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
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	55×	body	1024	valid
4.0ms	145×	body	128	valid
2.0ms	32×	body	512	valid
1.0ms	19×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify103.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune7.0ms (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

27.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_2481`
14×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
6×	`cancel-sign-sub-inv_binary64_2431`
5×	`add-cube-cbrt_binary64_2500`
4×	`difference-of-squares_binary64_2434` `add-log-exp_binary64_2504`
3×	`distribute-lft-out--_binary64_2417` `pow1_binary64_2526`
2×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416` `sqrt-div_binary64_2482`
1×	`flip3-+_binary64_2468` `flip--_binary64_2440` `pow1/2_binary64_2545` `flip-+_binary64_2439` `sub-neg_binary64_2458` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series47.0ms (1%)

Counts

2 → 9

Calls

2 calls:

30.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 170 to 142 computations (16.5% saved)

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune46.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.1b

Counts

50 → 3

Compiler

Compiled 583 to 383 computations (34.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_2465`
24×	`sqrt-prod_binary64_2481`
21×	`distribute-lft-out_binary64_2416`
18×	`times-frac_binary64_2471`
16×	`add-sqr-sqrt_binary64_2487`
15×	`add-cube-cbrt_binary64_2500`
7×	`add-exp-log_binary64_2503`
6×	`associate-/r*_binary64_2409`
5×	`add-log-exp_binary64_2504` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/l*_binary64_2410`
2×	`div-exp_binary64_2516` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `inv-pow_binary64_2550` `pow1/2_binary64_2545` `pow-flip_binary64_2539` `rec-exp_binary64_2515` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483` `1-exp_binary64_2509`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series48.0ms (1%)

Counts

3 → 12

Calls

3 calls:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.0ms	(sqrt.f64 (+.f64 x 1))
14.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 182 to 168 computations (7.7% saved)

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4911	1227
1	4911	1227

prune96.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	80	10	90

Error

0.0b

Counts

90 → 10

Compiler

Compiled 1371 to 1006 computations (26.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(cbrt.f64 (+.f64 1 x))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
18×	`add-cube-cbrt_binary64_2500`
13×	`cbrt-prod_binary64_2496`
10×	`add-exp-log_binary64_2503` `associate-r_binary64_2405`
9×	`times-frac_binary64_2471` `sqrt-prod_binary64_2481`
8×	`add-cbrt-cube_binary64_2501`
7×	`pow1_binary64_2526`
6×	`cbrt-div_binary64_2497`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `flip-+_binary64_2439`
3×	`associate-/r_binary64_2409` `unswap-sqr_binary64_2433` `distribute-lft-out_binary64_2416` `associate-/l_binary64_2410` `associate-l_binary64_2406`
2×	`associate-*r/_binary64_2407` `pow1/3_binary64_2547` `div-exp_binary64_2516` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482`
1×	`*-commutative_binary64_2396` `inv-pow_binary64_2550` `pow-flip_binary64_2539` `rec-exp_binary64_2515` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `1-exp_binary64_2509` `cbrt-unprod_binary64_2498`

Counts

4 → 90

Calls

4 calls:

14.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
9.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series280.0ms (5.8%)

Counts

4 → 30

Calls

4 calls:

102.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
80.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
50.0ms	(cbrt.f64 (+.f64 1 x))
47.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1101 to 969 computations (12% saved)

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4840	2640
1	4840	2640

prune182.0ms (3.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	120	10	130

Error

0.0b

Counts

130 → 10

Compiler

Compiled 3046 to 2346 computations (23% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

rewrite149.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_2465`
700×	`sqrt-prod_binary64_2481`
594×	`times-frac_binary64_2471`
280×	`distribute-lft-out_binary64_2416`
254×	`add-sqr-sqrt_binary64_2487`
252×	`add-cube-cbrt_binary64_2500`
36×	`associate-/l*_binary64_2410`
28×	`sqrt-div_binary64_2482`
24×	`associate-/r/_binary64_2411`
18×	`associate-/r*_binary64_2409`
17×	`add-exp-log_binary64_2503`
14×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
12×	`div-inv_binary64_2462`
11×	`add-cbrt-cube_binary64_2501`
8×	`div-exp_binary64_2516` `pow1_binary64_2526`
4×	`add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499`
3×	`pow1/2_binary64_2545` `pow-flip_binary64_2539` `sqrt-pow1_binary64_2483`
2×	`rec-exp_binary64_2515` `clear-num_binary64_2464` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `1-exp_binary64_2509`
1×	`inv-pow_binary64_2550` `associate-/l/_binary64_2412`

Counts

4 → 453

Calls

4 calls:

33.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series95.0ms (2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
21.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
21.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
20.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 408 to 368 computations (9.8% saved)

simplify226.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4875	14766
1	4875	14766

prune974.0ms (20.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	1	6	7
Picked	1	0	1
Done	1	1	2
Total	464	11	475

Error

Counts

475 → 11

Compiler

Compiled 11336 to 8340 computations (26.4% saved)

regimes239.0ms (5%)

Accuracy

Total 0.2b remaining (99.2%)

Threshold costs 0.2b (99.2%)

Compiler

Compiled 2918 to 2367 computations (18.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.9s (40.6%)

Algorithm

1×

intervals

Results

207.0ms	1966×	body	1024	valid
123.0ms	4259×	body	128	valid
77.0ms	1035×	body	512	valid
28.0ms	221×	body	2048	valid
26.0ms	519×	body	256	valid

Compiler

Compiled 1444 to 1173 computations (18.8% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.4%)

simplify103.0ms (2.1%)

prune7.0ms (0.1%)

localize5.0ms (0.1%)

rewrite15.0ms (0.3%)

series47.0ms (1%)

simplify38.0ms (0.8%)

prune46.0ms (1%)

localize6.0ms (0.1%)

rewrite30.0ms (0.6%)

series48.0ms (1%)

simplify79.0ms (1.7%)

prune96.0ms (2%)

localize10.0ms (0.2%)

rewrite38.0ms (0.8%)

series280.0ms (5.8%)

simplify99.0ms (2.1%)

prune182.0ms (3.8%)

localize13.0ms (0.3%)

rewrite149.0ms (3.1%)

series95.0ms (2%)

simplify226.0ms (4.7%)

prune974.0ms (20.3%)

regimes239.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (40.6%)

Profiling