Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
75%	25%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 6 to 6 computations (0% saved)

sample9.0ms (0.3%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 11 to 12 computations (-9.1% saved)

simplify166.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	4
1	10	4

prune9.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 x 1/3)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_7647` `add-sqr-sqrt_binary64_7669`
3×	`cancel-sign-sub-inv_binary64_7613` `add-log-exp_binary64_7686`
2×	`add-cube-cbrt_binary64_7682`
1×	`sub-neg_binary64_7640` `diff-log_binary64_7739` `add-cbrt-cube_binary64_7683` `flip--_binary64_7622` `flip3--_binary64_7651` `add-exp-log_binary64_7685` `pow1_binary64_7708` `difference-of-squares_binary64_7616` `distribute-lft-out--_binary64_7599`

Counts

1 → 16

Calls

1 calls:

4.0ms

(-.f64 x 1/3)

series29.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

29.0ms

(-.f64 x 1/3)

simplify98.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4819	121
1	4819	121

prune19.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	2	20

Merged error: 0.0b

Counts

20 → 2

Compiler

Compiled 173 to 138 computations (20.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))
0.0b	(-.f64 (pow.f64 x 3) 1/27)
0.2b	(*.f64 x (+.f64 x 1/3))
19.2b	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (+.f64 1/9 (*.f64 x (+.f64 x 1/3))))

rewrite47.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_7669`
32×	`*-un-lft-identity_binary64_7647`
24×	`times-frac_binary64_7653`
20×	`difference-of-squares_binary64_7616` `add-cube-cbrt_binary64_7682`
8×	`add-cbrt-cube_binary64_7683` `add-exp-log_binary64_7685` `associate-/l*_binary64_7592` `add-log-exp_binary64_7686`
6×	`pow1_binary64_7708`
5×	`unpow-prod-down_binary64_7726` `distribute-lft-out--_binary64_7599` `cube-prod_binary64_7675` `sqr-pow_binary64_7619`
4×	`associate-r_binary64_7587`
3×	`flip-+_binary64_7621` `associate-l_binary64_7588` `cancel-sign-sub-inv_binary64_7613` `associate-/r*_binary64_7591` `flip3-+_binary64_7650`
2×	`flip--_binary64_7622` `flip3--_binary64_7651` `associate-*r/_binary64_7589` `associate-/r/_binary64_7593` `associate-/l/_binary64_7594` `distribute-rgt-in_binary64_7597` `associate-+r+_binary64_7579` `distribute-lft-in_binary64_7596`
1×	`sub-neg_binary64_7640` `diff-log_binary64_7739` `div-exp_binary64_7698` `unswap-sqr_binary64_7615` `div-sub_binary64_7652` `prod-exp_binary64_7696` `sum-log_binary64_7738` `distribute-lft-out_binary64_7598` `+-commutative_binary64_7577` `cbrt-unprod_binary64_7680` `div-inv_binary64_7644` `pow-prod-down_binary64_7718` `frac-2neg_binary64_7658` `clear-num_binary64_7646` `cbrt-undiv_binary64_7681` `*-commutative_binary64_7578`

Counts

4 → 107

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (+.f64 1/9 (*.f64 x (+.f64 x 1/3))))
12.0ms	(-.f64 (pow.f64 x 3) 1/27)
7.0ms	(*.f64 x (+.f64 x 1/3))
4.0ms	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))

series333.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (+.f64 1/9 (*.f64 x (+.f64 x 1/3))))
86.0ms	(-.f64 (pow.f64 x 3) 1/27)
60.0ms	(*.f64 x (+.f64 x 1/3))
18.0ms	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))

simplify123.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4951	2384
1	4951	2384

prune192.0ms (5.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	118	3	121

Merged error: 0b

Counts

121 → 3

Compiler

Compiled 2958 to 2366 computations (20% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))
0.1b	(/.f64 1 (/.f64 (+.f64 1/9 (*.f64 x (+.f64 x 1/3))) (-.f64 (pow.f64 x 3) 1/27)))
0.2b	(*.f64 x (+.f64 x 1/3))
19.7b	(/.f64 (+.f64 1/9 (*.f64 x (+.f64 x 1/3))) (-.f64 (pow.f64 x 3) 1/27))

rewrite77.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

212×	`add-sqr-sqrt_binary64_7669`
210×	`times-frac_binary64_7653`
132×	`*-un-lft-identity_binary64_7647`
98×	`add-cube-cbrt_binary64_7682`
64×	`difference-of-squares_binary64_7616`
38×	`associate-/r*_binary64_7591`
19×	`add-exp-log_binary64_7685`
16×	`unpow-prod-down_binary64_7726` `distribute-lft-out--_binary64_7599` `cube-prod_binary64_7675` `sqr-pow_binary64_7619`
13×	`add-cbrt-cube_binary64_7683`
11×	`associate-/r/_binary64_7593`
8×	`div-exp_binary64_7698`
7×	`pow1_binary64_7708`
6×	`div-inv_binary64_7644` `associate-/l*_binary64_7592` `add-log-exp_binary64_7686`
5×	`flip--_binary64_7622` `flip3--_binary64_7651`
4×	`cbrt-undiv_binary64_7681` `associate-r_binary64_7587`
3×	`flip-+_binary64_7621` `associate-l_binary64_7588` `flip3-+_binary64_7650`
2×	`rec-exp_binary64_7697` `1-exp_binary64_7691` `frac-2neg_binary64_7658` `associate-*r/_binary64_7589` `clear-num_binary64_7646` `associate-/l/_binary64_7594` `distribute-rgt-in_binary64_7597` `associate-+r+_binary64_7579` `distribute-lft-in_binary64_7596`
1×	`unswap-sqr_binary64_7615` `prod-exp_binary64_7696` `sum-log_binary64_7738` `distribute-lft-out_binary64_7598` `+-commutative_binary64_7577` `cbrt-unprod_binary64_7680` `pow-prod-down_binary64_7718` `pow-flip_binary64_7721` `inv-pow_binary64_7732` `*-commutative_binary64_7578`

Counts

4 → 231

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 (+.f64 1/9 (*.f64 x (+.f64 x 1/3))) (-.f64 (pow.f64 x 3) 1/27)))
14.0ms	(/.f64 (+.f64 1/9 (*.f64 x (+.f64 x 1/3))) (-.f64 (pow.f64 x 3) 1/27))
8.0ms	(*.f64 x (+.f64 x 1/3))
4.0ms	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))

series282.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(/.f64 1 (/.f64 (+.f64 1/9 (*.f64 x (+.f64 x 1/3))) (-.f64 (pow.f64 x 3) 1/27)))
64.0ms	(*.f64 x (+.f64 x 1/3))
38.0ms	(/.f64 (+.f64 1/9 (*.f64 x (+.f64 x 1/3))) (-.f64 (pow.f64 x 3) 1/27))
18.0ms	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))

simplify146.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4899	7614
1	4899	7614

prune542.0ms (16%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	243	3	246

Merged error: 0b

Counts

246 → 3

Compiler

Compiled 6565 to 5337 computations (18.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) (pow.f64 x 3))
0.2b	(*.f64 x (+.f64 x 1/3))
0.5b	(.f64 (+.f64 1/9 (.f64 x (+.f64 x 1/3))) (+.f64 (pow.f64 x 3) 1/27))
25.4b	(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 1/27 1/27)) (.f64 (+.f64 1/9 (.f64 x (+.f64 x 1/3))) (+.f64 (pow.f64 x 3) 1/27)))

rewrite82.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_7669`
30×	`*-un-lft-identity_binary64_7647`
26×	`unpow-prod-down_binary64_7726` `cube-prod_binary64_7675` `add-cube-cbrt_binary64_7682`
25×	`add-exp-log_binary64_7685`
20×	`associate-r_binary64_7587`
18×	`unswap-sqr_binary64_7615` `swap-sqr_binary64_7614` `associate-l_binary64_7588`
15×	`add-cbrt-cube_binary64_7683`
13×	`flip-+_binary64_7621` `flip3-+_binary64_7650`
12×	`prod-exp_binary64_7696` `sqr-pow_binary64_7619`
8×	`pow1_binary64_7708` `frac-times_binary64_7657` `associate-/r/_binary64_7593`
6×	`pow-to-exp_binary64_7716` `associate-*r/_binary64_7589` `pow-exp_binary64_7715`
4×	`times-frac_binary64_7653` `cube-mult_binary64_7677` `cbrt-unprod_binary64_7680` `associate-/l_binary64_7592` `add-log-exp_binary64_7686` `unpow3_binary64_7713` `associate-l/_binary64_7590`
3×	`pow-prod-down_binary64_7718` `*-commutative_binary64_7578`
2×	`div-exp_binary64_7698` `distribute-lft-out_binary64_7598` `difference-of-squares_binary64_7616` `associate-/l/_binary64_7594` `cbrt-undiv_binary64_7681` `distribute-rgt-in_binary64_7597` `distribute-lft-in_binary64_7596`
1×	`div-sub_binary64_7652` `flip--_binary64_7622` `flip3--_binary64_7651` `div-inv_binary64_7644` `pow-sqr_binary64_7620` `frac-2neg_binary64_7658` `pow2_binary64_7728` `clear-num_binary64_7646` `associate-/r*_binary64_7591` `pow-prod-up_binary64_7717`

Counts

4 → 166

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 1/27 1/27)) (.f64 (+.f64 1/9 (.f64 x (+.f64 x 1/3))) (+.f64 (pow.f64 x 3) 1/27)))
14.0ms	(.f64 (+.f64 1/9 (.f64 x (+.f64 x 1/3))) (+.f64 (pow.f64 x 3) 1/27))
12.0ms	(*.f64 (pow.f64 x 3) (pow.f64 x 3))
7.0ms	(*.f64 x (+.f64 x 1/3))

series390.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 1/27 1/27)) (.f64 (+.f64 1/9 (.f64 x (+.f64 x 1/3))) (+.f64 (pow.f64 x 3) 1/27)))
57.0ms	(*.f64 (pow.f64 x 3) (pow.f64 x 3))
52.0ms	(*.f64 x (+.f64 x 1/3))
32.0ms	(.f64 (+.f64 1/9 (.f64 x (+.f64 x 1/3))) (+.f64 (pow.f64 x 3) 1/27))

simplify100.0ms (3%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5029	2750

prune333.0ms (9.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	178	3	181

Merged error: 0b

Counts

181 → 3

Compiler

Compiled 5071 to 4038 computations (20.4% saved)

regimes13.0ms (0.4%)

Compiler: Compiled 45 to 39 computations (13.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	4
1	14	4

end0.0ms (0%)

sample332.0ms (9.8%)

Algorithm

1×

intervals

Results

148.0ms

8000×

body

128

valid

Compiler

Compiled 52 to 47 computations (9.6% saved)

Details

analyze3.0ms (0.1%)

sample9.0ms (0.3%)

simplify166.0ms (4.9%)

prune9.0ms (0.3%)

localize3.0ms (0.1%)

rewrite5.0ms (0.2%)

series29.0ms (0.9%)

simplify98.0ms (2.9%)

prune19.0ms (0.6%)

localize10.0ms (0.3%)

rewrite47.0ms (1.4%)

series333.0ms (9.9%)

simplify123.0ms (3.6%)

prune192.0ms (5.7%)

localize16.0ms (0.5%)

rewrite77.0ms (2.3%)

series282.0ms (8.4%)

simplify146.0ms (4.3%)

prune542.0ms (16%)

localize14.0ms (0.4%)

rewrite82.0ms (2.4%)

series390.0ms (11.5%)

simplify100.0ms (3%)

prune333.0ms (9.9%)

regimes13.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample332.0ms (9.8%)

Profiling