Details

analyze758.0ms (15.6%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 35 to 33 computations (5.7% saved)

simplify235.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4805	19
1	4805	19

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

Merged error: 2.0b

Counts

2 → 2

Compiler

Compiled 43 to 36 computations (16.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
3.9b	(/.f64 (.f64 y t) (.f64 2 z))
5.8b	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_13557`
24×	`add-sqr-sqrt_binary64_13578`
18×	`add-cbrt-cube_binary64_13590` `add-exp-log_binary64_13592`
16×	`times-frac_binary64_13563`
14×	`add-cube-cbrt_binary64_13589`
8×	`add-log-exp_binary64_13593`
6×	`associate-/r*_binary64_13503`
5×	`cbrt-undiv_binary64_13588` `div-exp_binary64_13605` `difference-of-squares_binary64_13526` `distribute-lft-out--_binary64_13511`
4×	`prod-exp_binary64_13603` `cbrt-unprod_binary64_13587` `pow1_binary64_13615` `associate-/l*_binary64_13504`
2×	`clear-num_binary64_13556` `flip3--_binary64_13561` `flip--_binary64_13532` `div-inv_binary64_13554` `frac-2neg_binary64_13568` `associate-/r/_binary64_13505`
1×	`sub-neg_binary64_13550` `+-commutative_binary64_13489` `distribute-lft-out_binary64_13510` `flip3-+_binary64_13560` `flip-+_binary64_13531` `diff-log_binary64_13646` `sum-log_binary64_13645`

Counts

4 → 83

Calls

4 calls:

20.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
10.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
8.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
6.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series397.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
122.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
89.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
53.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4975	1896
1	4975	1896

prune102.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	4	97

Merged error: 0.3b

Counts

97 → 4

Compiler

Compiled 1940 to 1000 computations (48.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)))
0.4b	(/.f64 2 (/.f64 t z))
5.1b	(/.f64 y (/.f64 2 (/.f64 t z)))
5.8b	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))

rewrite171.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

519×	`times-frac_binary64_13563`
300×	`add-sqr-sqrt_binary64_13578`
254×	`*-un-lft-identity_binary64_13557`
244×	`add-cube-cbrt_binary64_13589`
65×	`associate-/r*_binary64_13503`
23×	`div-inv_binary64_13554`
20×	`add-cbrt-cube_binary64_13590` `add-exp-log_binary64_13592`
16×	`difference-of-squares_binary64_13526`
10×	`cbrt-undiv_binary64_13588` `div-exp_binary64_13605`
9×	`associate-/l*_binary64_13504`
8×	`associate-/r/_binary64_13505`
6×	`add-log-exp_binary64_13593`
4×	`pow1_binary64_13615` `distribute-lft-out--_binary64_13511`
3×	`clear-num_binary64_13556` `frac-2neg_binary64_13568`
1×	`flip3--_binary64_13561` `+-commutative_binary64_13489` `distribute-lft-out_binary64_13510` `flip--_binary64_13532` `flip3-+_binary64_13560` `flip-+_binary64_13531` `sum-log_binary64_13645`

Counts

4 → 327

Calls

4 calls:

53.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)))
47.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
17.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
6.0ms	(/.f64 2 (/.f64 t z))

series321.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
122.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)))
41.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
25.0ms	(/.f64 2 (/.f64 t z))

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5003	8017

prune383.0ms (7.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	336	3	339
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	338	5	343

Merged error: 0.2b

Counts

343 → 5

Compiler

Compiled 7998 to 3674 computations (54.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 2 (/.f64 z t))
0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)))
5.1b	(/.f64 y (*.f64 2 (/.f64 z t)))
5.8b	(/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z))

rewrite55.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_13578`
34×	`*-un-lft-identity_binary64_13557`
28×	`times-frac_binary64_13563`
24×	`add-cube-cbrt_binary64_13589`
20×	`add-cbrt-cube_binary64_13590` `add-exp-log_binary64_13592`
13×	`associate-r_binary64_13499`
6×	`cbrt-undiv_binary64_13588` `div-exp_binary64_13605` `pow1_binary64_13615` `associate-/r_binary64_13503` `associate-/l_binary64_13504` `add-log-exp_binary64_13593`
4×	`prod-exp_binary64_13603` `cbrt-unprod_binary64_13587` `difference-of-squares_binary64_13526` `distribute-lft-out--_binary64_13511`
3×	`div-inv_binary64_13554` `associate-l_binary64_13500` `associate-/r/_binary64_13505`
2×	`clear-num_binary64_13556` `associate-*r/_binary64_13501` `unswap-sqr_binary64_13525` `frac-2neg_binary64_13568`
1×	`flip3--_binary64_13561` `+-commutative_binary64_13489` `distribute-lft-out_binary64_13510` `flip--_binary64_13532` `*-commutative_binary64_13490` `flip3-+_binary64_13560` `flip-+_binary64_13531` `pow-prod-down_binary64_13625` `sum-log_binary64_13645`

Counts

4 → 105

Calls

4 calls:

17.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)))
12.0ms	(/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z))
10.0ms	(/.f64 y (*.f64 2 (/.f64 z t)))
8.0ms	(*.f64 2 (/.f64 z t))

series470.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z))
151.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)))
47.0ms	(/.f64 y (*.f64 2 (/.f64 z t)))
23.0ms	(*.f64 2 (/.f64 z t))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5119	1964

prune104.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

Compiler

Compiled 2265 to 1133 computations (50% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))
0.0b	(+.f64 x (/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))))
0.2b	(/.f64 1/2 (/.f64 z t))
0.8b	(/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y)))

rewrite152.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

167×	`add-sqr-sqrt_binary64_13578`
163×	`times-frac_binary64_13563`
95×	`*-un-lft-identity_binary64_13557`
62×	`add-cube-cbrt_binary64_13589`
30×	`difference-of-squares_binary64_13526`
24×	`associate-/r*_binary64_13503`
13×	`add-exp-log_binary64_13592`
11×	`add-cbrt-cube_binary64_13590`
10×	`distribute-lft-out--_binary64_13511`
8×	`add-log-exp_binary64_13593`
7×	`div-inv_binary64_13554`
6×	`associate-/l*_binary64_13504`
5×	`div-exp_binary64_13605` `pow1_binary64_13615`
4×	`cbrt-undiv_binary64_13588` `associate-/r/_binary64_13505`
2×	`clear-num_binary64_13556` `frac-sub_binary64_13566` `flip3--_binary64_13561` `distribute-lft-out_binary64_13510` `flip--_binary64_13532` `frac-2neg_binary64_13568`
1×	`sub-neg_binary64_13550` `inv-pow_binary64_13639` `+-commutative_binary64_13489` `1-exp_binary64_13598` `flip3-+_binary64_13560` `flip-+_binary64_13531` `diff-log_binary64_13646` `sum-log_binary64_13645` `pow-flip_binary64_13628` `rec-exp_binary64_13604`

Counts

4 → 169

Calls

4 calls:

46.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))))
40.0ms	(/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y)))
40.0ms	(-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))
7.0ms	(/.f64 1/2 (/.f64 z t))

series195.0ms (4%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))))
57.0ms	(/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y)))
41.0ms	(-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))
29.0ms	(/.f64 1/2 (/.f64 z t))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5039	4027

prune184.0ms (3.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	181	4	185

Merged error: 0b

Counts

185 → 4

Compiler

Compiled 3962 to 1919 computations (51.6% saved)

regimes78.0ms (1.6%)

Compiler: Compiled 492 to 422 computations (14.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms (0%)

sample761.0ms (15.7%)

Algorithm

1×

intervals

Results

421.0ms

8000×

body

128

valid

Compiler

Compiled 114 to 99 computations (13.2% saved)

Details

analyze758.0ms (15.6%)

sample22.0ms (0.5%)

simplify235.0ms (4.9%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite52.0ms (1.1%)

series397.0ms (8.2%)

simplify71.0ms (1.5%)

prune102.0ms (2.1%)

localize9.0ms (0.2%)

rewrite171.0ms (3.5%)

series321.0ms (6.6%)

simplify129.0ms (2.7%)

prune383.0ms (7.9%)

localize9.0ms (0.2%)

rewrite55.0ms (1.1%)

series470.0ms (9.7%)

simplify69.0ms (1.4%)

prune104.0ms (2.1%)

localize9.0ms (0.2%)

rewrite152.0ms (3.1%)

series195.0ms (4%)

simplify90.0ms (1.9%)

prune184.0ms (3.8%)

regimes78.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample761.0ms (15.7%)

Profiling