Details

analyze364.0ms (7.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample61.0ms (1.3%)

Algorithm

1×

intervals

Results

26.0ms	73×	body	1024	valid
10.0ms	50×	body	512	valid
9.0ms	33×	body	2048	valid
3.0ms	78×	body	128	valid
2.0ms	20×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	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

52.3b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.5b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite67.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

52.1b

Rules

9×	`*-un-lft-identity_binary64_3147`
6×	`add-sqr-sqrt_binary64_3169`
5×	`pow1_binary64_3208` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
4×	`add-exp-log_binary64_3185` `log-prod_binary64_3233`
3×	`add-cbrt-cube_binary64_3183` `flip3-+_binary64_3150` `flip-+_binary64_3121` `sqrt-prod_binary64_3163`
2×	`sqrt-div_binary64_3164` `log-div_binary64_3234` `distribute-lft-out_binary64_3098`
1×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `log-pow_binary64_3236` `rem-log-exp_binary64_3188` `sum-log_binary64_3238` `+-commutative_binary64_3077`

Counts

3 → 42

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)))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 766 to 464 computations (39.4% saved)

series182.0ms (3.9%)

Error

0.0b

Counts

3 → 27

Calls

3 calls:

70.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
41.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
41.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))

Compiler

Compiled 716 to 609 computations (14.9% saved)

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4854	995
1	4854	995

prune63.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Error

0.0b

Counts

70 → 3

Compiler

Compiled 909 to 595 computations (34.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5/112 (pow.f64 x 7))
0.2b	(*.f64 3/40 (pow.f64 x 5))
0.3b	(*.f64 (pow.f64 x 3) 1/6)
23.6b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))

rewrite232.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-sqr-sqrt_binary64_3169`
19×	`add-exp-log_binary64_3185`
18×	`associate-l_binary64_3088`
17×	`-un-lft-identity_binary64_3147` `associate-r*_binary64_3087`
16×	`add-log-exp_binary64_3186`
15×	`add-cube-cbrt_binary64_3182`
12×	`unpow-prod-down_binary64_3226`
10×	`add-cbrt-cube_binary64_3183` `unswap-sqr_binary64_3115`
9×	`prod-exp_binary64_3196`
6×	`sqr-pow_binary64_3119`
4×	`sum-log_binary64_3238` `diff-log_binary64_3239` `pow1_binary64_3208` `flip3-+_binary64_3150` `frac-sub_binary64_3156` `flip-+_binary64_3121` `cube-prod_binary64_3175`
3×	`cancel-sign-sub-inv_binary64_3113` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `cbrt-unprod_binary64_3180` `*-commutative_binary64_3078`
1×	`flip3--_binary64_3151` `sub-neg_binary64_3140` `flip--_binary64_3122` `difference-of-squares_binary64_3116` `distribute-lft-out--_binary64_3099` `associate--l+_binary64_3084` `associate--r+_binary64_3083` `unpow3_binary64_3213` `cube-mult_binary64_3177`

Counts

4 → 106

Calls

4 calls:

14.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 5/112 (pow.f64 x 7))
5.0ms	(*.f64 3/40 (pow.f64 x 5))

Compiler

Compiled 3201 to 2555 computations (20.2% saved)

series192.0ms (4.1%)

Error

0.0b

Counts

4 → 17

Calls

4 calls:

54.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))
51.0ms	(*.f64 5/112 (pow.f64 x 7))
41.0ms	(*.f64 3/40 (pow.f64 x 5))
31.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 691 to 574 computations (16.9% saved)

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4991	2211
1	4991	2211

prune192.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	122	4	126

Error

Counts

126 → 4

Compiler

Compiled 3154 to 2499 computations (20.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (+.f64 x (/.f64 1/2 x)))
0.0b	(+.f64 x (/.f64 1/2 x))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-log-exp_binary64_3186` `*-un-lft-identity_binary64_3147`
4×	`sum-log_binary64_3238` `distribute-lft-out_binary64_3098`
2×	`pow1_binary64_3208` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169` `flip3-+_binary64_3150` `flip-+_binary64_3121` `+-commutative_binary64_3077`
1×	`associate-+r+_binary64_3079`

Counts

2 → 27

Calls

2 calls:

8.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
6.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 408 to 272 computations (33.3% saved)

series91.0ms (1.9%)

Error

Counts

2 → 12

Calls

2 calls:

47.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
39.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 232 to 186 computations (19.8% saved)

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4933	402
1	4933	402

prune27.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	39	4	43

Error

Counts

43 → 4

Compiler

Compiled 467 to 311 computations (33.4% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Compiler

Compiled 0 to 0 computations (0% saved)

regimes229.0ms (4.9%)

Accuracy

Total 0.2b remaining (71%)

Threshold costs 0.2b (71%)

Compiler

Compiled 1756 to 1338 computations (23.8% saved)

bsearch43.0ms (0.9%)

Steps

Iters	Range		Point
10	0.016678738206466207	1274349868.064525	1.0461861871581324
10	-46234677876.93667	-0.0003306153970869926	-1.262667212110832

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	58
1	97	58

end0.0ms (0%)

sample2.6s (56%)

Algorithm

1×

intervals

Results

888.0ms	2489×	body	1024	valid
373.0ms	1181×	body	2048	valid
269.0ms	1254×	body	512	valid
105.0ms	2363×	body	128	valid
77.0ms	664×	body	256	valid
21.0ms	49×	body	4096	valid

Compiler

Compiled 594 to 455 computations (23.4% saved)

Details

analyze364.0ms (7.7%)

sample61.0ms (1.3%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize7.0ms (0.1%)

rewrite67.0ms (1.4%)

series182.0ms (3.9%)

simplify80.0ms (1.7%)

prune63.0ms (1.3%)

localize12.0ms (0.3%)

rewrite232.0ms (4.9%)

series192.0ms (4.1%)

simplify82.0ms (1.7%)

prune192.0ms (4.1%)

localize6.0ms (0.1%)

rewrite39.0ms (0.8%)

series91.0ms (1.9%)

simplify76.0ms (1.6%)

prune27.0ms (0.6%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune0.0ms (0%)

regimes229.0ms (4.9%)

bsearch43.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.6s (56%)

Profiling