Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample68.0ms (0.3%)

Algorithm

1×

intervals

Results

31.0ms	53×	body	1024	valid
18.0ms	42×	body	512	valid
7.0ms	139×	body	128	valid
2.0ms	6×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify444.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune24.0ms (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: 29.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize18.0ms (0.1%)

Local error

Found 1 expressions with local error:

2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`sqrt-prod_binary64_14416` `add-sqr-sqrt_binary64_14422`
10×	`*-un-lft-identity_binary64_14400`
6×	`cancel-sign-sub-inv_binary64_14366`
4×	`difference-of-squares_binary64_14369`
3×	`add-cube-cbrt_binary64_14435` `add-log-exp_binary64_14439` `distribute-lft-out--_binary64_14352`
1×	`sub-neg_binary64_14393` `add-exp-log_binary64_14438` `distribute-lft-out_binary64_14351` `flip--_binary64_14375` `flip3--_binary64_14404` `pow1_binary64_14461` `diff-log_binary64_14492` `add-cbrt-cube_binary64_14436`

Counts

1 → 24

Calls

1 calls:

49.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series157.0ms (0.6%)

Counts

1 → 3

Calls

1 calls:

156.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify171.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4981	542
1	4981	542

prune413.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	16	11	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	12	28

Merged error: 0.1b

Counts

28 → 12

Compiler

Compiled 637 to 441 computations (30.8% saved)

localize127.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite85.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_14400`
20×	`sqrt-prod_binary64_14416` `distribute-lft-out_binary64_14351`
18×	`times-frac_binary64_14406`
13×	`add-cube-cbrt_binary64_14435` `add-sqr-sqrt_binary64_14422`
6×	`associate-/r*_binary64_14344` `add-exp-log_binary64_14438`
4×	`add-log-exp_binary64_14439` `add-cbrt-cube_binary64_14436`
3×	`pow1_binary64_14461` `associate-/l*_binary64_14345`
2×	`flip3-+_binary64_14403` `div-exp_binary64_14451` `flip-+_binary64_14374` `associate-/r/_binary64_14346`
1×	`1-exp_binary64_14444` `+-commutative_binary64_14330` `frac-2neg_binary64_14411` `cbrt-undiv_binary64_14434` `clear-num_binary64_14399` `rec-exp_binary64_14450` `pow-flip_binary64_14474` `div-inv_binary64_14397` `sum-log_binary64_14491` `inv-pow_binary64_14485`

Counts

2 → 59

Calls

2 calls:

36.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
31.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series204.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

114.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
90.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify237.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (184.0ms)

Iter	Nodes	Cost
0	4980	1269
1	4980	1269

prune1.6s (5.9%)

Pruning

34 alts after pruning (32 fresh and 2 done)

	Pruned	Kept	Total
New	43	22	65
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	43	34	77

Merged error: 0.0b

Counts

77 → 34

Compiler

Compiled 1743 to 1287 computations (26.2% saved)

localize41.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite197.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64_14400`
48×	`times-frac_binary64_14406`
36×	`sqrt-prod_binary64_14416` `distribute-lft-out_binary64_14351`
31×	`add-cube-cbrt_binary64_14435` `add-sqr-sqrt_binary64_14422`
24×	`distribute-lft-neg-in_binary64_14357` `distribute-rgt-neg-in_binary64_14358`
16×	`associate-/r*_binary64_14344`
4×	`add-exp-log_binary64_14438` `add-log-exp_binary64_14439` `neg-mul-1_binary64_14396` `add-cbrt-cube_binary64_14436`
3×	`associate-/l*_binary64_14345`
2×	`distribute-neg-frac_binary64_14364` `flip3-+_binary64_14403` `pow1_binary64_14461` `flip-+_binary64_14374` `associate-/r/_binary64_14346`
1×	`+-commutative_binary64_14330` `frac-2neg_binary64_14411` `cbrt-undiv_binary64_14434` `clear-num_binary64_14399` `div-exp_binary64_14451` `div-inv_binary64_14397` `sum-log_binary64_14491`

Counts

2 → 95

Calls

2 calls:

60.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
58.0ms	(/.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

series253.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

159.0ms	(/.f64 -1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
94.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify386.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (306.0ms)

Iter	Nodes	Cost
0	5102	2354

prune2.7s (10.1%)

Pruning

52 alts after pruning (49 fresh and 3 done)

	Pruned	Kept	Total
New	79	22	101
Fresh	4	27	31
Picked	0	1	1
Done	0	2	2
Total	83	52	135

Merged error: 0.0b

Counts

135 → 52

Compiler

Compiled 2912 to 2213 computations (24% saved)

localize42.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 -1 (neg.f64 (*.f64 (sqrt.f64 1) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_14400`
18×	`times-frac_binary64_14406`
13×	`add-cube-cbrt_binary64_14435` `add-sqr-sqrt_binary64_14422`
6×	`associate-/r*_binary64_14344`
4×	`add-exp-log_binary64_14438` `distribute-lft-neg-in_binary64_14357` `sqrt-prod_binary64_14416` `distribute-lft-out_binary64_14351` `distribute-rgt-neg-in_binary64_14358` `add-log-exp_binary64_14439` `neg-mul-1_binary64_14396` `add-cbrt-cube_binary64_14436`
3×	`associate-/l*_binary64_14345`
2×	`distribute-neg-frac_binary64_14364` `flip3-+_binary64_14403` `associate-*r/_binary64_14342` `pow1_binary64_14461` `flip-+_binary64_14374` `associate-/r/_binary64_14346`
1×	`+-commutative_binary64_14330` `frac-2neg_binary64_14411` `cbrt-undiv_binary64_14434` `clear-num_binary64_14399` `div-exp_binary64_14451` `div-inv_binary64_14397` `sum-log_binary64_14491`

Counts

2 → 55

Calls

2 calls:

45.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
20.0ms	(/.f64 -1 (neg.f64 (*.f64 (sqrt.f64 1) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series145.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

97.0ms	(/.f64 -1 (neg.f64 (*.f64 (sqrt.f64 1) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
47.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify152.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	5087	1334

prune1.5s (5.7%)

Pruning

57 alts after pruning (53 fresh and 4 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	4	44	48
Picked	0	1	1
Done	0	3	3
Total	56	57	113

Merged error: 0.0b

Counts

113 → 57

Compiler

Compiled 1141 to 842 computations (26.2% saved)

regimes1.9s (7.2%)

Compiler: Compiled 4606 to 3806 computations (17.4% saved)

bsearch3.2s (11.9%)

simplify135.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	14
1	13	14

end12.0ms (0%)

sample12.6s (46.5%)

Algorithm

1×

intervals

Results

734.0ms	1963×	body	1024	valid
540.0ms	1036×	body	512	valid
443.0ms	4279×	body	128	valid
134.0ms	242×	body	2048	valid
86.0ms	480×	body	256	valid

Compiler

Compiled 2287 to 1892 computations (17.3% saved)

Pareto

Details

analyze5.0ms (0%)

sample68.0ms (0.3%)

simplify444.0ms (1.6%)

prune24.0ms (0.1%)

localize18.0ms (0.1%)

rewrite56.0ms (0.2%)

series157.0ms (0.6%)

simplify171.0ms (0.6%)

prune413.0ms (1.5%)

localize127.0ms (0.5%)

rewrite85.0ms (0.3%)

series204.0ms (0.8%)

simplify237.0ms (0.9%)

prune1.6s (5.9%)

localize41.0ms (0.2%)

rewrite197.0ms (0.7%)

series253.0ms (0.9%)

simplify386.0ms (1.4%)

prune2.7s (10.1%)

localize42.0ms (0.2%)

rewrite88.0ms (0.3%)

series145.0ms (0.5%)

simplify152.0ms (0.6%)

prune1.5s (5.7%)

regimes1.9s (7.2%)

bsearch3.2s (11.9%)

simplify135.0ms (0.5%)

end12.0ms (0%)

sample12.6s (46.5%)

Profiling