Details

analyze798.0ms (11.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4840	8
1	4840	8
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample53.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	80×	body	1024	valid
9.0ms	53×	body	512	valid
4.0ms	96×	body	128	valid
3.0ms	7×	body	2048	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4840	8
1	4840	8

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Compiler

Compiled 10 to 10 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

7×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 28

Calls

2 calls:

6.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 321 to 218 computations (32.1% saved)

series70.0ms (1%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

45.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
11.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 324 to 294 computations (9.3% saved)

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5074	484

prune34.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

0.2b

Counts

41 → 3

Compiler

Compiled 450 to 337 computations (25.1% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) 1)
0.2b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.2b	(sqrt.f64 (+.f64 (exp.f64 x) 1))
0.6b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))

rewrite213.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

94×	`sqrt-prod_binary64`
58×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`pow1/2_binary64` `add-cube-cbrt_binary64` `swap-sqr_binary64`
10×	`rem-sqrt-square_binary64` `associate-l_binary64` `associate-r_binary64`
9×	`pow-prod-up_binary64` `flip3-+_binary64` `flip-+_binary64` `unswap-sqr_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`sqr-abs_binary64` `frac-times_binary64`
2×	`associate-l/_binary64` `associate-r/_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-square-sqrt_binary64` `*-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 136

Calls

4 calls:

22.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
4.0ms	(+.f64 (exp.f64 x) 1)
4.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))
4.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))

Compiler

Compiled 2978 to 2161 computations (27.4% saved)

series172.0ms (2.4%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

44.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))
42.0ms	(sqrt.f64 (+.f64 (exp.f64 x) 1))
41.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
16.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 1120 to 978 computations (12.7% saved)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5004	2142

prune143.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	160	3	163

Error

0.2b

Counts

163 → 3

Compiler

Compiled 2456 to 1808 computations (26.4% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
1.6b	(pow.f64 (sqrt.f64 2) 5)
11.1b	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
14.4b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite713.0ms (9.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
27×	`add-log-exp_binary64`
22×	`associate-*l/_binary64`
18×	`frac-add_binary64`
16×	`sum-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64` `associate-/r*_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
5×	`sqr-pow_binary64`
4×	`associate-*r/_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64` `div-exp_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `+-commutative_binary64` `pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-pow2_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 119

Calls

4 calls:

23.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
16.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
6.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
3.0ms	(pow.f64 (sqrt.f64 2) 5)

Compiler

Compiled 8172 to 7371 computations (9.8% saved)

series239.0ms (3.3%)

Error

0.2b

Counts

4 → 16

Calls

4 calls:

110.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
106.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
0.0ms	(pow.f64 (sqrt.f64 2) 5)
0.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))

Compiler

Compiled 946 to 873 computations (7.7% saved)

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4973	6253
1	4973	6253

prune570.0ms (7.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	135	3	138

Error

0.2b

Counts

138 → 3

Compiler

Compiled 7765 to 7002 computations (9.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
1.6b	(pow.f64 (sqrt.f64 2) 5)
11.1b	(+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
14.4b	(+.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite727.0ms (10.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
22×	`frac-add_binary64`
21×	`associate-*r/_binary64`
15×	`add-log-exp_binary64` `sqrt-prod_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
10×	`add-exp-log_binary64` `associate-/r*_binary64`
7×	`sum-log_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
5×	`associate-*l/_binary64` `sqr-pow_binary64`
3×	`associate-+l+_binary64` `pow-unpow_binary64` `pow-pow_binary64` `div-exp_binary64` `associate-/l*_binary64`
2×	`+-commutative_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-+r+_binary64` `pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-pow2_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 126

Calls

4 calls:

62.0ms	(+.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
52.0ms	(+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
6.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
3.0ms	(pow.f64 (sqrt.f64 2) 5)

Compiler

Compiled 7702 to 7044 computations (8.5% saved)

series278.0ms (3.9%)

Error

0.2b

Counts

4 → 13

Calls

4 calls:

157.0ms	(+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
100.0ms	(+.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
0.0ms	(pow.f64 (sqrt.f64 2) 5)
0.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))

Compiler

Compiled 889 to 829 computations (6.7% saved)

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5196	5612

prune515.0ms (7.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Error

0.2b

Counts

142 → 3

Compiler

Compiled 7362 to 6701 computations (9% saved)

regimes158.0ms (2.2%)

Accuracy

Total 0.2b remaining (88.7%)

Threshold costs 0.2b (88.7%)

Compiler

Compiled 1559 to 1434 computations (8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms (0%)

sample2.1s (28.5%)

Algorithm

1×

intervals

Results

739.0ms	2606×	body	1024	valid
199.0ms	1314×	body	512	valid
133.0ms	3056×	body	128	valid
108.0ms	328×	body	2048	valid
65.0ms	696×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 499 to 460 computations (7.8% saved)

Details

analyze798.0ms (11.1%)

sample53.0ms (0.7%)

simplify64.0ms (0.9%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

rewrite39.0ms (0.5%)

series70.0ms (1%)

simplify40.0ms (0.6%)

prune34.0ms (0.5%)

localize6.0ms (0.1%)

rewrite213.0ms (3%)

series172.0ms (2.4%)

simplify83.0ms (1.1%)

prune143.0ms (2%)

localize22.0ms (0.3%)

rewrite713.0ms (9.9%)

series239.0ms (3.3%)

simplify82.0ms (1.1%)

prune570.0ms (7.9%)

localize23.0ms (0.3%)

rewrite727.0ms (10.1%)

series278.0ms (3.9%)

simplify83.0ms (1.2%)

prune515.0ms (7.2%)

regimes158.0ms (2.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (28.5%)

Profiling