Details

analyze276.0ms (5.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	699	52
1	699	52
0	3	3
1	3	3

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
81.1%	18.7%	0.1%	9
81.1%	18.7%	0.1%	10
81.1%	15.6%	3.3%	11
84.3%	10.9%	4.8%	12
84.3%	10.9%	4.8%	13
84.3%	8.6%	7.2%	14

Symmetry

(sort x y)

Compiler

Compiled 10 to 10 computations (0% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	21×	body	128	invalid

Compiler

Compiled 19 to 22 computations (-15.8% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	321	13
1	321	13

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`add-sqr-sqrt_binary64_3851` `cancel-sign-sub-inv_binary64_3795`
10×	`*-un-lft-identity_binary64_3829` `times-frac_binary64_3835`
8×	`add-cube-cbrt_binary64_3864`
3×	`add-log-exp_binary64_3868`
2×	`difference-of-squares_binary64_3798`
1×	`diff-log_binary64_3921` `pow1_binary64_3890` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `frac-sub_binary64_3838` `flip3--_binary64_3833` `sub-neg_binary64_3822` `flip--_binary64_3804` `div-inv_binary64_3826` `distribute-lft-out--_binary64_3781`

Counts

1 → 28

Calls

1 calls:

12.0ms

(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 522 to 337 computations (35.4% saved)

series161.0ms (3.3%)

Error

0.0b

Counts

1 → 18

Calls

1 calls:

150.0ms

(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 317 to 279 computations (12% saved)

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5337	546

prune32.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Error

Counts

47 → 4

Compiler

Compiled 559 to 345 computations (38.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
0.5b	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
0.5b	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))) (cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (*.f64 x y) 2))))

rewrite227.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`cbrt-prod_binary64_3860`
23×	`add-sqr-sqrt_binary64_3851`
18×	`cbrt-div_binary64_3861`
15×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829`
11×	`pow1_binary64_3890`
9×	`pow1/3_binary64_3911` `flip3-+_binary64_3832` `flip-+_binary64_3803`
6×	`add-exp-log_binary64_3867` `swap-sqr_binary64_3796` `associate-l_binary64_3770` `associate-r_binary64_3769`
4×	`add-log-exp_binary64_3868` `add-cbrt-cube_binary64_3865` `frac-times_binary64_3839` `unswap-sqr_binary64_3797`
2×	`pow-prod-down_binary64_3900` `pow-prod-up_binary64_3899` `pow-sqr_binary64_3802` `associate-l/_binary64_3772` `associate-r/_binary64_3771`
1×	`pow2_binary64_3910` `pow-plus_binary64_3892` `prod-exp_binary64_3878` `cbrt-unprod_binary64_3862` `*-commutative_binary64_3760`

Counts

4 → 87

Calls

4 calls:

16.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))) (cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (*.f64 x y) 2))))
5.0ms	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
5.0ms	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
5.0ms	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))

Compiler

Compiled 4124 to 2664 computations (35.4% saved)

series992.0ms (20.1%)

Error

Counts

4 → 60

Calls

4 calls:

291.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))) (cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (*.f64 x y) 2))))
203.0ms	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
194.0ms	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
193.0ms	(cbrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))

Compiler

Compiled 7016 to 5554 computations (20.8% saved)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5043	4144

prune296.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

Counts

151 → 4

Compiler

Compiled 5767 to 3760 computations (34.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))
0.0b	(sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
0.0b	(sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))) (sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (*.f64 x y) 2))))

rewrite195.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-sqr-sqrt_binary64_3851`
24×	`sqrt-prod_binary64_3845`
21×	`pow1_binary64_3890`
16×	`sqrt-div_binary64_3846`
14×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829`
10×	`pow1/2_binary64_3909` `sqrt-pow1_binary64_3847`
9×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
8×	`swap-sqr_binary64_3796`
6×	`add-exp-log_binary64_3867` `add-log-exp_binary64_3868` `add-cbrt-cube_binary64_3865` `associate-l_binary64_3770` `associate-r_binary64_3769`
5×	`pow-prod-up_binary64_3899`
4×	`rem-sqrt-square_binary64_3842` `frac-times_binary64_3839` `unswap-sqr_binary64_3797`
3×	`pow-prod-down_binary64_3900` `pow-sqr_binary64_3802`
2×	`associate-l/_binary64_3772` `associate-r/_binary64_3771`
1×	`pow2_binary64_3910` `pow-plus_binary64_3892` `prod-exp_binary64_3878` `cbrt-unprod_binary64_3862` `sqrt-unprod_binary64_3849` `sqr-abs_binary64_3844` `rem-square-sqrt_binary64_3841` `*-commutative_binary64_3760` `sum-log_binary64_3920` `+-commutative_binary64_3759`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))) (sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (*.f64 x y) 2))))
5.0ms	(+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))
5.0ms	(sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))

Compiler

Compiled 3447 to 2239 computations (35% saved)

series497.0ms (10.1%)

Error

Counts

4 → 58

Calls

4 calls:

147.0ms	(+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))
131.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))) (sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (*.f64 x y) 2))))
89.0ms	(sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))
88.0ms	(sqrt.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)))

Compiler

Compiled 2722 to 2116 computations (22.3% saved)

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5809	2610

prune168.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	157	4	161

Error

Counts

161 → 4

Compiler

Compiled 3328 to 2104 computations (36.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))
0.1b	(pow.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)) 3)
42.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)) 3))

rewrite97.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`cbrt-prod_binary64_3860`
9×	`add-cube-cbrt_binary64_3864` `add-sqr-sqrt_binary64_3851` `*-un-lft-identity_binary64_3829`
6×	`unpow-prod-down_binary64_3908` `cube-prod_binary64_3857`
5×	`add-log-exp_binary64_3868`
4×	`pow1_binary64_3890` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `cube-div_binary64_3858`
3×	`flip3-+_binary64_3832` `flip-+_binary64_3803` `pow-unpow_binary64_3906`
2×	`cbrt-div_binary64_3861` `unpow3_binary64_3895` `cube-mult_binary64_3859` `sqr-pow_binary64_3801`
1×	`pow1/3_binary64_3911` `rem-cbrt-cube_binary64_3853` `pow-pow_binary64_3901` `pow-to-exp_binary64_3898` `pow-exp_binary64_3897` `rem-cube-cbrt_binary64_3852` `sum-log_binary64_3920` `+-commutative_binary64_3759`

Counts

3 → 59

Calls

3 calls:

6.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)) 3))
6.0ms	(pow.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)) 3)
5.0ms	(+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))

Compiler

Compiled 1466 to 1006 computations (31.4% saved)

series571.0ms (11.5%)

Error

Counts

3 → 72

Calls

3 calls:

197.0ms	(pow.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)) 3)
165.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2)) 3))
142.0ms	(+.f64 (.f64 -1/8 z) (/.f64 (.f64 x y) 2))

Compiler

Compiled 2541 to 2165 computations (14.8% saved)

simplify90.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4953	2728
1	4953	2728

prune109.0ms (2.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	131	4	135

Error

Counts

135 → 4

Compiler

Compiled 2218 to 1316 computations (40.7% saved)

regimes147.0ms (3%)

Accuracy

Total 0.0b remaining (43.8%)

Threshold costs 0.0b (43.8%)

Compiler

Compiled 1236 to 1081 computations (12.5% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	13
1	28	13

Remove

(sort x y)

Compiler

Compiled 18 to 18 computations (0% saved)

end0.0ms (0%)

sample734.0ms (14.8%)

Algorithm

1×

intervals

Results

254.0ms	8000×	body	128	valid
15.0ms	523×	body	128	invalid

Compiler

Compiled 189 to 167 computations (11.6% saved)

Details

analyze276.0ms (5.6%)

sample26.0ms (0.5%)

simplify25.0ms (0.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite39.0ms (0.8%)

series161.0ms (3.3%)

simplify56.0ms (1.1%)

prune32.0ms (0.7%)

localize12.0ms (0.2%)

rewrite227.0ms (4.6%)

series992.0ms (20.1%)

simplify81.0ms (1.6%)

prune296.0ms (6%)

localize9.0ms (0.2%)

rewrite195.0ms (4%)

series497.0ms (10.1%)

simplify79.0ms (1.6%)

prune168.0ms (3.4%)

localize9.0ms (0.2%)

rewrite97.0ms (2%)

series571.0ms (11.5%)

simplify90.0ms (1.8%)

prune109.0ms (2.2%)

regimes147.0ms (3%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

end0.0ms (0%)

sample734.0ms (14.8%)

Profiling