Details

analyze630.0ms (12.5%)

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
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 23 to 25 computations (-8.7% saved)

simplify169.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	1196	13
1	1196	13

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

8.2b

Counts

2 → 2

Compiler

Compiled 29 to 28 computations (3.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 2 (-.f64 y t))
0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
8.4b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

rewrite62.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64_14406`
180×	`add-sqr-sqrt_binary64_14422`
171×	`*-un-lft-identity_binary64_14400`
121×	`add-cube-cbrt_binary64_14435`
67×	`associate-r_binary64_14340`
25×	`difference-of-squares_binary64_14369` `distribute-lft-out--_binary64_14352`
24×	`associate-/l*_binary64_14345`
19×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
16×	`associate-/r/_binary64_14346`
10×	`div-inv_binary64_14397`
8×	`associate-/r*_binary64_14344` `flip--_binary64_14375` `flip3--_binary64_14404`
7×	`cbrt-undiv_binary64_14434` `div-exp_binary64_14451`
5×	`pow1_binary64_14461`
3×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449` `add-log-exp_binary64_14439` `associate-l_binary64_14341` `unswap-sqr_binary64_14368`
2×	`frac-2neg_binary64_14411` `clear-num_binary64_14399`
1×	`associate-/l/_binary64_14347` `pow-prod-down_binary64_14471` `associate-r/_binary64_14342` `-commutative_binary64_14331`

Counts

3 → 228

Calls

3 calls:

23.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
9.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
5.0ms	(/.f64 2 (-.f64 y t))

series156.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

76.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
55.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
24.0ms	(/.f64 2 (-.f64 y t))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5031	4394

prune432.0ms (8.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	227	10	237
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	228	11	239

Error

Counts

239 → 11

Compiler

Compiled 4476 to 2094 computations (53.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 y t))
0.5b	(cbrt.f64 (-.f64 y t))
0.5b	(cbrt.f64 (-.f64 y t))
6.6b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

rewrite92.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`times-frac_binary64_14406`
135×	`add-sqr-sqrt_binary64_14422`
109×	`*-un-lft-identity_binary64_14400`
94×	`associate-r_binary64_14340`
85×	`add-cube-cbrt_binary64_14435`
62×	`cbrt-prod_binary64_14431`
40×	`add-exp-log_binary64_14438`
31×	`add-cbrt-cube_binary64_14436`
24×	`cbrt-div_binary64_14432`
15×	`cbrt-undiv_binary64_14434` `div-exp_binary64_14451` `associate-l_binary64_14341`
14×	`associate-/r/_binary64_14346`
12×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449` `difference-of-squares_binary64_14369` `flip--_binary64_14375` `flip3--_binary64_14404` `distribute-lft-out--_binary64_14352`
8×	`unswap-sqr_binary64_14368`
6×	`pow1_binary64_14461`
5×	`frac-times_binary64_14410` `div-inv_binary64_14397`
4×	`add-log-exp_binary64_14439`
3×	`associate-l/_binary64_14343` `pow1/3_binary64_14482` `associate-r/_binary64_14342`
1×	`pow-prod-down_binary64_14471` `*-commutative_binary64_14331`

Counts

4 → 192

Calls

4 calls:

58.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
3.0ms	(cbrt.f64 (-.f64 y t))
3.0ms	(cbrt.f64 (-.f64 y t))
3.0ms	(cbrt.f64 (-.f64 y t))

series406.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt.f64 (-.f64 y t))
108.0ms	(cbrt.f64 (-.f64 y t))
102.0ms	(cbrt.f64 (-.f64 y t))
84.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

simplify101.0ms (2%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5002	5542

prune206.0ms (4.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	205	10	215

Error

Counts

215 → 10

Compiler

Compiled 5926 to 1883 computations (68.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (*.f64 x 2) (-.f64 y t))
7.9b	(/.f64 (/.f64 (*.f64 x 2) (-.f64 y t)) z)

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64_14406`
36×	`add-sqr-sqrt_binary64_14422` `*-un-lft-identity_binary64_14400`
24×	`add-cube-cbrt_binary64_14435`
16×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
12×	`associate-/l*_binary64_14345`
10×	`associate-/r/_binary64_14346`
8×	`associate-/r*_binary64_14344`
7×	`cbrt-undiv_binary64_14434` `div-exp_binary64_14451`
6×	`difference-of-squares_binary64_14369` `div-inv_binary64_14397` `distribute-lft-out--_binary64_14352`
5×	`flip--_binary64_14375` `flip3--_binary64_14404`
2×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449` `frac-2neg_binary64_14411` `clear-num_binary64_14399` `add-log-exp_binary64_14439` `pow1_binary64_14461`
1×	`associate-/l/_binary64_14347`

Counts

2 → 91

Calls

2 calls:

9.0ms	(/.f64 (/.f64 (*.f64 x 2) (-.f64 y t)) z)
7.0ms	(/.f64 (*.f64 x 2) (-.f64 y t))

series110.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

75.0ms	(/.f64 (/.f64 (*.f64 x 2) (-.f64 y t)) z)
35.0ms	(/.f64 (*.f64 x 2) (-.f64 y t))

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4961	1739
1	4961	1739

prune73.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	98	9	107

Error

Counts

107 → 9

Compiler

Compiled 1581 to 708 computations (55.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 2 (-.f64 y t))
0.2b	(*.f64 x (/.f64 2 (-.f64 y t)))
7.9b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64_14438` `add-sqr-sqrt_binary64_14422`
44×	`*-un-lft-identity_binary64_14400`
40×	`times-frac_binary64_14406`
34×	`associate-r_binary64_14340`
31×	`add-cbrt-cube_binary64_14436`
30×	`add-cube-cbrt_binary64_14435`
22×	`prod-exp_binary64_14449`
12×	`cbrt-unprod_binary64_14433` `div-exp_binary64_14451`
10×	`pow1_binary64_14461`
7×	`cbrt-undiv_binary64_14434` `difference-of-squares_binary64_14369` `distribute-lft-out--_binary64_14352`
5×	`associate-/r*_binary64_14344`
4×	`pow-prod-down_binary64_14471` `associate-r/_binary64_14342` `associate-/r/_binary64_14346` `associate-l*_binary64_14341`
3×	`1-exp_binary64_14444` `rec-exp_binary64_14450` `div-inv_binary64_14397` `add-log-exp_binary64_14439` `associate-/l*_binary64_14345`
2×	`flip--_binary64_14375` `flip3--_binary64_14404` `*-commutative_binary64_14331` `unswap-sqr_binary64_14368`
1×	`associate-*l/_binary64_14343` `frac-2neg_binary64_14411` `frac-times_binary64_14410` `clear-num_binary64_14399` `un-div-inv_binary64_14398`

Counts

3 → 123

Calls

3 calls:

13.0ms	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
10.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
5.0ms	(/.f64 2 (-.f64 y t))

series133.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

71.0ms	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
37.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
24.0ms	(/.f64 2 (-.f64 y t))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5276	1736

prune104.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	134	7	141

Error

Counts

141 → 7

Compiler

Compiled 2013 to 1114 computations (44.7% saved)

regimes628.0ms (12.5%)

Accuracy

Total 1.7b remaining (99.9%)

Threshold costs 0b (0%)

Compiler

Compiled 6180 to 4982 computations (19.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	49
1	28	49

end0.0ms (0%)

sample1.4s (27.5%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
25.0ms	701×	body	128	invalid

Compiler

Compiled 954 to 745 computations (21.9% saved)

Details

analyze630.0ms (12.5%)

sample19.0ms (0.4%)

simplify169.0ms (3.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite62.0ms (1.2%)

series156.0ms (3.1%)

simplify95.0ms (1.9%)

prune432.0ms (8.6%)

localize11.0ms (0.2%)

rewrite92.0ms (1.8%)

series406.0ms (8.1%)

simplify101.0ms (2%)

prune206.0ms (4.1%)

localize7.0ms (0.1%)

rewrite23.0ms (0.5%)

series110.0ms (2.2%)

simplify58.0ms (1.2%)

prune73.0ms (1.4%)

localize10.0ms (0.2%)

rewrite38.0ms (0.8%)

series133.0ms (2.6%)

simplify71.0ms (1.4%)

prune104.0ms (2.1%)

regimes628.0ms (12.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27.5%)

Profiling