Details

analyze273.0ms (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample68.0ms (1.4%)

Algorithm

1×

intervals

Results

32.0ms	74×	body	1024	valid
12.0ms	38×	body	2048	valid
10.0ms	45×	body	512	valid
4.0ms	75×	body	128	valid
3.0ms	23×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

prune2.0ms (0%)

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: 51.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
12.8b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series188.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
49.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
36.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4924	862
1	4924	862

prune266.0ms (5.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 3796 to 2752 computations (27.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
18.9b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

3 → 70

Calls

3 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))

series164.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

64.0ms	(*.f64 3/40 (pow.f64 x 5))
53.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
47.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4845	1006
1	4845	1006

prune86.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Merged error: 0b

Counts

83 → 4

Compiler

Compiled 1450 to 1123 computations (22.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/8 (pow.f64 x 3))
0.3b	(/.f64 1/16 (pow.f64 x 5))
11.4b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
18.4b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite125.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64` `times-frac_binary64`
47×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `cancel-sign-sub-inv_binary64` `log-div_binary64`
4×	`unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 164

Calls

4 calls:

48.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
47.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series237.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
64.0ms	(/.f64 1/16 (pow.f64 x 5))
53.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
43.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4968	3700
1	4968	3700

prune260.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	176	4	180

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 4193 to 3334 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.1b	(/.f64 1/8 (pow.f64 x 3))
8.3b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite125.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
97×	`*-un-lft-identity_binary64`
87×	`add-sqr-sqrt_binary64`
80×	`cancel-sign-sub-inv_binary64`
74×	`add-cube-cbrt_binary64`
42×	`associate-+r+_binary64`
31×	`unpow-prod-down_binary64` `cube-prod_binary64`
18×	`add-log-exp_binary64`
12×	`associate-/r*_binary64`
11×	`sqr-pow_binary64`
10×	`add-exp-log_binary64` `unpow3_binary64` `cube-mult_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64` `difference-of-squares_binary64` `sum-log_binary64`
4×	`diff-log_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `log-div_binary64` `frac-sub_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 203

Calls

4 calls:

32.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
27.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
27.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
8.0ms	(/.f64 1/8 (pow.f64 x 3))

series201.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
47.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
45.0ms	(/.f64 1/8 (pow.f64 x 3))
37.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4935	3378
1	4935	3378

prune266.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

219 → 4

Compiler

Compiled 4382 to 3141 computations (28.3% saved)

regimes22.0ms (0.4%)

Compiler: Compiled 56 to 47 computations (16.1% saved)

bsearch47.0ms (1%)

Steps

Iters	Range		Point
11	6.8709511896062876e-12	7633400058.804611	0.9487808926335013
9	-7.4976101139693725	-4.805475330156994e-05	-1.0530574990243888

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (44.1%)

Algorithm

1×

intervals

Results

930.0ms	2413×	body	1024	valid
426.0ms	1250×	body	2048	valid
280.0ms	1311×	body	512	valid
111.0ms	2330×	body	128	valid
83.0ms	665×	body	256	valid
15.0ms	31×	body	4096	valid

Compiler

Compiled 139 to 111 computations (20.1% saved)

Details

analyze273.0ms (5.6%)

sample68.0ms (1.4%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite22.0ms (0.4%)

series188.0ms (3.8%)

simplify55.0ms (1.1%)

prune266.0ms (5.4%)

localize9.0ms (0.2%)

rewrite26.0ms (0.5%)

series164.0ms (3.3%)

simplify92.0ms (1.9%)

prune86.0ms (1.7%)

localize13.0ms (0.3%)

rewrite125.0ms (2.5%)

series237.0ms (4.8%)

simplify89.0ms (1.8%)

prune260.0ms (5.3%)

localize10.0ms (0.2%)

rewrite125.0ms (2.5%)

series201.0ms (4.1%)

simplify88.0ms (1.8%)

prune266.0ms (5.4%)

regimes22.0ms (0.4%)

bsearch47.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (44.1%)

Profiling