Details

analyze11.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	50%	50%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample219.0ms (8.5%)

Algorithm

1×

intervals

Results

211.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify99.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

prune4.0ms (0.2%)

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: 0.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.6b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
10×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`add-log-exp_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-sqr-1_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

1 → 36

Calls

1 calls:

12.0ms

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

series38.0ms (1.5%)

Counts

1 → 3

Calls

1 calls:

38.0ms

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

Compiler

Compiled 48 to 42 computations (12.5% saved)

simplify93.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4848	523
1	4848	523

prune41.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Merged error: 0.1b

Counts

40 → 7

Compiler

Compiled 569 to 380 computations (33.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))
0.2b	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x 1))) (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (-.f64 x 1)))))
0.4b	(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (-.f64 x 1))))

rewrite51.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64`
48×	`add-sqr-sqrt_binary64`
36×	`sqrt-div_binary64`
28×	`*-un-lft-identity_binary64`
20×	`pow1_binary64`
19×	`associate-l_binary64`
16×	`add-cube-cbrt_binary64`
14×	`associate-r_binary64`
13×	`sqrt-pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow-prod-down_binary64` `associate-*r/_binary64`
9×	`pow1/2_binary64` `flip3--_binary64` `flip--_binary64`
8×	`difference-of-squares_binary64`
6×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `difference-of-sqr-1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64`
3×	`sqrt-unprod_binary64`
2×	`associate-l/_binary64` `-commutative_binary64`

Counts

4 → 130

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x 1))) (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (-.f64 x 1)))))
12.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (-.f64 x 1))))
5.0ms	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))
5.0ms	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))

series108.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (-.f64 x 1))))
26.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x 1))) (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 (-.f64 x 1)))))
19.0ms	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))
19.0ms	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))

Compiler

Compiled 394 to 342 computations (13.2% saved)

simplify74.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4937	2084
1	4937	2084

prune171.0ms (6.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	136	13	149

Merged error: 0.0b

Counts

149 → 13

Compiler

Compiled 2808 to 2047 computations (27.1% saved)

localize12.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.2b	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x 1))) (.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4)))
0.4b	(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4))

rewrite38.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64`
36×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`associate-l_binary64`
18×	`add-exp-log_binary64`
12×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64` `prod-exp_binary64`
9×	`unpow-prod-down_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64`
6×	`unswap-sqr_binary64` `difference-of-squares_binary64`
4×	`cbrt-unprod_binary64` `sqrt-pow1_binary64`
3×	`add-log-exp_binary64` `difference-of-sqr-1_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `pow-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64`

Counts

3 → 91

Calls

3 calls:

16.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x 1))) (.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4)))
10.0ms	(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4))
4.0ms	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))

series110.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4))
42.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x 1))) (.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4)))
18.0ms	(sqrt.f64 (sqrt.f64 (-.f64 x 1)))

Compiler

Compiled 354 to 305 computations (13.8% saved)

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4997	1668
1	4997	1668

prune121.0ms (4.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

Compiler

Compiled 2120 to 1569 computations (26% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.3b	(.f64 (pow.f64 (-.f64 x 1) 1/4) (.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4)))
0.4b	(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4))

rewrite32.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`prod-exp_binary64`
17×	`associate-l_binary64`
16×	`unpow-prod-down_binary64`
14×	`*-un-lft-identity_binary64`
12×	`associate-r_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow-to-exp_binary64` `add-cube-cbrt_binary64` `pow-exp_binary64`
6×	`unswap-sqr_binary64` `sqrt-prod_binary64`
4×	`cbrt-unprod_binary64` `sqr-pow_binary64` `difference-of-squares_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

2 → 69

Calls

2 calls:

16.0ms	(.f64 (pow.f64 (-.f64 x 1) 1/4) (.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4)))
10.0ms	(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4))

series70.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

50.0ms	(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4))
20.0ms	(.f64 (pow.f64 (-.f64 x 1) 1/4) (.f64 (sqrt.f64 x) (pow.f64 (-.f64 x 1) 1/4)))

Compiler

Compiled 206 to 178 computations (13.6% saved)

simplify59.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4870	1130
1	4870	1130

prune74.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	75	11	86

Merged error: 0.0b

Counts

86 → 11

Compiler

Compiled 1246 to 886 computations (28.9% saved)

regimes124.0ms (4.8%)

Compiler: Compiled 1095 to 895 computations (18.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	21
1	21	21

end0.0ms (0%)

sample919.0ms (35.7%)

Algorithm

1×

intervals

Results

236.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 538 to 442 computations (17.8% saved)

Details

analyze11.0ms (0.4%)

sample219.0ms (8.5%)

simplify99.0ms (3.9%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

rewrite16.0ms (0.6%)

series38.0ms (1.5%)

simplify93.0ms (3.6%)

prune41.0ms (1.6%)

localize11.0ms (0.4%)

rewrite51.0ms (2%)

series108.0ms (4.2%)

simplify74.0ms (2.9%)

prune171.0ms (6.7%)

localize12.0ms (0.5%)

rewrite38.0ms (1.5%)

series110.0ms (4.3%)

simplify64.0ms (2.5%)

prune121.0ms (4.7%)

localize8.0ms (0.3%)

rewrite32.0ms (1.3%)

series70.0ms (2.7%)

simplify59.0ms (2.3%)

prune74.0ms (2.9%)

regimes124.0ms (4.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample919.0ms (35.7%)

Profiling