Details

analyze21.0ms (0.6%)

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 8 to 6 computations (25% saved)

sample34.0ms (1%)

Algorithm

1×

intervals

Results

14.0ms	117×	body	1024	valid
4.0ms	63×	body	512	valid
3.0ms	256×	pre	128	true
2.0ms	42×	body	256	valid
2.0ms	13×	body	2048	valid
0.0ms	21×	body	128	valid

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64` `sub-neg_binary64` `+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	11	6
3	9	6

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

57.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	57.9b	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 10 to 8 computations (20% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

7.7b	(-.f64 (exp.f64 x) 1)

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

57.9b

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
2×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
1×	`diff-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`

Counts

1 → 18

Calls

1 calls:

5.0ms

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

Compiler

Compiled 169 to 110 computations (34.9% saved)

series15.0ms (0.4%)

Error

0.1b

Counts

1 → 6

Calls

1 calls:

7.0ms

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

Compiler

Compiled 109 to 84 computations (22.9% saved)

simplify105.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

603×	`unsub-neg_binary64`
502×	`distribute-lft-out_binary64`
405×	`sub-neg_binary64`
337×	`distribute-rgt-out_binary64`
291×	`*-commutative_binary64`

Counts

24 → 14

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	254
1	96	241
2	202	235
3	401	232
4	956	232
5	2184	232
6	3777	232
7	4630	232
8	4950	232
9	4851	232

prune14.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	10	4	14
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	11	4	15

Error

0.0b

Counts

15 → 4

Alt Table

Status	Error	Program
	57.9b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)))
	58.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
	57.9b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
▶	0.5b	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24)))))))

Compiler

Compiled 195 to 133 computations (31.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.3b	(*.f64 x 1/24)
0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))

rewrite88.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`

Counts

4 → 75

Calls

4 calls:

6.0ms	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))

Compiler

Compiled 1570 to 1091 computations (30.5% saved)

series50.0ms (1.5%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

13.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
12.0ms	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
9.0ms	(+.f64 1/6 (*.f64 x 1/24))
6.0ms	(*.f64 x 1/24)

Compiler

Compiled 628 to 446 computations (29% saved)

simplify128.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

463×	`associate-+l+_binary64`
367×	`*-commutative_binary64`
348×	`associate-+r+_binary64`
274×	`+-commutative_binary64`
233×	`sub-neg_binary64`

Counts

95 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	140	1332
1	343	1164
2	1248	1158
3	1878	1156
4	3094	1153
5	4392	1153
6	4801	1153
7	4859	1153

prune39.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
	57.9b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)))
	58.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
▶	57.9b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
✓	0.5b	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24)))))))

Compiler

Compiled 792 to 544 computations (31.3% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
0.1b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
7.7b	(-.f64 (exp.f64 x) 1)

rewrite56.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
20×	`cbrt-prod_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`

Counts

3 → 82

Calls

3 calls:

6.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
5.0ms	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
4.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 867 to 630 computations (27.3% saved)

series35.0ms (1%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

11.0ms	(pow.f64 (-.f64 (exp.f64 x) 1) 3)
8.0ms	(-.f64 (exp.f64 x) 1)
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))

Compiler

Compiled 392 to 318 computations (18.9% saved)

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

506×	`associate-l_binary64`
497×	`exp-prod_binary64`
448×	`associate-r_binary64`
348×	`log-prod_binary64`
251×	`distribute-rgt-in_binary64`

Counts

100 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	1311
1	225	1243
2	654	1215
3	2747	1209
4	4644	1206
5	5088	1206

prune25.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	75	4	79

Error

0.0b

Counts

79 → 4

Alt Table

Status	Error	Program
	58.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
✓	57.9b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
✓	0.5b	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24)))))))
▶	57.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3))

Compiler

Compiled 518 to 364 computations (29.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3)
0.1b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3))
7.6b	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

rewrite292.0ms (8.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

545×	`*-un-lft-identity_binary64`
372×	`add-sqr-sqrt_binary64`
320×	`times-frac_binary64`
238×	`unpow-prod-down_binary64` `cube-prod_binary64`
192×	`distribute-lft-out_binary64`

Counts

4 → 433

Calls

4 calls:

32.0ms	(pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3)
31.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
3.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 5052 to 3577 computations (29.2% saved)

series97.0ms (2.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

34.0ms	(pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3)
23.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3))
13.0ms	(pow.f64 (exp.f64 x) 3)
13.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

Compiler

Compiled 961 to 736 computations (23.4% saved)

simplify533.0ms (15.9%)

Algorithm

1×	egg-herbie

Rules

580×	`distribute-rgt-in_binary64`
295×	`log-prod_binary64`
233×	`sqr-pow_binary64`
230×	`exp-prod_binary64`
172×	`cancel-sign-sub-inv_binary64`

Counts

457 → 428

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	20034
1	784	19300
2	2494	17512
3	4475	17512
4	4920	17512

prune72.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	427	1	428
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	428	4	432

Error

0.0b

Counts

432 → 4

Alt Table

Status	Error	Program
	57.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (exp.f64 (*.f64 3 x)) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) 3))
	58.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
	57.9b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
	0.5b	(+.f64 x (.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24)))))))

Compiler

Compiled 2055 to 1431 computations (30.4% saved)

regimes191.0ms (5.7%)

Accuracy

Total 0.3b remaining (95.9%)

Threshold costs 0.3b (95.9%)

Compiler

Compiled 2614 to 1969 computations (24.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	23	28
2	23	28

end1.0ms (0%)

Compiler: Compiled 20 to 16 computations (20% saved)

sample1.4s (40.7%)

Algorithm

1×

intervals

Results

646.0ms	4045×	body	1024	valid
138.0ms	2003×	body	512	valid
94.0ms	8000×	pre	128	true
56.0ms	422×	body	2048	valid
40.0ms	1006×	body	256	valid
10.0ms	524×	body	128	valid

Compiler

Compiled 85 to 65 computations (23.5% saved)

Details

analyze21.0ms (0.6%)

sample34.0ms (1%)

simplify9.0ms (0.3%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite32.0ms (1%)

series15.0ms (0.4%)

simplify105.0ms (3.1%)

prune14.0ms (0.4%)

localize9.0ms (0.3%)

rewrite88.0ms (2.6%)

series50.0ms (1.5%)

simplify128.0ms (3.8%)

prune39.0ms (1.2%)

localize5.0ms (0.2%)

rewrite56.0ms (1.7%)

series35.0ms (1%)

simplify111.0ms (3.3%)

prune25.0ms (0.8%)

localize14.0ms (0.4%)

rewrite292.0ms (8.7%)

series97.0ms (2.9%)

simplify533.0ms (15.9%)

prune72.0ms (2.2%)

regimes191.0ms (5.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.4s (40.7%)

Profiling