Details

analyze29.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample28.0ms (1.1%)

Algorithm

1×

intervals

Results

12.0ms	79×	body	1024	valid
3.0ms	42×	body	512	valid
2.0ms	99×	body	128	valid
2.0ms	10×	body	2048	valid
1.0ms	26×	body	256	valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify17.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

32×	`distribute-rgt-in_binary64`
27×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`
25×	`sub-neg_binary64`
17×	`div-sub_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

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

39.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	39.8b	(/.f64 (-.f64 (exp.f64 x) 1) x)

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

4.0b	(-.f64 (exp.f64 x) 1)

rewrite31.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

39.7b

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 201 to 126 computations (37.3% saved)

series14.0ms (0.6%)

Error

0.0b

Counts

1 → 6

Calls

1 calls:

7.0ms

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

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify104.0ms (4.2%)

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

prune15.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	11	3	14
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	12	3	15

Error

0.0b

Counts

15 → 3

Alt Table

Status	Error	Program
	39.8b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)) x)
	39.8b	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
▶	21.6b	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)

Compiler

Compiled 183 to 120 computations (34.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)
4.2b	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)

rewrite94.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64`
9×	`times-frac_binary64` `associate-l_binary64`

Counts

4 → 93

Calls

4 calls:

7.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
5.0ms	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)
4.0ms	(*.f64 x 1/6)

Compiler

Compiled 1926 to 1242 computations (35.5% saved)

series67.0ms (2.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

24.0ms	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)
14.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
13.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(*.f64 x 1/6)

Compiler

Compiled 565 to 407 computations (28% saved)

simplify124.0ms (5%)

Algorithm

1×	egg-herbie

Rules

805×	`div-sub_binary64`
663×	`distribute-rgt-in_binary64`
637×	`distribute-lft-in_binary64`
305×	`*-commutative_binary64`
265×	`cancel-sign-sub-inv_binary64`

Counts

117 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2010
1	358	1788
2	1216	1786
3	3741	1718
4	4660	1718
5	6445	1718

prune48.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	83	3	86

Error

0.0b

Counts

86 → 3

Alt Table

Status	Error	Program
	39.8b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3)) x)
▶	39.8b	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
✓	21.6b	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)

Compiler

Compiled 1174 to 745 computations (36.5% saved)

localize8.0ms (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)
4.0b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite101.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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`

Counts

3 → 97

Calls

3 calls:

14.0ms	(/.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)

Compiler

Compiled 1881 to 1255 computations (33.3% saved)

series44.0ms (1.8%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

13.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
12.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
9.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 595 to 438 computations (26.4% saved)

simplify159.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

472×	`div-sub_binary64`
295×	`associate-l_binary64`
251×	`exp-prod_binary64`
246×	`associate-r_binary64`
236×	`log-prod_binary64`

Counts

115 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2470
1	363	2137
2	903	1877
3	3041	1877
4	4441	1877
5	4956	1877
6	4912	1877

prune59.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	96	3	99

Error

0.0b

Counts

99 → 3

Alt Table

Status	Error	Program
✓	21.6b	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)
▶	39.7b	(/.f64 (/.f64 (+.f64 (exp.f64 (+.f64 x x)) -1) (+.f64 (exp.f64 x) 1)) x)
	39.8b	(/.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3)) (*.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)))) x)

Compiler

Compiled 1364 to 875 computations (35.9% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 (exp.f64 (+.f64 x x)) -1) (+.f64 (exp.f64 x) 1))
4.2b	(+.f64 (exp.f64 (+.f64 x x)) -1)

rewrite66.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
13×	`distribute-lft-out_binary64`

Counts

2 → 64

Calls

2 calls:

13.0ms	(/.f64 (+.f64 (exp.f64 (+.f64 x x)) -1) (+.f64 (exp.f64 x) 1))
7.0ms	(+.f64 (exp.f64 (+.f64 x x)) -1)

Compiler

Compiled 1233 to 650 computations (47.3% saved)

series29.0ms (1.2%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

12.0ms	(/.f64 (+.f64 (exp.f64 (+.f64 x x)) -1) (+.f64 (exp.f64 x) 1))
9.0ms	(+.f64 (exp.f64 (+.f64 x x)) -1)

Compiler

Compiled 382 to 287 computations (24.9% saved)

simplify129.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

439×	`div-sub_binary64`
197×	`associate-l_binary64`
196×	`times-frac_binary64`
192×	`cancel-sign-sub-inv_binary64`
185×	`associate-/l*_binary64`

Counts

76 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1800
1	291	1654
2	796	1430
3	2395	1430
4	4346	1430
5	4979	1430
6	4928	1430

prune41.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	70	3	73

Error

0.0b

Counts

73 → 3

Alt Table

Status	Error	Program
	21.6b	(/.f64 (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))) x)
	39.7b	(/.f64 (/.f64 (log.f64 (exp.f64 (-.f64 (exp.f64 (+.f64 x x)) 1))) (+.f64 (exp.f64 x) 1)) x)
	39.8b	(/.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 x) 2) 3) (pow.f64 -1 3)) (*.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)))) x)

Compiler

Compiled 1101 to 618 computations (43.9% saved)

regimes192.0ms (7.8%)

Accuracy

Total 0.3b remaining (76.6%)

Threshold costs 0.3b (76.6%)

Compiler

Compiled 1821 to 1323 computations (27.3% saved)

bsearch16.0ms (0.6%)

Steps

Iters	Range		Point
9	-0.04386819696353222	-5.0435575817306455e-11	-0.00016108891433325626

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	52
1	36	52
2	35	52

end1.0ms (0.1%)

Compiler: Compiled 35 to 26 computations (25.7% saved)

sample1.0s (41.2%)

Algorithm

1×

intervals

Results

412.0ms	2709×	body	1024	valid
112.0ms	1308×	body	512	valid
83.0ms	3064×	body	128	valid
47.0ms	273×	body	2048	valid
34.0ms	646×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 104 to 76 computations (26.9% saved)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

Details

analyze29.0ms (1.2%)

sample28.0ms (1.1%)

simplify17.0ms (0.7%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite31.0ms (1.3%)

series14.0ms (0.6%)

simplify104.0ms (4.2%)

prune15.0ms (0.6%)

localize8.0ms (0.3%)

rewrite94.0ms (3.8%)

series67.0ms (2.7%)

simplify124.0ms (5%)

prune48.0ms (2%)

localize8.0ms (0.3%)

rewrite101.0ms (4.1%)

series44.0ms (1.8%)

simplify159.0ms (6.5%)

prune59.0ms (2.4%)

localize8.0ms (0.3%)

rewrite66.0ms (2.7%)

series29.0ms (1.2%)

simplify129.0ms (5.3%)

prune41.0ms (1.7%)

regimes192.0ms (7.8%)

bsearch16.0ms (0.6%)

simplify4.0ms (0.2%)

end1.0ms (0.1%)

sample1.0s (41.2%)

Profiling

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9