Details

analyze335.0ms (10.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify33.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune4.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite173.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `associate-/r/_binary64` `associate-/r*_binary64`
3×	`add-log-exp_binary64`
2×	`div-inv_binary64` `associate-/l/_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

Compiler

Compiled 2038 to 1659 computations (18.6% saved)

series90.0ms (2.7%)

Error

0.0b

Counts

3 → 17

Calls

3 calls:

34.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
19.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

Compiler

Compiled 425 to 398 computations (6.4% saved)

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6419	2047

prune126.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	2	118

Error

Counts

118 → 2

Compiler

Compiled 2021 to 1631 computations (19.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite237.0ms (7.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

98×	`sqrt-prod_binary64`
91×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
11×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64` `associate-/l*_binary64`
8×	`sqrt-div_binary64`
7×	`associate-/r*_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
2×	`flip3--_binary64` `associate-/l/_binary64` `flip--_binary64` `flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (-.f64 1 x))
3.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 3038 to 2537 computations (16.5% saved)

series94.0ms (2.9%)

Error

Counts

4 → 21

Calls

4 calls:

21.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
21.0ms	(sqrt.f64 (-.f64 1 x))
21.0ms	(sqrt.f64 (+.f64 1 x))
15.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 635 to 563 computations (11.3% saved)

simplify117.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5646	3065

prune174.0ms (5.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	2	160

Error

Counts

160 → 2

Compiler

Compiled 2970 to 2461 computations (17.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(cbrt.f64 (pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3))
1.0b	(pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3)

rewrite236.0ms (7.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

86×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
12×	`cbrt-prod_binary64`
9×	`distribute-lft-out--_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`unpow-prod-down_binary64` `pow1_binary64` `cube-prod_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-/r*_binary64`
3×	`pow-unpow_binary64`
2×	`unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `div-inv_binary64` `associate-/l/_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64` `pow1/3_binary64` `rem-cbrt-cube_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms	(pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3)
2.0ms	(cbrt.f64 (pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3))

Compiler

Compiled 3311 to 2794 computations (15.6% saved)

series163.0ms (5%)

Error

Counts

4 → 20

Calls

4 calls:

69.0ms	(pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3)
39.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
21.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
17.0ms	(cbrt.f64 (pow.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3))

Compiler

Compiled 647 to 608 computations (6% saved)

simplify117.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4889	2923
1	4889	2923

prune192.0ms (5.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	157	2	159

Error

Counts

159 → 2

Compiler

Compiled 3128 to 2624 computations (16.1% saved)

regimes119.0ms (3.6%)

Accuracy

Total 0.0b remaining (91.2%)

Threshold costs 0.0b (91.2%)

Compiler

Compiled 1307 to 1164 computations (10.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms (0%)

sample939.0ms (28.6%)

Algorithm

1×

intervals

Results

372.0ms

8000×

body

128

valid

Compiler

Compiled 270 to 242 computations (10.4% saved)

Details

analyze335.0ms (10.2%)

sample22.0ms (0.7%)

simplify33.0ms (1%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

rewrite173.0ms (5.3%)

series90.0ms (2.7%)

simplify78.0ms (2.4%)

prune126.0ms (3.8%)

localize8.0ms (0.3%)

rewrite237.0ms (7.2%)

series94.0ms (2.9%)

simplify117.0ms (3.6%)

prune174.0ms (5.3%)

localize10.0ms (0.3%)

rewrite236.0ms (7.2%)

series163.0ms (5%)

simplify117.0ms (3.6%)

prune192.0ms (5.9%)

regimes119.0ms (3.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample939.0ms (28.6%)

Profiling