Details

analyze254.0ms (8%)

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)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify308.0ms (9.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4772	16
1	4772	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: 0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

15.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series149.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
53.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
29.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify98.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4947	1180
1	4947	1180

prune88.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 0.0b

Counts

72 → 8

Compiler

Compiled 1366 to 927 computations (32.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite83.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`
18×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-rgt-out--_binary64`
10×	`associate-/r_binary64` `associate-l*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `neg-mul-1_binary64`
5×	`associate-/l*_binary64`
4×	`flip3--_binary64` `difference-of-sqr-1_binary64` `flip--_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 139

Calls

4 calls:

29.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
25.0ms	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)
11.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
4.0ms	(-.f64 (*.f64 m m) m)

series211.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(-.f64 (*.f64 m m) m)
58.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
50.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
32.0ms	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)

simplify83.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4931	2919
1	4931	2919

prune119.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	151	8	159

Merged error: 0.0b

Counts

159 → 8

Compiler

Compiled 3020 to 1040 computations (65.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 m) v)
0.0b	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
0.2b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.3b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite52.0ms (1.6%)

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`
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 → 114

Calls

4 calls:

15.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
12.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
8.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
7.0ms	(/.f64 (-.f64 1 m) v)

series186.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
51.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
47.0ms	(/.f64 (-.f64 1 m) v)
32.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4950	1851
1	4950	1851

prune115.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Merged error: 0.0b

Counts

134 → 7

Compiler

Compiled 2315 to 1484 computations (35.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 m) v)
0.2b	(.f64 (sqrt.f64 m) (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1))
0.3b	(*.f64 m (/.f64 (-.f64 1 m) v))
0.4b	(.f64 (.f64 (sqrt.f64 m) (-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)) (sqrt.f64 m))

rewrite64.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
31×	`associate-r_binary64` `add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`pow1_binary64`
10×	`associate-l_binary64`
7×	`distribute-lft-out--_binary64` `sqrt-prod_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
5×	`pow-prod-down_binary64` `associate-*r/_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `flip--_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 132

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 m) (-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)) (sqrt.f64 m))
13.0ms	(.f64 (sqrt.f64 m) (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1))
12.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
10.0ms	(/.f64 (-.f64 1 m) v)

series233.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(.f64 (sqrt.f64 m) (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1))
66.0ms	(.f64 (.f64 (sqrt.f64 m) (-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)) (sqrt.f64 m))
47.0ms	(/.f64 (-.f64 1 m) v)
45.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5213	2364

prune146.0ms (4.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	145	6	151

Merged error: 0.0b

Counts

151 → 6

Compiler

Compiled 3035 to 1713 computations (43.6% saved)

regimes31.0ms (1%)

Compiler: Compiled 232 to 176 computations (24.1% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

end0.0ms (0%)

sample714.0ms (22.4%)

Algorithm

1×

intervals

Results

255.0ms	8000×	body	128	valid
167.0ms	8054×	pre	128	true
2.0ms	54×	body	128	invalid

Compiler

Compiled 147 to 111 computations (24.5% saved)

Details

analyze254.0ms (8%)

sample23.0ms (0.7%)

simplify308.0ms (9.7%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite39.0ms (1.2%)

series149.0ms (4.7%)

simplify98.0ms (3.1%)

prune88.0ms (2.8%)

localize8.0ms (0.3%)

rewrite83.0ms (2.6%)

series211.0ms (6.6%)

simplify83.0ms (2.6%)

prune119.0ms (3.7%)

localize7.0ms (0.2%)

rewrite52.0ms (1.6%)

series186.0ms (5.9%)

simplify75.0ms (2.4%)

prune115.0ms (3.6%)

localize9.0ms (0.3%)

rewrite64.0ms (2%)

series233.0ms (7.3%)

simplify66.0ms (2.1%)

prune146.0ms (4.6%)

regimes31.0ms (1%)

bsearch0.0ms (0%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample714.0ms (22.4%)

Profiling