Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	64×	body	1024	valid
6.0ms	142×	body	128	valid
3.0ms	31×	body	512	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite78.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
118×	`times-frac_binary64`
117×	`*-un-lft-identity_binary64`
76×	`sqrt-prod_binary64`
56×	`add-cube-cbrt_binary64`
27×	`cancel-sign-sub-inv_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
11×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `pow-flip_binary64` `sqrt-div_binary64`
4×	`associate-/r/_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 187

Calls

4 calls:

43.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series184.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
56.0ms	(/.f64 1 (sqrt.f64 x))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4917	3679
1	4917	3679

prune592.0ms (11.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	189	10	199
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	189	11	200

Merged error: 19.2b

Counts

200 → 11

Compiler

Compiled 9608 to 7715 computations (19.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.1b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
42×	`sqrt-prod_binary64`
38×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/l*_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `sqrt-div_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 113

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series330.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
69.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
52.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
27.0ms	(sqrt.f64 (+.f64 1 x))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5015	2693

prune211.0ms (4.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	8	1	9
Picked	1	0	1
Done	1	0	1
Total	133	3	136

Merged error: 0.2b

Counts

136 → 3

Compiler

Compiled 3733 to 2579 computations (30.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite69.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
49×	`add-sqr-sqrt_binary64`
42×	`distribute-lft-out_binary64`
40×	`add-cube-cbrt_binary64`
27×	`associate-/l*_binary64`
26×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`div-exp_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rec-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 165

Calls

4 calls:

25.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

series308.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
59.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
53.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
25.0ms	(sqrt.f64 (+.f64 1 x))

simplify114.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4963	4060
1	4963	4060

prune670.0ms (13.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	172	8	180

Merged error: 0.0b

Counts

180 → 8

Compiler

Compiled 9652 to 7003 computations (27.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite72.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64`
159×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
119×	`add-cube-cbrt_binary64`
87×	`sqrt-prod_binary64`
49×	`distribute-lft-out_binary64`
21×	`associate-/l*_binary64`
20×	`associate-/r/_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`associate-/r*_binary64`
10×	`div-inv_binary64`
9×	`pow1_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`div-exp_binary64`
4×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `inv-pow_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 250

Calls

4 calls:

14.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series336.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
77.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
46.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
45.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify143.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4944	9714
1	4944	9714

prune607.0ms (12%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	261	9	270

Merged error: 0b

Counts

270 → 9

Compiler

Compiled 10434 to 7672 computations (26.5% saved)

regimes27.0ms (0.5%)

Compiler: Compiled 244 to 190 computations (22.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	13	25

end0.0ms (0%)

sample1.0s (20.2%)

Algorithm

1×

intervals

Results

336.0ms	2257×	body	1024	valid
165.0ms	4235×	body	128	valid
110.0ms	1011×	body	512	valid
36.0ms	497×	body	256	valid

Compiler

Compiled 285 to 225 computations (21.1% saved)

Details

analyze1.0ms (0%)

sample25.0ms (0.5%)

simplify11.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite78.0ms (1.5%)

series184.0ms (3.6%)

simplify94.0ms (1.9%)

prune592.0ms (11.7%)

localize7.0ms (0.1%)

rewrite56.0ms (1.1%)

series330.0ms (6.5%)

simplify72.0ms (1.4%)

prune211.0ms (4.2%)

localize9.0ms (0.2%)

rewrite69.0ms (1.4%)

series308.0ms (6.1%)

simplify114.0ms (2.3%)

prune670.0ms (13.3%)

localize11.0ms (0.2%)

rewrite72.0ms (1.4%)

series336.0ms (6.6%)

simplify143.0ms (2.8%)

prune607.0ms (12%)

regimes27.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (20.2%)

Profiling