_binary64_2828`
6×	`sqrt-prod_binary64_2822`
5×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841`
4×	`add-exp-log_binary64_2844` `log-prod_binary64_2892`
3×	`add-cbrt-cube_binary64_2842`
2×	`sqrt-div_binary64_2823` `difference-of-squares_binary64_2775` `flip3-+_binary64_2809` `log-div_binary64_2893` `flip-+_binary64_2780` `distribute-lft-out_binary64_2757`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `flip3--_binary64_2810` `flip--_binary64_2781` `difference-of-sqr-1_binary64_2776` `rem-sqrt-square_binary64_2819` `log-pow_binary64_2895` `rem-log-exp_binary64_2847` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

3 → 45

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 804 to 493 computations (38.7% saved)

series129.0ms (3.3%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

52.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
34.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
26.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 506 to 442 computations (12.6% saved)

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5038	944

prune52.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Error

0.0b

Counts

64 → 3

Compiler

Compiled 849 to 553 computations (34.9% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`*-un-lft-identity_binary64_2806`
5×	`log-prod_binary64_2892`
2×	`pow1_binary64_2867` `log-div_binary64_2893` `add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `distribute-lft-out_binary64_2757` `add-exp-log_binary64_2844`
1×	`log-pow_binary64_2895` `flip3-+_binary64_2809` `flip-+_binary64_2780` `distribute-lft-out--_binary64_2758` `rem-log-exp_binary64_2847` `add-log-exp_binary64_2845` `add-cbrt-cube_binary64_2842`

Counts

1 → 16

Calls

1 calls:

8.0ms

(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))

Compiler

Compiled 275 to 188 computations (31.6% saved)

series36.0ms (0.9%)

Error

0.0b

Counts

1 → 4

Calls

1 calls:

33.0ms

(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))

Compiler

Compiled 117 to 108 computations (7.7% saved)

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4690	329
1	4690	329

prune19.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	20	3	23

Error

Counts

23 → 3

Compiler

Compiled 272 to 197 computations (27.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 1/2 x))
0.0b	(-.f64 (log.f64 (+.f64 1 (*.f64 (/.f64 1/2 x) (/.f64 -1/2 x)))) (log.f64 (/.f64 1/2 x)))
0.3b	(*.f64 (/.f64 1/2 x) (/.f64 -1/2 x))
3.3b	(log.f64 (+.f64 1 (*.f64 (/.f64 1/2 x) (/.f64 -1/2 x))))

rewrite214.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

49×	`add-sqr-sqrt_binary64_2828`
40×	`times-frac_binary64_2812`
39×	`*-un-lft-identity_binary64_2806`
35×	`add-cube-cbrt_binary64_2841`
32×	`log-prod_binary64_2892`
20×	`add-exp-log_binary64_2844`
16×	`add-cbrt-cube_binary64_2842`
13×	`pow1_binary64_2867` `associate-l_binary64_2747` `associate-r_binary64_2746` `associate--r+_binary64_2742`
7×	`log-pow_binary64_2895`
6×	`log-div_binary64_2893`
5×	`div-exp_binary64_2857`
4×	`add-log-exp_binary64_2845` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `unswap-sqr_binary64_2774` `div-inv_binary64_2803` `cancel-sign-sub-inv_binary64_2772` `distribute-lft-out--_binary64_2758`
3×	`rem-log-exp_binary64_2847` `associate--l+_binary64_2743`
2×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `associate--l-_binary64_2744`
1×	`pow-prod-down_binary64_2877` `frac-times_binary64_2816` `associate-l/_binary64_2749` `associate-r/_binary64_2748` `*-commutative_binary64_2737` `diff-log_binary64_2898` `flip3--_binary64_2810` `sub-neg_binary64_2799` `flip--_binary64_2781` `difference-of-squares_binary64_2775` `associate--r-_binary64_2745`

Counts

4 → 127

Calls

4 calls:

10.0ms	(*.f64 (/.f64 1/2 x) (/.f64 -1/2 x))
9.0ms	(-.f64 (log.f64 (+.f64 1 (*.f64 (/.f64 1/2 x) (/.f64 -1/2 x)))) (log.f64 (/.f64 1/2 x)))
3.0ms	(log.f64 (+.f64 1 (*.f64 (/.f64 1/2 x) (/.f64 -1/2 x))))
2.0ms	(log.f64 (/.f64 1/2 x))

Compiler

Compiled 3064 to 2429 computations (20.7% saved)

series157.0ms (4.1%)

Error

Counts

4 → 13

Calls

4 calls:

50.0ms	(log.f64 (/.f64 1/2 x))
41.0ms	(-.f64 (log.f64 (+.f64 1 (*.f64 (/.f64 1/2 x) (/.f64 -1/2 x)))) (log.f64 (/.f64 1/2 x)))
29.0ms	(log.f64 (+.f64 1 (*.f64 (/.f64 1/2 x) (/.f64 -1/2 x))))
26.0ms	(*.f64 (/.f64 1/2 x) (/.f64 -1/2 x))

Compiler

Compiled 535 to 476 computations (11% saved)

simplify72.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5256	2136

prune163.0ms (4.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	140	3	143

Error

Counts

143 → 3

Compiler

Compiled 2740 to 2076 computations (24.2% saved)

regimes74.0ms (1.9%)

Accuracy

Total 0.2b remaining (99.6%)

Threshold costs 0.2b (99.6%)

Compiler

Compiled 358 to 307 computations (14.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	23
1	24	23

Removed

()

end0.0ms (0%)

sample2.0s (51.4%)

Algorithm

1×

intervals

Results

640.0ms	4004×	body	2048	nan
341.0ms	8000×	body	128	valid
266.0ms	2072×	body	1024	nan
100.0ms	997×	body	512	nan
29.0ms	466×	body	256	nan
16.0ms	491×	body	128	nan
1.0ms	4×	body	4096	nan

Compiler

Compiled 113 to 99 computations (12.4% saved)

Details

analyze504.0ms (13.1%)

sample54.0ms (1.4%)

simplify147.0ms (3.8%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite64.0ms (1.7%)

series129.0ms (3.3%)

simplify65.0ms (1.7%)

prune52.0ms (1.4%)

localize8.0ms (0.2%)

rewrite24.0ms (0.6%)

series36.0ms (0.9%)

simplify62.0ms (1.6%)

prune19.0ms (0.5%)

localize10.0ms (0.3%)

rewrite214.0ms (5.6%)

series157.0ms (4.1%)

simplify72.0ms (1.9%)

prune163.0ms (4.2%)

regimes74.0ms (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.0s (51.4%)

Profiling