Details

analyze53.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid
0.0ms	1×	body	128	nan

Compiler

Compiled 29 to 29 computations (0% saved)

simplify306.0ms (8.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	1572	18
1	1572	18

prune5.0ms (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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 64 to 59 computations (7.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(/.f64 1 (*.f64 x 9))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_13839`
22×	`add-exp-log_binary64_13877`
20×	`add-sqr-sqrt_binary64_13861`
16×	`add-cbrt-cube_binary64_13875`
15×	`associate-r_binary64_13779`
14×	`pow1_binary64_13900`
12×	`add-cube-cbrt_binary64_13874`
7×	`prod-exp_binary64_13888`
6×	`add-log-exp_binary64_13878` `cancel-sign-sub-inv_binary64_13805`
5×	`distribute-lft-in_binary64_13788` `cbrt-unprod_binary64_13872` `pow-prod-down_binary64_13910` `distribute-rgt-in_binary64_13789`
4×	`div-exp_binary64_13890` `sqrt-prod_binary64_13855` `distribute-lft-out_binary64_13790` `associate-l_binary64_13780`
3×	`times-frac_binary64_13845` `associate-/l*_binary64_13784` `distribute-lft-out--_binary64_13791` `div-inv_binary64_13836`
2×	`sub-neg_binary64_13832` `rec-exp_binary64_13889` `unswap-sqr_binary64_13807` `associate--l+_binary64_13776` `cbrt-undiv_binary64_13873` `difference-of-squares_binary64_13808` `-commutative_binary64_13770` `1-exp_binary64_13883` `pow-flip_binary64_13913` `associate-r/_binary64_13781`
1×	`inv-pow_binary64_13924` `flip--_binary64_13814` `flip3-+_binary64_13842` `+-commutative_binary64_13769` `flip-+_binary64_13813` `sum-log_binary64_13930` `clear-num_binary64_13838` `associate-/r*_binary64_13783` `difference-of-sqr-1_binary64_13809` `frac-2neg_binary64_13850` `flip3--_binary64_13843`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series163.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
33.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
33.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 1 (*.f64 x 9))

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4908	1419
1	4908	1419

prune449.0ms (12%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

Compiler

Compiled 7769 to 6337 computations (18.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) (+.f64 y -1))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1))))
0.3b	(/.f64 1/9 x)

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_13839`
20×	`add-sqr-sqrt_binary64_13861`
16×	`add-cube-cbrt_binary64_13874`
13×	`add-exp-log_binary64_13877` `add-cbrt-cube_binary64_13875`
12×	`associate-*r/_binary64_13781`
11×	`pow1_binary64_13900`
9×	`times-frac_binary64_13845` `add-log-exp_binary64_13878` `associate-l_binary64_13780`
6×	`associate-r_binary64_13779` `flip3-+_binary64_13842` `flip-+_binary64_13813` `distribute-lft-out_binary64_13790` `frac-add_binary64_13847`
5×	`distribute-lft-in_binary64_13788` `distribute-rgt-in_binary64_13789`
4×	`sqrt-prod_binary64_13855` `cbrt-unprod_binary64_13872` `pow-prod-down_binary64_13910` `prod-exp_binary64_13888`
3×	`associate-/l_binary64_13784` `sum-log_binary64_13930` `associate-/r_binary64_13783`
2×	`unswap-sqr_binary64_13807` `*-commutative_binary64_13770`
1×	`div-exp_binary64_13890` `+-commutative_binary64_13769` `cbrt-undiv_binary64_13873` `associate-+r+_binary64_13771` `clear-num_binary64_13838` `div-inv_binary64_13836` `frac-2neg_binary64_13850`

Counts

4 → 100

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
17.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1))))
11.0ms	(+.f64 (/.f64 1/9 x) (+.f64 y -1))
3.0ms	(/.f64 1/9 x)

series183.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1))))
59.0ms	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
23.0ms	(+.f64 (/.f64 1/9 x) (+.f64 y -1))
20.0ms	(/.f64 1/9 x)

simplify100.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4905	1824
1	4905	1824

prune353.0ms (9.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

Compiler

Compiled 6379 to 5048 computations (20.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(/.f64 1/9 x)
0.3b	(/.f64 1/9 x)
0.5b	(*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))

rewrite52.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-sqr-sqrt_binary64_13861`
70×	`sqrt-prod_binary64_13855`
62×	`times-frac_binary64_13845`
55×	`add-cube-cbrt_binary64_13874` `*-un-lft-identity_binary64_13839`
22×	`associate-r_binary64_13779`
21×	`pow1_binary64_13900`
19×	`associate-l_binary64_13780`
18×	`swap-sqr_binary64_13806`
12×	`add-exp-log_binary64_13877` `add-cbrt-cube_binary64_13875`
11×	`unswap-sqr_binary64_13807`
8×	`sqrt-pow1_binary64_13857` `pow1/2_binary64_13919`
6×	`associate-/l_binary64_13784` `associate-/r_binary64_13783` `div-inv_binary64_13836`
5×	`pow-prod-up_binary64_13909`
4×	`add-log-exp_binary64_13878` `sqrt-div_binary64_13856` `rem-sqrt-square_binary64_13852` `pow-prod-down_binary64_13910`
3×	`pow-sqr_binary64_13812`
2×	`div-exp_binary64_13890` `sqr-abs_binary64_13854` `cbrt-undiv_binary64_13873` `cbrt-unprod_binary64_13872` `*-commutative_binary64_13770` `clear-num_binary64_13838` `prod-exp_binary64_13888` `frac-2neg_binary64_13850`
1×	`pow-plus_binary64_13902` `sqrt-unprod_binary64_13859` `associate-l/_binary64_13782` `frac-times_binary64_13849` `pow2_binary64_13920` `associate-r/_binary64_13781` `rem-square-sqrt_binary64_13851`

Counts

4 → 165

Calls

4 calls:

21.0ms	(*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))
6.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1/9 x)
3.0ms	(/.f64 1/9 x)

series96.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(*.f64 3 (sqrt.f64 x))
26.0ms	(*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))
21.0ms	(/.f64 1/9 x)
20.0ms	(/.f64 1/9 x)

simplify89.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4917	1765
1	4917	1765

prune348.0ms (9.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	178	11	189

Merged error: 0.0b

Counts

189 → 11

Compiler

Compiled 5918 to 4515 computations (23.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 1/9 (/.f64 1 x)) (+.f64 y -1))
0.2b	(.f64 (sqrt.f64 x) (+.f64 (.f64 1/9 (/.f64 1 x)) (+.f64 y -1)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (*.f64 1/9 (/.f64 1 x)) (+.f64 y -1))))
0.4b	(*.f64 1/9 (/.f64 1 x))

rewrite61.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_13861`
25×	`associate-*r/_binary64_13781`
20×	`add-exp-log_binary64_13877`
17×	`associate-r_binary64_13779` `*-un-lft-identity_binary64_13839`
16×	`add-cube-cbrt_binary64_13874` `add-cbrt-cube_binary64_13875`
13×	`pow1_binary64_13900`
12×	`frac-add_binary64_13847` `associate-l_binary64_13780`
11×	`times-frac_binary64_13845`
9×	`flip3-+_binary64_13842` `add-log-exp_binary64_13878` `flip-+_binary64_13813`
8×	`prod-exp_binary64_13888`
7×	`un-div-inv_binary64_13837`
6×	`cbrt-unprod_binary64_13872`
5×	`unswap-sqr_binary64_13807` `distribute-lft-in_binary64_13788` `pow-prod-down_binary64_13910` `distribute-rgt-in_binary64_13789`
4×	`sqrt-prod_binary64_13855`
3×	`sum-log_binary64_13930` `*-commutative_binary64_13770`
2×	`div-exp_binary64_13890`
1×	`rec-exp_binary64_13889` `+-commutative_binary64_13769` `cbrt-undiv_binary64_13873` `associate-+r+_binary64_13771` `1-exp_binary64_13883` `div-inv_binary64_13836`

Counts

4 → 111

Calls

4 calls:

16.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (*.f64 1/9 (/.f64 1 x)) (+.f64 y -1))))
14.0ms	(.f64 (sqrt.f64 x) (+.f64 (.f64 1/9 (/.f64 1 x)) (+.f64 y -1)))
10.0ms	(+.f64 (*.f64 1/9 (/.f64 1 x)) (+.f64 y -1))
9.0ms	(*.f64 1/9 (/.f64 1 x))

series185.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (*.f64 1/9 (/.f64 1 x)) (+.f64 y -1))))
61.0ms	(.f64 (sqrt.f64 x) (+.f64 (.f64 1/9 (/.f64 1 x)) (+.f64 y -1)))
23.0ms	(+.f64 (*.f64 1/9 (/.f64 1 x)) (+.f64 y -1))
21.0ms	(*.f64 1/9 (/.f64 1 x))

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4935	1992
1	4935	1992

prune121.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	123	11	134

Merged error: 0.0b

Counts

134 → 11

Compiler

Compiled 2347 to 1622 computations (30.9% saved)

regimes78.0ms (2.1%)

Compiler: Compiled 755 to 646 computations (14.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	21
1	27	21

end0.0ms (0%)

sample792.0ms (21.2%)

Algorithm

1×

intervals

Results

350.0ms	8000×	body	128	valid
6.0ms	134×	body	128	nan
3.0ms	69×	body	128	invalid

Compiler

Compiled 287 to 247 computations (13.9% saved)

Details

analyze53.0ms (1.4%)

sample18.0ms (0.5%)

simplify306.0ms (8.2%)

prune5.0ms (0.1%)

localize10.0ms (0.3%)

rewrite41.0ms (1.1%)

series163.0ms (4.3%)

simplify63.0ms (1.7%)

prune449.0ms (12%)

localize10.0ms (0.3%)

rewrite57.0ms (1.5%)

series183.0ms (4.9%)

simplify100.0ms (2.7%)

prune353.0ms (9.4%)

localize11.0ms (0.3%)

rewrite52.0ms (1.4%)

series96.0ms (2.6%)

simplify89.0ms (2.4%)

prune348.0ms (9.3%)

localize10.0ms (0.3%)

rewrite61.0ms (1.6%)

series185.0ms (4.9%)

simplify88.0ms (2.3%)

prune121.0ms (3.2%)

regimes78.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample792.0ms (21.2%)

Profiling