Details

analyze261.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 32 to 28 computations (12.5% saved)

sample119.0ms (1.4%)

Algorithm

1×

intervals

Results

41.0ms	138×	body	512	valid
27.0ms	287×	body	128	nan
24.0ms	62×	body	1024	valid
6.0ms	32×	body	256	valid
2.0ms	24×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify209.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5168	50

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 7.5b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.1b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_14205` `sqrt-prod_binary64_14199`
40×	`*-un-lft-identity_binary64_14183`
24×	`cancel-sign-sub-inv_binary64_14149`
16×	`difference-of-squares_binary64_14152`
12×	`add-cube-cbrt_binary64_14218` `distribute-lft-out--_binary64_14135` `add-log-exp_binary64_14222`
4×	`sub-neg_binary64_14176` `flip--_binary64_14158` `distribute-lft-out_binary64_14134` `add-cbrt-cube_binary64_14219` `flip3--_binary64_14187` `diff-log_binary64_14275` `pow1_binary64_14244` `add-exp-log_binary64_14221`

Counts

4 → 96

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series278.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
72.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
66.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
65.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5136	2211

prune377.0ms (4.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Merged error: 1.2b

Counts

109 → 6

Compiler

Compiled 6996 to 5055 computations (27.7% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
2.4b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_14183`
49×	`sqrt-prod_binary64_14199`
45×	`add-sqr-sqrt_binary64_14205`
21×	`add-cube-cbrt_binary64_14218`
19×	`distribute-lft-out_binary64_14134`
18×	`times-frac_binary64_14189` `cancel-sign-sub-inv_binary64_14149`
12×	`difference-of-squares_binary64_14152`
10×	`add-log-exp_binary64_14222`
9×	`distribute-lft-out--_binary64_14135`
8×	`add-exp-log_binary64_14221`
6×	`add-cbrt-cube_binary64_14219` `associate-/r*_binary64_14127`
5×	`pow1_binary64_14244`
3×	`sub-neg_binary64_14176` `flip--_binary64_14158` `associate-/l*_binary64_14128` `flip3--_binary64_14187` `diff-log_binary64_14275`
2×	`associate-/r/_binary64_14129` `div-exp_binary64_14234`
1×	`clear-num_binary64_14182` `inv-pow_binary64_14268` `div-inv_binary64_14180` `cbrt-undiv_binary64_14217` `flip3-+_binary64_14186` `1-exp_binary64_14227` `pow-flip_binary64_14257` `frac-2neg_binary64_14194` `rec-exp_binary64_14233` `flip-+_binary64_14157`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series255.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
66.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
63.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
58.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4974	2625
1	4974	2625

prune358.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Merged error: 0.7b

Counts

135 → 6

Compiler

Compiled 6624 to 4630 computations (30.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
2.4b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite69.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_14183`
54×	`sqrt-prod_binary64_14199`
46×	`add-sqr-sqrt_binary64_14205`
36×	`times-frac_binary64_14189`
34×	`distribute-lft-out_binary64_14134`
30×	`add-cube-cbrt_binary64_14218`
12×	`associate-/r*_binary64_14127` `cancel-sign-sub-inv_binary64_14149` `add-exp-log_binary64_14221`
8×	`add-cbrt-cube_binary64_14219` `difference-of-squares_binary64_14152` `add-log-exp_binary64_14222`
6×	`associate-/l*_binary64_14128` `distribute-lft-out--_binary64_14135` `pow1_binary64_14244`
4×	`associate-/r/_binary64_14129` `div-exp_binary64_14234`
2×	`clear-num_binary64_14182` `sub-neg_binary64_14176` `flip--_binary64_14158` `inv-pow_binary64_14268` `div-inv_binary64_14180` `cbrt-undiv_binary64_14217` `flip3-+_binary64_14186` `flip3--_binary64_14187` `diff-log_binary64_14275` `1-exp_binary64_14227` `pow-flip_binary64_14257` `frac-2neg_binary64_14194` `rec-exp_binary64_14233` `flip-+_binary64_14157`

Counts

4 → 138

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series252.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
65.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
64.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
51.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5730	3036

prune442.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	150	6	156

Merged error: 0.2b

Counts

156 → 6

Compiler

Compiled 8141 to 5819 computations (28.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite71.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_14183`
59×	`sqrt-prod_binary64_14199`
54×	`times-frac_binary64_14189`
49×	`distribute-lft-out_binary64_14134`
47×	`add-sqr-sqrt_binary64_14205`
39×	`add-cube-cbrt_binary64_14218`
18×	`associate-/r*_binary64_14127`
16×	`add-exp-log_binary64_14221`
10×	`add-cbrt-cube_binary64_14219`
9×	`associate-/l*_binary64_14128`
7×	`pow1_binary64_14244`
6×	`cancel-sign-sub-inv_binary64_14149` `associate-/r/_binary64_14129` `div-exp_binary64_14234` `add-log-exp_binary64_14222`
4×	`difference-of-squares_binary64_14152`
3×	`clear-num_binary64_14182` `inv-pow_binary64_14268` `div-inv_binary64_14180` `cbrt-undiv_binary64_14217` `flip3-+_binary64_14186` `1-exp_binary64_14227` `pow-flip_binary64_14257` `frac-2neg_binary64_14194` `rec-exp_binary64_14233` `flip-+_binary64_14157` `distribute-lft-out--_binary64_14135`
1×	`sub-neg_binary64_14176` `flip--_binary64_14158` `flip3--_binary64_14187` `diff-log_binary64_14275`

Counts

4 → 159

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

series255.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
58.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4904	3440
1	4904	3440

prune498.0ms (6.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	171	6	177

Merged error: 0.0b

Counts

177 → 6

Compiler

Compiled 8382 to 5911 computations (29.5% saved)

regimes244.0ms (3%)

Compiler: Compiled 2795 to 2491 computations (10.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

end0.0ms (0%)

sample3.9s (48.1%)

Algorithm

1×

intervals

Results

1.3s	4421×	body	512	valid
925.0ms	9560×	body	128	nan
678.0ms	1740×	body	1024	valid
194.0ms	1022×	body	256	valid
83.0ms	817×	body	128	valid

Compiler

Compiled 355 to 314 computations (11.5% saved)

Details

analyze261.0ms (3.2%)

sample119.0ms (1.4%)

simplify209.0ms (2.5%)

prune4.0ms (0%)

localize23.0ms (0.3%)

rewrite57.0ms (0.7%)

series278.0ms (3.4%)

simplify86.0ms (1.1%)

prune377.0ms (4.6%)

localize23.0ms (0.3%)

rewrite61.0ms (0.7%)

series255.0ms (3.1%)

simplify75.0ms (0.9%)

prune358.0ms (4.4%)

localize24.0ms (0.3%)

rewrite69.0ms (0.8%)

series252.0ms (3.1%)

simplify97.0ms (1.2%)

prune442.0ms (5.4%)

localize26.0ms (0.3%)

rewrite71.0ms (0.9%)

series255.0ms (3.1%)

simplify83.0ms (1%)

prune498.0ms (6.1%)

regimes244.0ms (3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (48.1%)

Profiling