Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample35.0ms (1.7%)

Algorithm

1×

intervals

Results

17.0ms	113×	body	1280	valid
7.0ms	73×	body	640	valid
2.0ms	256×	pre	80	true
2.0ms	36×	body	320	valid
1.0ms	29×	body	160	valid
0.0ms	5×	body	80	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	6
1	10	6

prune3.0ms (0.1%)

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: 58.9b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

7.0b	(-.f64 (exp.f64 x) 1)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

1 → 15

Calls

1 calls:

4.0ms

(-.f64 (exp.f64 x) 1)

series2.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

2.0ms

(-.f64 (exp.f64 x) 1)

simplify49.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5146	196

prune21.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	2	19

Merged error: 0.0b

Counts

19 → 2

Compiler

Compiled 176 to 112 computations (36.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))
0.4b	(*.f64 x 1/6)

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`add-log-exp_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`

Counts

2 → 41

Calls

2 calls:

7.0ms	(.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series10.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))
2.0ms	(*.f64 x 1/6)

simplify75.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4909	519
1	4909	519

prune27.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	47	2	49

Merged error: 0.0b

Counts

49 → 2

Compiler

Compiled 718 to 458 computations (36.2% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 2)
6.9b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite24.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64` `times-frac_binary64`
24×	`difference-of-sqr--1_binary64`
20×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out_binary64`
9×	`unpow-prod-down_binary64`
8×	`associate-/l*_binary64`
7×	`unpow2_binary64` `sqr-pow_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `pow-pow_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64` `exp-prod_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 97

Calls

3 calls:

12.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
3.0ms	(pow.f64 (exp.f64 x) 2)

series20.0ms (1%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
3.0ms	(pow.f64 (exp.f64 x) 2)

simplify102.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5199	1795

prune60.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	105	3	108

Merged error: 0.0b

Counts

108 → 3

Compiler

Compiled 1719 to 1116 computations (35.1% saved)

localize15.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 4)
0.1b	(pow.f64 (exp.f64 x) 6)
0.3b	(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 6)) (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
6.8b	(+.f64 -1 (pow.f64 (exp.f64 x) 6))

rewrite30.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
22×	`distribute-lft-out_binary64`
21×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
8×	`pow-pow_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `exp-prod_binary64`
5×	`associate-/r*_binary64`
4×	`associate-/l*_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `pow-exp_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 97

Calls

4 calls:

15.0ms	(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 6)) (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
5.0ms	(+.f64 -1 (pow.f64 (exp.f64 x) 6))
3.0ms	(pow.f64 (exp.f64 x) 6)
3.0ms	(pow.f64 (exp.f64 x) 4)

series57.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 6)) (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
9.0ms	(+.f64 -1 (pow.f64 (exp.f64 x) 6))
7.0ms	(pow.f64 (exp.f64 x) 6)
5.0ms	(pow.f64 (exp.f64 x) 4)

simplify96.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5126	2398

prune110.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	109	3	112

Merged error: 0.0b

Counts

112 → 3

Compiler

Compiled 3274 to 2222 computations (32.1% saved)

regimes41.0ms (1.9%)

Compiler: Compiled 185 to 143 computations (22.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	13	16

end0.0ms (0%)

sample1.3s (60.6%)

Algorithm

1×

intervals

Results

533.0ms	3444×	body	1280	valid
245.0ms	2529×	body	640	valid
82.0ms	8000×	pre	80	true
75.0ms	1247×	body	320	valid
22.0ms	581×	body	160	valid
4.0ms	199×	body	80	valid

Compiler

Compiled 93 to 72 computations (22.6% saved)

Details

analyze2.0ms (0.1%)

sample35.0ms (1.7%)

simplify13.0ms (0.6%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

rewrite5.0ms (0.2%)

series2.0ms (0.1%)

simplify49.0ms (2.4%)

prune21.0ms (1%)

localize6.0ms (0.3%)

rewrite12.0ms (0.6%)

series10.0ms (0.5%)

simplify75.0ms (3.6%)

prune27.0ms (1.3%)

localize6.0ms (0.3%)

rewrite24.0ms (1.1%)

series20.0ms (1%)

simplify102.0ms (4.9%)

prune60.0ms (2.9%)

localize15.0ms (0.7%)

rewrite30.0ms (1.4%)

series57.0ms (2.7%)

simplify96.0ms (4.6%)

prune110.0ms (5.2%)

regimes41.0ms (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample1.3s (60.6%)

Profiling