Details

analyze265.0ms (7.3%)

Algorithm

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample57.0ms (1.6%)

Algorithm

1×

intervals

Results

21.0ms	139×	body	2048	nan
11.0ms	256×	body	128	valid
9.0ms	76×	body	1024	nan
3.0ms	28×	body	512	nan
1.0ms	20×	body	256	nan
1.0ms	16×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify260.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5604	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

Merged error: 33.4b

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	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
31.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_419`
7×	`add-sqr-sqrt_binary64_441`
6×	`sqrt-prod_binary64_435`
5×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1_binary64_480`
4×	`log-prod_binary64_505` `add-exp-log_binary64_457`
3×	`add-cbrt-cube_binary64_455`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `difference-of-squares_binary64_388` `distribute-lft-out_binary64_370` `flip-+_binary64_393` `log-div_binary64_506`
1×	`rem-log-exp_binary64_460` `pow1/2_binary64_499` `difference-of-sqr-1_binary64_389` `sum-log_binary64_510` `flip3--_binary64_423` `log-pow_binary64_508` `sqrt-pow1_binary64_437` `flip--_binary64_394` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

3 → 45

Calls

3 calls:

8.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
8.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series197.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
57.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
44.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4891	923
1	4891	923

prune51.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0b

Counts

55 → 2

Compiler

Compiled 840 to 557 computations (33.7% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_441`
15×	`sqrt-prod_binary64_435`
13×	`*-un-lft-identity_binary64_419`
12×	`sqrt-div_binary64_436`
10×	`associate-r_binary64_359`
8×	`add-cube-cbrt_binary64_454` `pow1_binary64_480`
7×	`associate-l_binary64_360`
6×	`add-exp-log_binary64_457`
5×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393` `add-cbrt-cube_binary64_455`
4×	`unswap-sqr_binary64_387` `frac-times_binary64_429`
3×	`pow-prod-down_binary64_490` `log-prod_binary64_505` `flip3--_binary64_423` `flip--_binary64_394`
2×	`associate-l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `associate-r/_binary64_361` `sqrt-pow1_binary64_437` `log-div_binary64_506`
1×	`sqrt-unprod_binary64_439` `rem-log-exp_binary64_460` `difference-of-sqr-1_binary64_389` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `log-pow_binary64_508` `*-commutative_binary64_350` `+-commutative_binary64_349`

Counts

3 → 68

Calls

3 calls:

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

series203.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

81.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
67.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
54.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify100.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4900	1681
1	4900	1681

prune85.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0b

Counts

79 → 2

Compiler

Compiled 1527 to 1157 computations (24.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.5b	(.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) 1)))) (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
31.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))
31.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite55.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`sqrt-prod_binary64_435`
32×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
21×	`pow1_binary64_480`
16×	`sqrt-div_binary64_436`
14×	`add-cube-cbrt_binary64_454`
11×	`swap-sqr_binary64_386`
10×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
7×	`flip3-+_binary64_422` `associate-r_binary64_359` `distribute-lft-out_binary64_370` `associate-l_binary64_360` `flip-+_binary64_393`
6×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`pow-prod-up_binary64_489`
4×	`difference-of-squares_binary64_388` `unswap-sqr_binary64_387` `frac-times_binary64_429` `rem-sqrt-square_binary64_432`
3×	`pow-prod-down_binary64_490` `pow-sqr_binary64_392`
2×	`associate-l/_binary64_362` `difference-of-sqr-1_binary64_389` `flip3--_binary64_423` `associate-r/_binary64_361` `flip--_binary64_394`
1×	`sqrt-unprod_binary64_439` `rem-square-sqrt_binary64_431` `sqr-abs_binary64_434` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `pow-plus_binary64_482` `*-commutative_binary64_350` `+-commutative_binary64_349` `pow2_binary64_500`

Counts

4 → 111

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) 1)))) (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
8.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series207.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) 1)))) (sqrt.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
57.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
45.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
38.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4889	1960
1	4889	1960

prune134.0ms (3.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

Compiler

Compiled 2691 to 1735 computations (35.5% saved)

regimes52.0ms (1.4%)

Compiler: Compiled 330 to 248 computations (24.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.8s (48.4%)

Algorithm

1×

intervals

Results

622.0ms	3989×	body	2048	nan
359.0ms	8000×	body	128	valid
243.0ms	2009×	body	1024	nan
100.0ms	1048×	body	512	nan
30.0ms	490×	body	256	nan
19.0ms	510×	body	128	nan
3.0ms	6×	body	4096	nan

Compiler

Compiled 101 to 78 computations (22.8% saved)

Details

analyze265.0ms (7.3%)

sample57.0ms (1.6%)

simplify260.0ms (7.1%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite24.0ms (0.7%)

series197.0ms (5.4%)

simplify55.0ms (1.5%)

prune51.0ms (1.4%)

localize10.0ms (0.3%)

rewrite28.0ms (0.8%)

series203.0ms (5.6%)

simplify100.0ms (2.7%)

prune85.0ms (2.3%)

localize10.0ms (0.3%)

rewrite55.0ms (1.5%)

series207.0ms (5.7%)

simplify74.0ms (2%)

prune134.0ms (3.7%)

regimes52.0ms (1.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (48.4%)

Profiling