Details

analyze314.0ms (4.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4754	20
1	4754	20
0	2	2
1	2	2

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%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample14.0ms (0.2%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify152.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	5248	10

prune4.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_15082`
3×	`add-log-exp_binary64_15121`
2×	`times-frac_binary64_15088` `distribute-lft-out_binary64_15033`
1×	`sum-log_binary64_15173` `frac-add_binary64_15090` `add-cube-cbrt_binary64_15117` `flip-+_binary64_15056` `add-cbrt-cube_binary64_15118` `pow1_binary64_15143` `+-commutative_binary64_15012` `add-exp-log_binary64_15120` `add-sqr-sqrt_binary64_15104` `flip3-+_binary64_15085`

Counts

1 → 14

Calls

1 calls:

13.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series18.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

18.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4854	239
1	4854	239

prune13.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Error

0.0b

Counts

18 → 2

Compiler

Compiled 222 to 168 computations (24.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/4 (*.f64 y y))
0.4b	(/.f64 1/4 (*.f64 x x))
3.8b	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
30.9b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite73.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-sqr-sqrt_binary64_15104`
194×	`times-frac_binary64_15088`
112×	`*-un-lft-identity_binary64_15082`
84×	`difference-of-squares_binary64_15051`
42×	`distribute-lft-out--_binary64_15034`
30×	`add-cube-cbrt_binary64_15117`
26×	`div-inv_binary64_15079`
16×	`add-cbrt-cube_binary64_15118` `add-exp-log_binary64_15120`
15×	`associate-/l*_binary64_15027`
11×	`associate-/r*_binary64_15026`
7×	`cancel-sign-sub-inv_binary64_15048`
6×	`add-log-exp_binary64_15121`
5×	`div-exp_binary64_15133` `cbrt-undiv_binary64_15116`
4×	`pow1_binary64_15143`
3×	`associate-/l/_binary64_15029` `frac-2neg_binary64_15093` `frac-sub_binary64_15091` `flip3--_binary64_15086` `clear-num_binary64_15081` `flip--_binary64_15057` `associate-/r/_binary64_15028`
2×	`prod-exp_binary64_15131` `cbrt-unprod_binary64_15115`
1×	`div-sub_binary64_15087` `sub-neg_binary64_15075` `diff-log_binary64_15174`

Counts

4 → 185

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
10.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
7.0ms	(/.f64 1/4 (*.f64 y y))
5.0ms	(/.f64 1/4 (*.f64 x x))

series109.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
28.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
17.0ms	(/.f64 1/4 (*.f64 y y))
16.0ms	(/.f64 1/4 (*.f64 x x))

simplify126.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4908	6428
1	4908	6428

prune314.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Error

Counts

199 → 4

Compiler

Compiled 5799 to 3823 computations (34.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

rewrite99.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64_15104`
71×	`cbrt-prod_binary64_15113`
63×	`*-un-lft-identity_binary64_15082`
42×	`times-frac_binary64_15088`
33×	`cbrt-div_binary64_15114`
28×	`difference-of-squares_binary64_15051`
16×	`distribute-lft-out--_binary64_15034`
15×	`add-cube-cbrt_binary64_15117`
14×	`swap-sqr_binary64_15049`
12×	`associate-l_binary64_15023` `associate-r_binary64_15022`
11×	`frac-sub_binary64_15091` `flip3--_binary64_15086` `pow1_binary64_15143` `flip--_binary64_15057`
9×	`pow1/3_binary64_15164` `frac-times_binary64_15092`
6×	`add-exp-log_binary64_15120`
4×	`unswap-sqr_binary64_15050` `add-cbrt-cube_binary64_15118` `add-log-exp_binary64_15121`
3×	`associate-l/_binary64_15025` `associate-r/_binary64_15024`
2×	`pow-prod-down_binary64_15153` `pow-prod-up_binary64_15152` `pow-sqr_binary64_15055`
1×	`prod-exp_binary64_15131` `pow2_binary64_15163` `cbrt-unprod_binary64_15115` `*-commutative_binary64_15013` `pow-plus_binary64_15145`

Counts

4 → 135

Calls

4 calls:

35.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
16.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series457.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
116.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
104.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
101.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4870	4157
1	4870	4157

prune540.0ms (7.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	147	4	151

Error

Counts

151 → 4

Compiler

Compiled 7895 to 6142 computations (22.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 -1/2 x))
0.1b	(*.f64 (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))) (/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))))
0.1b	(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
0.1b	(/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))

rewrite315.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

591×	`*-un-lft-identity_binary64_15082`
538×	`times-frac_binary64_15088`
522×	`add-sqr-sqrt_binary64_15104`
265×	`sqrt-prod_binary64_15098`
151×	`difference-of-squares_binary64_15051`
119×	`distribute-lft-out_binary64_15033`
87×	`add-cube-cbrt_binary64_15117`
82×	`associate-r_binary64_15022`
61×	`associate-l_binary64_15023`
59×	`distribute-lft-out--_binary64_15034`
21×	`associate-/r*_binary64_15026`
20×	`add-cbrt-cube_binary64_15118` `add-exp-log_binary64_15120`
14×	`associate-/l*_binary64_15027`
12×	`associate-/r/_binary64_15028`
9×	`sqrt-div_binary64_15099`
7×	`pow1_binary64_15143`
6×	`div-exp_binary64_15133` `associate-/l/_binary64_15029` `cbrt-undiv_binary64_15116`
5×	`div-inv_binary64_15079`
4×	`unswap-sqr_binary64_15050` `prod-exp_binary64_15131` `cbrt-unprod_binary64_15115` `add-log-exp_binary64_15121`
3×	`frac-sub_binary64_15091` `frac-add_binary64_15090` `flip3--_binary64_15086` `flip-+_binary64_15056` `flip--_binary64_15057` `flip3-+_binary64_15085`
2×	`frac-2neg_binary64_15093` `rem-sqrt-square_binary64_15095` `clear-num_binary64_15081`
1×	`pow-prod-down_binary64_15153` `frac-times_binary64_15092` `pow1/2_binary64_15162` `sqrt-pow1_binary64_15100` `div-sub_binary64_15087` `-commutative_binary64_15013` `associate-l/_binary64_15025` `associate-*r/_binary64_15024`

Counts

4 → 393

Calls

4 calls:

152.0ms	(*.f64 (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))) (/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))))
39.0ms	(/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
35.0ms	(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
4.0ms	(sqrt.f64 (/.f64 -1/2 x))

series1.2s (17%)

Counts

4 → 12

Calls

4 calls:

904.0ms	(*.f64 (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))) (/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))))
138.0ms	(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
133.0ms	(/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
15.0ms	(sqrt.f64 (/.f64 -1/2 x))

simplify196.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5201	17477

prune2.1s (29.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	405	0	405
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	405	4	409

Error

Counts

409 → 4

Compiler

Compiled 19291 to 14989 computations (22.3% saved)

regimes87.0ms (1.2%)

Accuracy

Total 0.0b remaining (57.8%)

Threshold costs 0.0b (57.8%)

Compiler

Compiled 967 to 805 computations (16.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample687.0ms (9.8%)

Algorithm

1×

intervals

Results

227.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 339 to 285 computations (15.9% saved)

Details

analyze314.0ms (4.5%)

sample14.0ms (0.2%)

simplify152.0ms (2.2%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

rewrite14.0ms (0.2%)

series18.0ms (0.3%)

simplify85.0ms (1.2%)

prune13.0ms (0.2%)

localize11.0ms (0.2%)

rewrite73.0ms (1%)

series109.0ms (1.6%)

simplify126.0ms (1.8%)

prune314.0ms (4.5%)

localize16.0ms (0.2%)

rewrite99.0ms (1.4%)

series457.0ms (6.5%)

simplify106.0ms (1.5%)

prune540.0ms (7.7%)

localize14.0ms (0.2%)

rewrite315.0ms (4.5%)

series1.2s (17%)

simplify196.0ms (2.8%)

prune2.1s (29.3%)

regimes87.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample687.0ms (9.8%)

Profiling