Details

analyze55.0ms (1.8%)

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)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	7×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify297.0ms (9.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	1572	18
1	1572	18

prune4.0ms (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: 0.3b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite44.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_15277`
21×	`*-un-lft-identity_binary64_15242`
18×	`add-sqr-sqrt_binary64_15263`
16×	`add-cbrt-cube_binary64_15275`
15×	`associate-r_binary64_15184`
14×	`pow1_binary64_15300`
10×	`add-cube-cbrt_binary64_15274`
7×	`prod-exp_binary64_15288`
6×	`add-log-exp_binary64_15278`
5×	`cbrt-unprod_binary64_15272` `pow-prod-down_binary64_15310`
4×	`associate-l_binary64_15185` `distribute-lft-out_binary64_15195` `div-exp_binary64_15290` `sqrt-prod_binary64_15257`
3×	`div-inv_binary64_15239` `times-frac_binary64_15248` `distribute-lft-out--_binary64_15196` `associate-/l*_binary64_15189`
2×	`distribute-rgt-in_binary64_15194` `sub-neg_binary64_15235` `rec-exp_binary64_15289` `-commutative_binary64_15175` `cbrt-undiv_binary64_15273` `difference-of-squares_binary64_15211` `associate-r/_binary64_15186` `1-exp_binary64_15283` `pow-flip_binary64_15313` `unswap-sqr_binary64_15210` `distribute-lft-in_binary64_15193` `associate--l+_binary64_15181`
1×	`difference-of-sqr-1_binary64_15212` `inv-pow_binary64_15324` `flip3--_binary64_15246` `flip3-+_binary64_15245` `flip-+_binary64_15216` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `sum-log_binary64_15330` `associate-/r*_binary64_15188` `flip--_binary64_15217` `+-commutative_binary64_15174`

Counts

4 → 93

Calls

4 calls:

18.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
7.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series165.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.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))
22.0ms	(/.f64 1 (*.f64 x 9))

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4916	1293
1	4916	1293

prune131.0ms (4.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	10	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

Compiler

Compiled 2055 to 1500 computations (27% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite76.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64_15248`
62×	`add-sqr-sqrt_binary64_15263` `*-un-lft-identity_binary64_15242`
50×	`add-cube-cbrt_binary64_15274`
20×	`add-exp-log_binary64_15277`
16×	`add-cbrt-cube_binary64_15275`
14×	`associate-r_binary64_15184`
13×	`associate-/l*_binary64_15189`
11×	`pow1_binary64_15300`
9×	`add-log-exp_binary64_15278`
6×	`div-exp_binary64_15290`
5×	`div-inv_binary64_15239`
4×	`associate-l_binary64_15185` `distribute-lft-out--_binary64_15196` `difference-of-squares_binary64_15211` `cbrt-unprod_binary64_15272` `pow-prod-down_binary64_15310` `sqrt-prod_binary64_15257` `prod-exp_binary64_15288`
3×	`sub-neg_binary64_15235` `cbrt-undiv_binary64_15273` `associate-/r*_binary64_15188` `associate--l+_binary64_15181`
2×	`distribute-rgt-in_binary64_15194` `distribute-lft-out_binary64_15195` `-commutative_binary64_15175` `difference-of-sqr-1_binary64_15212` `diff-log_binary64_15331` `flip3--_binary64_15246` `associate-r/_binary64_15186` `unswap-sqr_binary64_15210` `flip--_binary64_15217` `distribute-lft-in_binary64_15193`
1×	`associate-/l/_binary64_15191` `rec-exp_binary64_15289` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `1-exp_binary64_15283` `sum-log_binary64_15330`

Counts

4 → 141

Calls

4 calls:

26.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
23.0ms	(-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1)
8.0ms	(/.f64 (/.f64 1 x) 9)
6.0ms	(*.f64 3 (sqrt.f64 x))

series155.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
30.0ms	(*.f64 3 (sqrt.f64 x))
27.0ms	(-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1)
22.0ms	(/.f64 (/.f64 1 x) 9)

simplify88.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4926	2233
1	4926	2233

prune182.0ms (6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	152	11	163

Merged error: 0.0b

Counts

163 → 11

Compiler

Compiled 3173 to 2300 computations (27.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite51.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_15242`
20×	`add-sqr-sqrt_binary64_15263`
16×	`add-cube-cbrt_binary64_15274`
13×	`add-exp-log_binary64_15277` `add-cbrt-cube_binary64_15275`
11×	`pow1_binary64_15300`
9×	`associate-l_binary64_15185` `times-frac_binary64_15248`
6×	`associate-r/_binary64_15186` `add-log-exp_binary64_15278` `associate-r*_binary64_15184`
5×	`distribute-rgt-in_binary64_15194` `distribute-lft-in_binary64_15193`
4×	`distribute-lft-out_binary64_15195` `cbrt-unprod_binary64_15272` `pow-prod-down_binary64_15310` `sqrt-prod_binary64_15257` `prod-exp_binary64_15288`
3×	`flip3-+_binary64_15245` `flip-+_binary64_15216` `associate-/l_binary64_15189` `associate-/r_binary64_15188`
2×	`*-commutative_binary64_15175` `unswap-sqr_binary64_15210`
1×	`cbrt-undiv_binary64_15273` `div-inv_binary64_15239` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `div-exp_binary64_15290` `sum-log_binary64_15330` `+-commutative_binary64_15174`

Counts

4 → 91

Calls

4 calls:

16.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
15.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
9.0ms	(+.f64 (/.f64 1/9 x) y)
3.0ms	(/.f64 1/9 x)

series192.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
59.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
33.0ms	(+.f64 (/.f64 1/9 x) y)
22.0ms	(/.f64 1/9 x)

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4911	1547
1	4911	1547

prune105.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	105	9	114

Merged error: 0.0b

Counts

114 → 9

Compiler

Compiled 1940 to 1348 computations (30.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_15263`
19×	`*-un-lft-identity_binary64_15242`
17×	`add-cube-cbrt_binary64_15274`
10×	`add-exp-log_binary64_15277` `add-cbrt-cube_binary64_15275`
9×	`associate-l_binary64_15185` `times-frac_binary64_15248`
8×	`pow1_binary64_15300` `add-log-exp_binary64_15278`
7×	`associate-r_binary64_15184`
4×	`associate-*r/_binary64_15186` `sqrt-prod_binary64_15257`
3×	`distribute-rgt-in_binary64_15194` `flip3-+_binary64_15245` `flip-+_binary64_15216` `associate-/l_binary64_15189` `associate-/r_binary64_15188` `unswap-sqr_binary64_15210` `distribute-lft-in_binary64_15193`
2×	`*-commutative_binary64_15175` `cbrt-unprod_binary64_15272` `pow-prod-down_binary64_15310` `sum-log_binary64_15330` `associate-+r+_binary64_15176` `prod-exp_binary64_15288`
1×	`neg-sub0_binary64_15237` `distribute-lft-out_binary64_15195` `cbrt-undiv_binary64_15273` `div-inv_binary64_15239` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `div-exp_binary64_15290` `associate-+l-_binary64_15179` `+-commutative_binary64_15174` `neg-log_binary64_15332`

Counts

4 → 91

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) y))
12.0ms	(.f64 3 (+.f64 (neg.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) y))))
9.0ms	(+.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) y)))
4.0ms	(/.f64 1/9 x)

series263.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(.f64 3 (+.f64 (neg.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) y))))
84.0ms	(+.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) y)))
62.0ms	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) y))
20.0ms	(/.f64 1/9 x)

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4951	1685
1	4951	1685

prune98.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 0.0b

Counts

112 → 9

Compiler

Compiled 2029 to 1194 computations (41.2% saved)

regimes40.0ms (1.3%)

Compiler: Compiled 324 to 280 computations (13.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	21
1	26	21

end0.0ms (0%)

sample737.0ms (24.5%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	128	valid
5.0ms	111×	body	128	nan
3.0ms	69×	body	128	invalid

Compiler

Compiled 206 to 179 computations (13.1% saved)

Details

analyze55.0ms (1.8%)

sample19.0ms (0.6%)

simplify297.0ms (9.9%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

rewrite44.0ms (1.5%)

series165.0ms (5.5%)

simplify75.0ms (2.5%)

prune131.0ms (4.4%)

localize10.0ms (0.3%)

rewrite76.0ms (2.5%)

series155.0ms (5.1%)

simplify88.0ms (2.9%)

prune182.0ms (6%)

localize8.0ms (0.3%)

rewrite51.0ms (1.7%)

series192.0ms (6.4%)

simplify75.0ms (2.5%)

prune105.0ms (3.5%)

localize12.0ms (0.4%)

rewrite44.0ms (1.5%)

series263.0ms (8.7%)

simplify68.0ms (2.3%)

prune98.0ms (3.3%)

regimes40.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample737.0ms (24.5%)

Profiling