Details

analyze249.0ms (8.1%)

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 (0.8%)

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)

simplify307.0ms (10%)

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: 0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

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

series184.0ms (6%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
64.0ms	(*.f64 m (-.f64 1 m))
54.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5461	1056

prune93.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	10	82

Merged error: 0b

Counts

82 → 10

Compiler

Compiled 1515 to 1016 computations (32.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite78.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 185

Calls

3 calls:

40.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
11.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
6.0ms	(/.f64 v (-.f64 1 m))

series162.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
53.0ms	(/.f64 v (-.f64 1 m))
48.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

simplify91.0ms (3%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5012	3769

prune192.0ms (6.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	194	10	204

Merged error: 0b

Counts

204 → 10

Compiler

Compiled 4026 to 2356 computations (41.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.3b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
24×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-l_binary64` `difference-of-squares_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
2×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

2 → 61

Calls

2 calls:

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

series93.0ms (3%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
46.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))

simplify58.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5020	987

prune67.0ms (2.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	67	10	77

Merged error: 0b

Counts

77 → 10

Compiler

Compiled 1359 to 886 computations (34.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
0.4b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))

rewrite58.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
15.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

series270.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
67.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
64.0ms	(*.f64 m (-.f64 1 m))
49.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify60.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5287	1775

prune106.0ms (3.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	4	6
Picked	0	1	1
Done	1	2	3
Total	113	8	121

Merged error: 0b

Counts

121 → 8

Compiler

Compiled 2229 to 1298 computations (41.8% saved)

regimes63.0ms (2%)

Compiler: Compiled 563 to 428 computations (24% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms (0%)

sample755.0ms (24.5%)

Algorithm

1×

intervals

Results

248.0ms	8000×	body	128	valid
162.0ms	8067×	pre	128	true
2.0ms	67×	body	128	invalid

Compiler

Compiled 211 to 161 computations (23.7% saved)

Details

analyze249.0ms (8.1%)

sample23.0ms (0.8%)

simplify307.0ms (10%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

rewrite37.0ms (1.2%)

series184.0ms (6%)

simplify67.0ms (2.2%)

prune93.0ms (3%)

localize8.0ms (0.2%)

rewrite78.0ms (2.5%)

series162.0ms (5.3%)

simplify91.0ms (3%)

prune192.0ms (6.2%)

localize7.0ms (0.2%)

rewrite30.0ms (1%)

series93.0ms (3%)

simplify58.0ms (1.9%)

prune67.0ms (2.2%)

localize9.0ms (0.3%)

rewrite58.0ms (1.9%)

series270.0ms (8.8%)

simplify60.0ms (1.9%)

prune106.0ms (3.4%)

regimes63.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample755.0ms (24.5%)

Profiling