Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample221.0ms (2.5%)

Algorithm

1×

intervals

Results

149.0ms	95×	body	2560	valid
51.0ms	88×	body	1280	valid
6.0ms	33×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	24×	body	320	valid
1.0ms	15×	body	160	valid
0.0ms	1×	body	80	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	12
1	73	12

prune3.0ms (0%)

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: 59.8b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
3.8b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-exp-log_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

2 → 60

Calls

2 calls:

14.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

series25.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

15.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
10.0ms	(/.f64 1 (tan.f64 x))

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4846	1005
1	4846	1005

prune56.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	2	67

Merged error: 0.3b

Counts

67 → 2

Compiler

Compiled 958 to 605 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x 1/3)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
15×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
7×	`prod-exp_binary64`
5×	`pow1_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 x 1/3)

series12.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 1/45 (pow.f64 x 3))
2.0ms	(*.f64 x 1/3)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4920	710
1	4920	710

prune80.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Merged error: 0.2b

Counts

85 → 8

Compiler

Compiled 1720 to 1367 computations (20.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.4b	(*.f64 x (sqrt.f64 1/3))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
31×	`associate-r_binary64`
21×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `prod-exp_binary64`
9×	`unswap-sqr_binary64`
8×	`unpow-prod-down_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-unprod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `cube-prod_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`unpow3_binary64` `cube-mult_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
6.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 x (sqrt.f64 1/3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))

series21.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 x (sqrt.f64 1/3))
4.0ms	(*.f64 1/45 (pow.f64 x 3))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5157	952

prune131.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	107	12	119

Merged error: 0.1b

Counts

119 → 12

Compiler

Compiled 2723 to 2265 computations (16.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`associate-r_binary64`
37×	`add-sqr-sqrt_binary64`
29×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`unpow-prod-down_binary64` `prod-exp_binary64`
15×	`add-cbrt-cube_binary64`
13×	`sqrt-prod_binary64`
11×	`unswap-sqr_binary64`
10×	`associate-l_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cube-prod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

10.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
6.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 2/945 (pow.f64 x 5))

series31.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
7.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 1/45 (pow.f64 x 3))

simplify117.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4871	1207
1	4871	1207

prune150.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	7	3	10
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Merged error: 0.0b

Counts

134 → 7

Compiler

Compiled 3062 to 2609 computations (14.8% saved)

regimes29.0ms (0.3%)

Compiler: Compiled 177 to 151 computations (14.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms (0%)

sample7.7s (85.4%)

Algorithm

1×

intervals

Results

5.3s	3173×	body	2560	valid
1.4s	2562×	body	1280	valid
228.0ms	1221×	body	640	valid
124.0ms	8000×	pre	80	true
73.0ms	660×	body	320	valid
28.0ms	331×	body	160	valid
2.0ms	53×	body	80	valid

Compiler

Compiled 229 to 194 computations (15.3% saved)

Details

analyze6.0ms (0.1%)

sample221.0ms (2.5%)

simplify15.0ms (0.2%)

prune3.0ms (0%)

localize5.0ms (0.1%)

rewrite21.0ms (0.2%)

series25.0ms (0.3%)

simplify120.0ms (1.3%)

prune56.0ms (0.6%)

localize9.0ms (0.1%)

rewrite17.0ms (0.2%)

series12.0ms (0.1%)

simplify79.0ms (0.9%)

prune80.0ms (0.9%)

localize14.0ms (0.2%)

rewrite27.0ms (0.3%)

series21.0ms (0.2%)

simplify66.0ms (0.7%)

prune131.0ms (1.5%)

localize16.0ms (0.2%)

rewrite34.0ms (0.4%)

series31.0ms (0.3%)

simplify117.0ms (1.3%)

prune150.0ms (1.7%)

regimes29.0ms (0.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.7s (85.4%)

Profiling