Details

analyze438.0ms (7.7%)

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)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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 (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite201.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64`

Counts

3 → 100

Calls

3 calls:

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

series110.0ms (1.9%)

Error

0.0b

Counts

3 → 17

Calls

3 calls:

48.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
24.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
21.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

Compiler

Compiled 425 to 398 computations (6.4% saved)

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6419	2047

prune135.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	3	118

Error

0.0b

Counts

118 → 3

Compiler

Compiled 2029 to 1639 computations (19.2% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite324.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

62×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
58×	`sqrt-prod_binary64`
42×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
12×	`pow1_binary64`
10×	`add-exp-log_binary64` `sqrt-div_binary64` `distribute-lft-out_binary64`
9×	`associate-l_binary64`
8×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`sqrt-pow1_binary64` `associate-/r/_binary64`
4×	`pow1/2_binary64` `add-log-exp_binary64` `difference-of-squares_binary64` `rem-sqrt-square_binary64` `associate-/r*_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `flip--_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/l*_binary64`
2×	`frac-times_binary64` `associate-*l/_binary64` `distribute-lft-out--_binary64` `inv-pow_binary64` `pow-flip_binary64` `div-exp_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `associate-r/_binary64` `-commutative_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 145

Calls

4 calls:

28.0ms	(*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
6.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
6.0ms	(/.f64 1 (+.f64 1 x))
4.0ms	(sqrt.f64 (-.f64 1 x))

Compiler

Compiled 3196 to 2760 computations (13.6% saved)

series118.0ms (2.1%)

Error

Counts

4 → 24

Calls

4 calls:

32.0ms	(*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
28.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
22.0ms	(sqrt.f64 (-.f64 1 x))
16.0ms	(/.f64 1 (+.f64 1 x))

Compiler

Compiled 788 to 695 computations (11.8% saved)

simplify119.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5004	2372

prune254.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	168	4	172

Error

Counts

172 → 4

Compiler

Compiled 3224 to 2749 computations (14.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite161.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

49×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64` `times-frac_binary64`
30×	`sqrt-prod_binary64`
24×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64`
9×	`distribute-lft-out_binary64`
8×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`sqrt-div_binary64` `associate-/r*_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
4.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)))
3.0ms	(-.f64 1 (*.f64 x x))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2233 to 1597 computations (28.5% saved)

series164.0ms (2.9%)

Error

Counts

4 → 21

Calls

4 calls:

49.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
46.0ms	(-.f64 1 (*.f64 x x))
23.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
20.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)))

Compiler

Compiled 671 to 609 computations (9.2% saved)

simplify128.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5138	2141

prune147.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Error

Counts

123 → 4

Compiler

Compiled 2256 to 1644 computations (27.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite701.0ms (12.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

226×	`*-un-lft-identity_binary64`
155×	`add-sqr-sqrt_binary64`
150×	`sqrt-prod_binary64`
145×	`times-frac_binary64`
77×	`add-cube-cbrt_binary64`
72×	`cbrt-prod_binary64`
66×	`unpow-prod-down_binary64` `cube-prod_binary64`
50×	`difference-of-squares_binary64`
37×	`distribute-lft-out_binary64`
25×	`distribute-lft-out--_binary64`
12×	`associate-/r/_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`div-inv_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `associate-/r*_binary64`
3×	`sqrt-div_binary64` `pow-unpow_binary64` `pow-pow_binary64`
2×	`cube-div_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64`
1×	`pow1/3_binary64` `cbrt-div_binary64` `rem-cbrt-cube_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64` `sqrt-pow2_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64`

Counts

4 → 262

Calls

4 calls:

29.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
19.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
16.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 6748 to 5713 computations (15.3% saved)

series154.0ms (2.7%)

Error

Counts

4 → 26

Calls

4 calls:

44.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
38.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
28.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
21.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 708 to 681 computations (3.8% saved)

simplify163.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4933	6080
1	4933	6080

prune494.0ms (8.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	288	4	292

Error

Counts

292 → 4

Compiler

Compiled 5821 to 4834 computations (17% saved)

regimes314.0ms (5.5%)

Accuracy

Total 0.0b remaining (93.8%)

Threshold costs 0.0b (93.8%)

Compiler

Compiled 2202 to 1967 computations (10.7% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	33
1	36	33

end0.0ms (0%)

sample1.3s (23.1%)

Algorithm

1×

intervals

Results

434.0ms

8000×

body

128

valid

Compiler

Compiled 404 to 361 computations (10.6% saved)

Details

analyze438.0ms (7.7%)

sample37.0ms (0.6%)

simplify42.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite201.0ms (3.5%)

series110.0ms (1.9%)

simplify84.0ms (1.5%)

prune135.0ms (2.4%)

localize20.0ms (0.4%)

rewrite324.0ms (5.7%)

series118.0ms (2.1%)

simplify119.0ms (2.1%)

prune254.0ms (4.5%)

localize8.0ms (0.1%)

rewrite161.0ms (2.8%)

series164.0ms (2.9%)

simplify128.0ms (2.3%)

prune147.0ms (2.6%)

localize21.0ms (0.4%)

rewrite701.0ms (12.4%)

series154.0ms (2.7%)

simplify163.0ms (2.9%)

prune494.0ms (8.7%)

regimes314.0ms (5.5%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.3s (23.1%)

Profiling