Details

analyze3.0ms (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)

sample34.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	120×	body	1024	valid
5.0ms	73×	body	512	valid
3.0ms	256×	pre	128	true
2.0ms	16×	body	2048	valid
1.0ms	31×	body	256	valid
0.0ms	16×	body	128	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify103.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	9	6
1	9	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

Error

58.6b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

4.7b	(-.f64 (exp.f64 x) 1)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_100`
5×	`*-un-lft-identity_binary64_78`
3×	`add-log-exp_binary64_117` `cancel-sign-sub-inv_binary64_44`
2×	`add-cube-cbrt_binary64_113` `difference-of-squares_binary64_47`
1×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `add-exp-log_binary64_116` `difference-of-sqr-1_binary64_48` `sub-neg_binary64_71` `pow1_binary64_139`

Counts

1 → 18

Calls

1 calls:

8.0ms

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

series9.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify93.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4935	199
1	4935	199

prune48.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	17	4	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	4	22

Error

0.1b

Counts

22 → 4

Compiler

Compiled 205 to 132 computations (35.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6)))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_100`
7×	`add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
5×	`distribute-lft-in_binary64_27` `add-log-exp_binary64_117` `distribute-rgt-in_binary64_28`
4×	`associate-+r+_binary64_10`
2×	`-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-r/_binary64_20` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sum-log_binary64_169`

Counts

3 → 55

Calls

3 calls:

7.0ms	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6)))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series105.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

68.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
20.0ms	(*.f64 x 1/6)
16.0ms	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6)))))

simplify91.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4946	793
1	4946	793

prune64.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Error

0.1b

Counts

68 → 4

Compiler

Compiled 1044 to 712 computations (31.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

4.7b	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
4.7b	(-.f64 (exp.f64 x) 1)

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100`
12×	`*-un-lft-identity_binary64_78`
8×	`log-pow_binary64_167`
7×	`log-prod_binary64_164` `exp-prod_binary64_130`
6×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
4×	`add-log-exp_binary64_117` `exp-sum_binary64_124` `difference-of-squares_binary64_47`
3×	`pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `difference-of-sqr-1_binary64_48` `sub-neg_binary64_71`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `exp-diff_binary64_126` `rem-log-exp_binary64_119` `log-div_binary64_165`

Counts

2 → 42

Calls

2 calls:

10.0ms	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
7.0ms	(-.f64 (exp.f64 x) 1)

series110.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

99.0ms	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
11.0ms	(-.f64 (exp.f64 x) 1)

simplify122.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4985	426
1	4985	426

prune47.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	47	5	52

Error

0.1b

Counts

52 → 5

Compiler

Compiled 470 to 314 computations (33.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 2)
4.6b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_78`
33×	`add-sqr-sqrt_binary64_100`
32×	`times-frac_binary64_84`
24×	`difference-of-sqr--1_binary64_49`
21×	`add-cube-cbrt_binary64_113`
16×	`distribute-lft-out_binary64_29`
9×	`unpow-prod-down_binary64_157`
8×	`add-log-exp_binary64_117` `associate-/l*_binary64_23`
7×	`unpow2_binary64_143` `sqr-pow_binary64_50`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`pow1_binary64_139`
4×	`flip-+_binary64_52` `pow-pow_binary64_150` `associate-/r*_binary64_22` `flip3-+_binary64_81`
3×	`pow-unpow_binary64_155` `exp-prod_binary64_130`
2×	`+-commutative_binary64_8` `associate-/r/_binary64_24` `associate-/l/_binary64_25` `sum-log_binary64_169`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77`

Counts

4 → 109

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.0ms	(+.f64 (exp.f64 x) 1)
3.0ms	(pow.f64 (exp.f64 x) 2)

series125.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
19.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
12.0ms	(pow.f64 (exp.f64 x) 2)
10.0ms	(+.f64 (exp.f64 x) 1)

simplify118.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5077	1939

prune183.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	121	5	126

Error

0.1b

Counts

126 → 5

Compiler

Compiled 1920 to 1248 computations (35% saved)

regimes181.0ms (5%)

Accuracy

Total 0.4b remaining (91.3%)

Threshold costs 0.4b (91.3%)

Compiler

Compiled 1235 to 1004 computations (18.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

end0.0ms (0%)

sample2.0s (56.7%)

Algorithm

1×

intervals

Results

775.0ms	4073×	body	1024	valid
196.0ms	1959×	body	512	valid
141.0ms	8000×	pre	128	true
86.0ms	418×	body	2048	valid
67.0ms	998×	body	256	valid
17.0ms	552×	body	128	valid

Compiler

Compiled 336 to 270 computations (19.6% saved)

Details

analyze3.0ms (0.1%)

sample34.0ms (0.9%)

simplify103.0ms (2.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

rewrite10.0ms (0.3%)

series9.0ms (0.3%)

simplify93.0ms (2.6%)

prune48.0ms (1.3%)

localize6.0ms (0.2%)

rewrite27.0ms (0.8%)

series105.0ms (2.9%)

simplify91.0ms (2.5%)

prune64.0ms (1.8%)

localize7.0ms (0.2%)

rewrite21.0ms (0.6%)

series110.0ms (3.1%)

simplify122.0ms (3.4%)

prune47.0ms (1.3%)

localize7.0ms (0.2%)

rewrite35.0ms (1%)

series125.0ms (3.5%)

simplify118.0ms (3.3%)

prune183.0ms (5.1%)

regimes181.0ms (5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (56.7%)

Profiling