Details

analyze57.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
6.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify322.0ms (9.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	4945	16
1	4945	16

prune4.0ms (0.1%)

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: 0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(*.f64 m (-.f64 1 m))
0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

rewrite247.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64`
4×	`flip3--_binary64` `associate-*r/_binary64` `insert-posit16` `flip--_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

213.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
12.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(*.f64 m (-.f64 1 m))

series224.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
69.0ms	(*.f64 m (-.f64 1 m))
55.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
31.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify102.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5346	1475

prune117.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

Compiler

Compiled 1857 to 1248 computations (32.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
0.0b	(/.f64 (-.f64 1 m) v)
0.1b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.2b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite51.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`
14×	`difference-of-squares_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-/l*_binary64`
4×	`insert-posit16`
3×	`associate-/r*_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 118

Calls

4 calls:

14.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
13.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
10.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
8.0ms	(/.f64 (-.f64 1 m) v)

series189.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
50.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
46.0ms	(/.f64 (-.f64 1 m) v)
32.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)

simplify135.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4965	1914
1	4965	1914

prune127.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	130	9	139

Merged error: 0.0b

Counts

139 → 9

Compiler

Compiled 2389 to 1529 computations (36% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 m (/.f64 m v)) (+.f64 m (/.f64 (pow.f64 m 3) v)))
0.2b	(*.f64 m (/.f64 m v))
6.6b	(/.f64 (pow.f64 m 3) v)

rewrite46.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`associate-r_binary64` `add-exp-log_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`sqr-pow_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`associate-/r_binary64` `associate-r/_binary64` `associate-l_binary64` `insert-posit16`
2×	`diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `frac-sub_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 115

Calls

3 calls:

25.0ms	(-.f64 (*.f64 m (/.f64 m v)) (+.f64 m (/.f64 (pow.f64 m 3) v)))
8.0ms	(*.f64 m (/.f64 m v))
7.0ms	(/.f64 (pow.f64 m 3) v)

series100.0ms (3%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(-.f64 (*.f64 m (/.f64 m v)) (+.f64 m (/.f64 (pow.f64 m 3) v)))
30.0ms	(/.f64 (pow.f64 m 3) v)
26.0ms	(*.f64 m (/.f64 m v))

simplify115.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5000	1706

prune110.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	5	1	6
Picked	1	0	1
Done	0	2	2
Total	127	6	133

Merged error: 0b

Counts

133 → 6

Compiler

Compiled 2376 to 842 computations (64.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (sqrt.f64 (.f64 m (/.f64 m v))) (sqrt.f64 (*.f64 m (/.f64 m v))))
6.6b	(/.f64 (pow.f64 m 3) v)
13.1b	(sqrt.f64 (*.f64 m (/.f64 m v)))
13.1b	(sqrt.f64 (*.f64 m (/.f64 m v)))

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`pow1_binary64`
36×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
32×	`sqrt-pow1_binary64`
22×	`pow-prod-down_binary64`
12×	`pow1/2_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l*_binary64`
11×	`add-exp-log_binary64`
10×	`pow-prod-up_binary64`
8×	`add-cbrt-cube_binary64`
7×	`associate-*r/_binary64`
6×	`pow-sqr_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `sqr-pow_binary64` `associate-l_binary64` `insert-posit16` `unpow3_binary64` `cube-mult_binary64`
3×	`associate-/r*_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (.f64 m (/.f64 m v))) (sqrt.f64 (*.f64 m (/.f64 m v))))
7.0ms	(/.f64 (pow.f64 m 3) v)
5.0ms	(sqrt.f64 (*.f64 m (/.f64 m v)))
4.0ms	(sqrt.f64 (*.f64 m (/.f64 m v)))

series207.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt.f64 (*.f64 m (/.f64 m v)))
57.0ms	(sqrt.f64 (*.f64 m (/.f64 m v)))
46.0ms	(.f64 (sqrt.f64 (.f64 m (/.f64 m v))) (sqrt.f64 (*.f64 m (/.f64 m v))))
36.0ms	(/.f64 (pow.f64 m 3) v)

simplify127.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4982	1718
1	4982	1718

prune144.0ms (4.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	157	6	163

Merged error: 0b

Counts

163 → 6

Compiler

Compiled 3643 to 1168 computations (67.9% saved)

regimes52.0ms (1.6%)

Compiler: Compiled 359 to 254 computations (29.2% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms (0%)

sample746.0ms (22.4%)

Algorithm

1×

intervals

Results

264.0ms	8000×	body	80	valid
173.0ms	8063×	pre	80	true
2.0ms	63×	body	80	invalid

Compiler

Compiled 143 to 103 computations (28% saved)

Details

analyze57.0ms (1.7%)

sample24.0ms (0.7%)

simplify322.0ms (9.7%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite247.0ms (7.4%)

series224.0ms (6.7%)

simplify102.0ms (3.1%)

prune117.0ms (3.5%)

localize7.0ms (0.2%)

rewrite51.0ms (1.5%)

series189.0ms (5.7%)

simplify135.0ms (4.1%)

prune127.0ms (3.8%)

localize9.0ms (0.3%)

rewrite46.0ms (1.4%)

series100.0ms (3%)

simplify115.0ms (3.5%)

prune110.0ms (3.3%)

localize14.0ms (0.4%)

rewrite37.0ms (1.1%)

series207.0ms (6.2%)

simplify127.0ms (3.8%)

prune144.0ms (4.3%)

regimes52.0ms (1.6%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample746.0ms (22.4%)

Profiling