Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample14.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify97.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_2735`
23×	`add-sqr-sqrt_binary64_2757`
18×	`times-frac_binary64_2741`
17×	`distribute-lft-out_binary64_2686`
14×	`add-cube-cbrt_binary64_2770`
12×	`sqrt-prod_binary64_2751`
6×	`associate-/r*_binary64_2679`
4×	`add-cbrt-cube_binary64_2771` `add-exp-log_binary64_2773`
3×	`associate-/l*_binary64_2680` `pow1_binary64_2796`
2×	`flip-+_binary64_2709` `flip3-+_binary64_2738` `add-log-exp_binary64_2774` `associate-/r/_binary64_2681` `sqrt-div_binary64_2752`
1×	`sqrt-pow1_binary64_2753` `div-inv_binary64_2732` `clear-num_binary64_2734` `pow1/2_binary64_2815` `rem-sqrt-square_binary64_2748` `cbrt-undiv_binary64_2769` `div-exp_binary64_2786` `frac-2neg_binary64_2746`

Counts

2 → 57

Calls

4 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series54.0ms (2.3%)

Counts

2 → 10

Calls

2 calls:

37.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 194 to 166 computations (14.4% saved)

simplify72.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5642	943

prune74.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	3	68

Error

Counts

68 → 3

Compiler

Compiled 900 to 672 computations (25.3% saved)

localize6.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite38.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_2735`
48×	`add-sqr-sqrt_binary64_2757`
38×	`times-frac_binary64_2741`
29×	`distribute-lft-out_binary64_2686`
26×	`add-cube-cbrt_binary64_2770`
24×	`associate-r_binary64_2675`
18×	`sqrt-prod_binary64_2751`
16×	`add-exp-log_binary64_2773`
10×	`add-cbrt-cube_binary64_2771`
7×	`pow1_binary64_2796`
6×	`associate-/r*_binary64_2679`
4×	`div-exp_binary64_2786` `prod-exp_binary64_2784` `associate-/r/_binary64_2681`
3×	`flip-+_binary64_2709` `flip3-+_binary64_2738` `associate-l_binary64_2676` `associate-/l*_binary64_2680` `unswap-sqr_binary64_2703` `add-log-exp_binary64_2774`
2×	`div-inv_binary64_2732` `1-exp_binary64_2779` `cbrt-undiv_binary64_2769` `rec-exp_binary64_2785` `cbrt-unprod_binary64_2768` `sqrt-div_binary64_2752`
1×	`sqrt-pow1_binary64_2753` `clear-num_binary64_2734` `un-div-inv_binary64_2733` `pow1/2_binary64_2815` `pow-prod-down_binary64_2806` `rem-sqrt-square_binary64_2748` `-commutative_binary64_2666` `frac-2neg_binary64_2746` `associate-r/_binary64_2677` `pow-flip_binary64_2809` `inv-pow_binary64_2820`

Counts

3 → 108

Calls

6 calls:

16.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
3.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series87.0ms (3.7%)

Counts

3 → 15

Calls

3 calls:

37.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
33.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 324 to 278 computations (14.2% saved)

simplify85.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5376	1590

prune115.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Error

Counts

126 → 3

Compiler

Compiled 1799 to 1483 computations (17.6% saved)

localize8.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite57.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`*-un-lft-identity_binary64_2735`
89×	`add-sqr-sqrt_binary64_2757`
77×	`sqrt-prod_binary64_2751`
76×	`times-frac_binary64_2741`
53×	`distribute-lft-out_binary64_2686`
46×	`add-cube-cbrt_binary64_2770`
42×	`associate-r_binary64_2675`
10×	`add-cbrt-cube_binary64_2771` `add-exp-log_binary64_2773`
6×	`associate-l_binary64_2676` `associate-/l_binary64_2680` `pow1_binary64_2796` `unswap-sqr_binary64_2703` `associate-/r_binary64_2679`
4×	`associate-/r/_binary64_2681`
3×	`flip-+_binary64_2709` `flip3-+_binary64_2738` `add-log-exp_binary64_2774`
2×	`div-inv_binary64_2732` `cbrt-undiv_binary64_2769` `div-exp_binary64_2786` `prod-exp_binary64_2784` `cbrt-unprod_binary64_2768` `sqrt-div_binary64_2752`
1×	`sqrt-pow1_binary64_2753` `clear-num_binary64_2734` `pow1/2_binary64_2815` `pow-prod-down_binary64_2806` `rem-sqrt-square_binary64_2748` `-commutative_binary64_2666` `frac-2neg_binary64_2746` `associate-r/_binary64_2677`

Counts

3 → 146

Calls

6 calls:

25.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series103.0ms (4.4%)

Counts

3 → 13

Calls

3 calls:

45.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
40.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 382 to 305 computations (20.2% saved)

simplify89.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4999	2729
1	4999	2729

prune147.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	159	3	162

Error

Counts

162 → 3

Compiler

Compiled 2863 to 1783 computations (37.7% saved)

localize8.0ms (0.3%)

Local error

Found 8 expressions with local error:

33.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
0.2b	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
33.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

rewrite59.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`*-un-lft-identity_binary64_2735`
91×	`add-sqr-sqrt_binary64_2757`
90×	`times-frac_binary64_2741`
65×	`distribute-lft-out_binary64_2686`
58×	`add-cube-cbrt_binary64_2770`
54×	`cbrt-prod_binary64_2766`
48×	`cube-prod_binary64_2763` `unpow-prod-down_binary64_2814`
36×	`sqrt-prod_binary64_2751`
10×	`associate-/r/_binary64_2681`
9×	`add-cbrt-cube_binary64_2771` `add-exp-log_binary64_2773`
6×	`flip-+_binary64_2709` `flip3-+_binary64_2738` `pow1_binary64_2796` `associate-/r*_binary64_2679`
5×	`div-inv_binary64_2732`
4×	`add-log-exp_binary64_2774`
3×	`pow-unpow_binary64_2812` `associate-/l*_binary64_2680`
2×	`rem-cube-cbrt_binary64_2758` `unpow3_binary64_2801` `cbrt-undiv_binary64_2769` `div-exp_binary64_2786` `pow-exp_binary64_2803` `sqr-pow_binary64_2707` `cube-mult_binary64_2765` `cube-div_binary64_2764` `sqrt-div_binary64_2752`
1×	`sqrt-pow1_binary64_2753` `cbrt-div_binary64_2767` `pow-to-exp_binary64_2804` `clear-num_binary64_2734` `pow1/3_binary64_2817` `rem-cbrt-cube_binary64_2759` `pow1/2_binary64_2815` `rem-sqrt-square_binary64_2748` `frac-2neg_binary64_2746` `pow-pow_binary64_2807`

Counts

4 → 189

Calls

8 calls:

15.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
12.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
3.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))

series162.0ms (6.9%)

Counts

4 → 20

Calls

4 calls:

66.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
41.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
37.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 520 to 460 computations (11.5% saved)

simplify93.0ms (4%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5276	3843

prune206.0ms (8.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	209	3	212

Error

Counts

212 → 3

Compiler

Compiled 3321 to 2559 computations (22.9% saved)

regimes66.0ms (2.8%)

Accuracy

Total 0.2b remaining (99.1%)

Threshold costs 0.2b (99.1%)

Compiler

Compiled 516 to 424 computations (17.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample660.0ms (28.3%)

Algorithm

1×

intervals

Results

248.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 266 to 220 computations (17.3% saved)

Pareto

Details

analyze3.0ms (0.1%)

sample14.0ms (0.6%)

simplify97.0ms (4.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite21.0ms (0.9%)

series54.0ms (2.3%)

simplify72.0ms (3.1%)

prune74.0ms (3.2%)

localize6.0ms (0.3%)

rewrite38.0ms (1.6%)

series87.0ms (3.7%)

simplify85.0ms (3.6%)

prune115.0ms (4.9%)

localize8.0ms (0.3%)

rewrite57.0ms (2.5%)

series103.0ms (4.4%)

simplify89.0ms (3.8%)

prune147.0ms (6.3%)

localize8.0ms (0.3%)

rewrite59.0ms (2.5%)

series162.0ms (6.9%)

simplify93.0ms (4%)

prune206.0ms (8.8%)

regimes66.0ms (2.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample660.0ms (28.3%)

Profiling