Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample9.0ms (0.6%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify42.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	462	10
1	462	10

prune2.0ms (0.2%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))

rewrite10.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-/r*_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-/l*_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

1 → 50

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x 1) (-.f64 1 x))

series3.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

3.0ms

(/.f64 (+.f64 x 1) (-.f64 1 x))

simplify67.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5147	942

prune42.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	4	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0b

Counts

54 → 4

Compiler

Compiled 806 to 607 computations (24.7% saved)

localize7.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))
0.0b	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))

rewrite36.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`*-un-lft-identity_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`times-frac_binary64`
60×	`exp-prod_binary64`
38×	`add-cube-cbrt_binary64`
31×	`log-pow_binary64`
26×	`difference-of-squares_binary64`
19×	`distribute-lft-out_binary64`
13×	`distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `associate-/r/_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `log-prod_binary64` `div-inv_binary64` `flip--_binary64`
2×	`associate-/l/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

3 → 130

Calls

3 calls:

11.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))
10.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))

series10.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

4.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))
3.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))
3.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))

simplify91.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5651	2127

prune106.0ms (7.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	139	4	143

Merged error: 0b

Counts

143 → 4

Compiler

Compiled 2327 to 1798 computations (22.7% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 1 x))
0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)) 3))
0.0b	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)) 3)

rewrite43.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

186×	`*-un-lft-identity_binary64`
124×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
66×	`cbrt-prod_binary64`
61×	`add-cube-cbrt_binary64`
60×	`unpow-prod-down_binary64` `cube-prod_binary64`
42×	`difference-of-squares_binary64`
31×	`distribute-lft-out_binary64`
21×	`distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
4×	`pow1_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `add-log-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `flip3-+_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

3 → 206

Calls

3 calls:

12.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)) 3))
11.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)) 3)
9.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))

series13.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

7.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)) 3))
4.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)) 3)
3.0ms	(/.f64 (+.f64 x 1) (-.f64 1 x))

simplify80.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5764	4347

prune176.0ms (12.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	215	4	219

Merged error: 0b

Counts

219 → 4

Compiler

Compiled 3594 to 2819 computations (21.6% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(/.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)))
0.1b	(/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x)))

rewrite91.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Rules

774×	`times-frac_binary64`
762×	`*-un-lft-identity_binary64`
564×	`add-sqr-sqrt_binary64`
540×	`sqrt-prod_binary64`
292×	`add-cube-cbrt_binary64`
180×	`difference-of-squares_binary64`
100×	`distribute-lft-out_binary64`
90×	`distribute-lft-out--_binary64`
46×	`associate-/l*_binary64`
28×	`sqrt-div_binary64`
24×	`associate-/r/_binary64`
18×	`associate-/r*_binary64`
14×	`flip3--_binary64` `flip--_binary64`
12×	`div-inv_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 547

Calls

4 calls:

25.0ms	(/.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)))
10.0ms	(/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x)))
4.0ms	(sqrt.f64 (-.f64 1 x))
4.0ms	(sqrt.f64 (-.f64 1 x))

series19.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x)))
4.0ms	(sqrt.f64 (-.f64 1 x))
4.0ms	(sqrt.f64 (-.f64 1 x))
3.0ms	(/.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)))

simplify248.0ms (17%)

Algorithm

1×	egg-herbie

Counts

559 → 559

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5258	18203

Details

analyze3.0ms (0.2%)

sample9.0ms (0.6%)

simplify42.0ms (2.9%)

prune2.0ms (0.2%)

localize4.0ms (0.3%)

rewrite10.0ms (0.7%)

series3.0ms (0.2%)

simplify67.0ms (4.6%)

prune42.0ms (2.9%)

localize7.0ms (0.5%)

rewrite36.0ms (2.5%)

series10.0ms (0.7%)

simplify91.0ms (6.3%)

prune106.0ms (7.3%)

localize6.0ms (0.4%)

rewrite43.0ms (3%)

series13.0ms (0.9%)

simplify80.0ms (5.5%)

prune176.0ms (12.1%)

localize6.0ms (0.4%)

rewrite91.0ms (6.2%)

series19.0ms (1.3%)

simplify248.0ms (17%)

prune340.0ms (23.3%)

Profiling