Details

analyze45.0ms (1.6%)

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%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample14.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	128	nan

Compiler

Compiled 17 to 17 computations (0% saved)

simplify171.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	188	12
1	188	12

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: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2509`
7×	`add-log-exp_binary64_2526`
6×	`-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `associate-r*_binary64_2427`
4×	`sqrt-prod_binary64_2503` `add-exp-log_binary64_2525` `associate-+l+_binary64_2420` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548`
3×	`cancel-sign-sub-inv_binary64_2453` `associate-l_binary64_2428`
2×	`unswap-sqr_binary64_2455` `sum-log_binary64_2578`
1×	`sub-neg_binary64_2480` `associate-+l-_binary64_2422` `*-commutative_binary64_2418` `diff-log_binary64_2579` `prod-exp_binary64_2536` `flip-+_binary64_2461` `+-commutative_binary64_2417` `flip3-+_binary64_2490` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558`

Counts

2 → 39

Calls

2 calls:

8.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
6.0ms	(*.f64 y (sqrt.f64 x))

series105.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(*.f64 y (sqrt.f64 x))
42.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify55.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5082	594

prune77.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	40	5	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	6	46

Merged error: 0.0b

Counts

46 → 6

Compiler

Compiled 1256 to 727 computations (42.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_2503`
25×	`add-sqr-sqrt_binary64_2509`
18×	`associate-r_binary64_2427`
15×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `pow1_binary64_2548`
11×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
8×	`sqrt-pow1_binary64_2505`
4×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `add-log-exp_binary64_2526` `associate-l_binary64_2428` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567`
3×	`unswap-sqr_binary64_2455`
2×	`*-commutative_binary64_2418`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series342.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt.f64 (sqrt.f64 x))
99.0ms	(sqrt.f64 (sqrt.f64 x))
73.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
59.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify70.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5316	1029

prune111.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	100	6	106

Merged error: 0b

Counts

106 → 6

Compiler

Compiled 2178 to 966 computations (55.6% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`sqrt-prod_binary64_2503`
21×	`add-sqr-sqrt_binary64_2509`
19×	`add-exp-log_binary64_2525`
16×	`associate-r_binary64_2427`
13×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522`
11×	`add-cbrt-cube_binary64_2523`
10×	`prod-exp_binary64_2536`
9×	`add-log-exp_binary64_2526`
8×	`pow1_binary64_2548`
4×	`associate-+l+_binary64_2420` `sqrt-pow1_binary64_2505` `cbrt-unprod_binary64_2520` `associate-l_binary64_2428`
3×	`unswap-sqr_binary64_2455` `cancel-sign-sub-inv_binary64_2453` `unpow-prod-down_binary64_2566`
2×	`pow-exp_binary64_2555` `*-commutative_binary64_2418` `pow-to-exp_binary64_2556` `sum-log_binary64_2578` `rem-sqrt-square_binary64_2500` `pow1/2_binary64_2567`
1×	`sub-neg_binary64_2480` `associate-+l-_binary64_2422` `diff-log_binary64_2579` `flip-+_binary64_2461` `+-commutative_binary64_2417` `flip3-+_binary64_2490` `pow-prod-down_binary64_2558` `sqr-pow_binary64_2459`

Counts

4 → 86

Calls

4 calls:

10.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
9.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series376.0ms (13%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
102.0ms	(sqrt.f64 (sqrt.f64 x))
83.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
82.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))

simplify92.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4859	1507
1	4859	1507

prune109.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	98	6	104

Merged error: 0b

Counts

104 → 6

Compiler

Compiled 2013 to 1109 computations (44.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 y (fabs.f64 (cbrt.f64 x)))
0.3b	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_2509`
12×	`associate-r_binary64_2427`
11×	`add-exp-log_binary64_2525` `*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548`
9×	`cbrt-prod_binary64_2518`
6×	`sqrt-prod_binary64_2503`
4×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `add-log-exp_binary64_2526` `associate-l_binary64_2428`
2×	`*-commutative_binary64_2418` `pow1/3_binary64_2569`
1×	`unswap-sqr_binary64_2455`

Counts

4 → 64

Calls

4 calls:

8.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
4.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series483.0ms (16.7%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt.f64 x)
146.0ms	(cbrt.f64 x)
138.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
29.0ms	(*.f64 y (fabs.f64 (cbrt.f64 x)))

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	847
1	4961	847

prune58.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	76	6	82

Merged error: 0b

Counts

82 → 6

Compiler

Compiled 1276 to 482 computations (62.2% saved)

regimes43.0ms (1.5%)

Compiler: Compiled 260 to 202 computations (22.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample524.0ms (18.2%)

Algorithm

1×

intervals

Results

250.0ms	7999×	body	128	valid
4.0ms	129×	body	128	nan
2.0ms	58×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 97 to 77 computations (20.6% saved)

Details

analyze45.0ms (1.6%)

sample14.0ms (0.5%)

simplify171.0ms (5.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite17.0ms (0.6%)

series105.0ms (3.6%)

simplify55.0ms (1.9%)

prune77.0ms (2.7%)

localize10.0ms (0.4%)

rewrite30.0ms (1%)

series342.0ms (11.9%)

simplify70.0ms (2.4%)

prune111.0ms (3.9%)

localize16.0ms (0.5%)

rewrite36.0ms (1.3%)

series376.0ms (13%)

simplify92.0ms (3.2%)

prune109.0ms (3.8%)

localize9.0ms (0.3%)

rewrite20.0ms (0.7%)

series483.0ms (16.7%)

simplify59.0ms (2%)

prune58.0ms (2%)

regimes43.0ms (1.5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample524.0ms (18.2%)

Profiling