Details

analyze173.0ms (6.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	20
1	51	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
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	10
1	32	10

prune2.0ms (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

Error

6.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (*.f64 y y))
6.2b	(.f64 x (+.f64 1 (.f64 y y)))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_9989`
4×	`add-cbrt-cube_binary64_10003` `add-cube-cbrt_binary64_10002` `add-log-exp_binary64_10006` `add-exp-log_binary64_10005` `*-un-lft-identity_binary64_9967` `pow1_binary64_10028`
3×	`associate-l_binary64_9908` `associate-r_binary64_9907`
2×	`flip3-+_binary64_9970` `flip-+_binary64_9941` `associate-*r/_binary64_9909`
1×	`prod-exp_binary64_10016` `cbrt-unprod_binary64_10000` `distribute-lft-in_binary64_9916` `pow-prod-down_binary64_10038` `distribute-rgt-in_binary64_9917` `+-commutative_binary64_9897` `sum-log_binary64_10058` `unswap-sqr_binary64_9935` `*-commutative_binary64_9898`

Counts

2 → 33

Calls

2 calls:

6.0ms	(.f64 x (+.f64 1 (.f64 y y)))
3.0ms	(+.f64 1 (*.f64 y y))

series61.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

39.0ms	(.f64 x (+.f64 1 (.f64 y y)))
22.0ms	(+.f64 1 (*.f64 y y))

simplify62.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6035	428

prune38.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

6.4b

Counts

40 → 7

Compiler

Compiled 516 to 292 computations (43.4% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (sqrt.f64 (+.f64 1 (.f64 y y))))
0.1b	(.f64 (.f64 x (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (+.f64 1 (.f64 y y))))
6.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
6.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))

rewrite34.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-div_binary64_9984`
17×	`add-sqr-sqrt_binary64_9989`
13×	`pow1_binary64_10028` `sqrt-prod_binary64_9983`
12×	`associate-r_binary64_9907`
11×	`add-cbrt-cube_binary64_10003` `add-cube-cbrt_binary64_10002` `add-exp-log_binary64_10005` `*-un-lft-identity_binary64_9967`
10×	`associate-*r/_binary64_9909`
9×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
4×	`frac-times_binary64_9977` `prod-exp_binary64_10016` `cbrt-unprod_binary64_10000` `associate-l_binary64_9908` `pow-prod-down_binary64_10038` `add-log-exp_binary64_10006`
2×	`associate-l/_binary64_9910` `pow1/2_binary64_10047` `unswap-sqr_binary64_9935` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980` `-commutative_binary64_9898`

Counts

4 → 83

Calls

4 calls:

14.0ms	(.f64 (.f64 x (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (+.f64 1 (.f64 y y))))
7.0ms	(.f64 x (sqrt.f64 (+.f64 1 (.f64 y y))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

series119.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 x (sqrt.f64 (+.f64 1 (.f64 y y))))
40.0ms	(.f64 (.f64 x (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (+.f64 1 (.f64 y y))))
19.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
17.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

simplify96.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4884	1418
1	4884	1418

prune94.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Error

6.4b

Counts

102 → 7

Compiler

Compiled 1888 to 1127 computations (40.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (.f64 x (+.f64 1 (.f64 y y))))
6.2b	(.f64 x (+.f64 1 (.f64 y y)))
6.2b	(.f64 x (+.f64 1 (.f64 y y)))
6.2b	(.f64 x (+.f64 1 (.f64 y y)))

rewrite32.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_9989`
10×	`add-cbrt-cube_binary64_10003` `add-cube-cbrt_binary64_10002` `add-exp-log_binary64_10005` `*-un-lft-identity_binary64_9967` `pow1_binary64_10028`
9×	`associate-l_binary64_9908` `associate-r_binary64_9907`
8×	`associate-*r/_binary64_9909`
4×	`flip3-+_binary64_9970` `flip-+_binary64_9941` `add-log-exp_binary64_10006`
3×	`prod-exp_binary64_10016` `cbrt-unprod_binary64_10000` `distribute-lft-in_binary64_9916` `pow-prod-down_binary64_10038` `distribute-rgt-in_binary64_9917` `unswap-sqr_binary64_9935` `*-commutative_binary64_9898`
2×	`cbrt-div_binary64_9999`
1×	`pow1/3_binary64_10049` `cbrt-prod_binary64_9998`

Counts

4 → 77

Calls

4 calls:

6.0ms	(.f64 x (+.f64 1 (.f64 y y)))
6.0ms	(.f64 x (+.f64 1 (.f64 y y)))
6.0ms	(.f64 x (+.f64 1 (.f64 y y)))
4.0ms	(cbrt.f64 (.f64 x (+.f64 1 (.f64 y y))))

series257.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt.f64 (.f64 x (+.f64 1 (.f64 y y))))
41.0ms	(.f64 x (+.f64 1 (.f64 y y)))
38.0ms	(.f64 x (+.f64 1 (.f64 y y)))
37.0ms	(.f64 x (+.f64 1 (.f64 y y)))

simplify73.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4888	1070
1	4888	1070

prune118.0ms (4.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	89	7	96

Error

6.4b

Counts

96 → 7

Compiler

Compiled 2749 to 1523 computations (44.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (pow.f64 y 4))
6.2b	(.f64 x (/.f64 (-.f64 1 (pow.f64 y 4)) (-.f64 1 (.f64 y y))))
11.4b	(/.f64 (-.f64 1 (pow.f64 y 4)) (-.f64 1 (*.f64 y y)))

rewrite68.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_9989`
120×	`*-un-lft-identity_binary64_9967`
114×	`difference-of-squares_binary64_9936`
101×	`times-frac_binary64_9973`
56×	`associate-r_binary64_9907`
39×	`add-cube-cbrt_binary64_10002`
27×	`unpow-prod-down_binary64_10046`
25×	`sqr-pow_binary64_9939`
12×	`distribute-lft-out--_binary64_9919`
10×	`add-cbrt-cube_binary64_10003` `associate-/l*_binary64_9912` `add-exp-log_binary64_10005`
7×	`cancel-sign-sub-inv_binary64_9933`
5×	`add-log-exp_binary64_10006` `associate-/r*_binary64_9911` `pow1_binary64_10028`
4×	`flip--_binary64_9942` `flip3--_binary64_9971` `associate-/r/_binary64_9913`
3×	`associate-l_binary64_9908`
2×	`div-exp_binary64_10018` `prod-exp_binary64_10016` `cbrt-undiv_binary64_10001` `cbrt-unprod_binary64_10000` `associate-/l/_binary64_9914` `unswap-sqr_binary64_9935` `div-inv_binary64_9964`
1×	`sub-neg_binary64_9960` `pow-prod-down_binary64_10038` `diff-log_binary64_10059` `div-sub_binary64_9972` `associate-r/_binary64_9909` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `-commutative_binary64_9898`

Counts

3 → 182

Calls

3 calls:

30.0ms	(.f64 x (/.f64 (-.f64 1 (pow.f64 y 4)) (-.f64 1 (.f64 y y))))
12.0ms	(/.f64 (-.f64 1 (pow.f64 y 4)) (-.f64 1 (*.f64 y y)))
7.0ms	(-.f64 1 (pow.f64 y 4))

series256.0ms (9.8%)

Counts

3 → 9

Calls

3 calls:

135.0ms	(.f64 x (/.f64 (-.f64 1 (pow.f64 y 4)) (-.f64 1 (.f64 y y))))
70.0ms	(/.f64 (-.f64 1 (pow.f64 y 4)) (-.f64 1 (*.f64 y y)))
51.0ms	(-.f64 1 (pow.f64 y 4))

simplify85.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5728	3913

prune223.0ms (8.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	191	7	198

Error

6.4b

Counts

198 → 7

Compiler

Compiled 4101 to 2711 computations (33.9% saved)

regimes131.0ms (5%)

Accuracy

Total 0.2b remaining (3.8%)

Threshold costs 0.2b (3.8%)

Compiler

Compiled 1164 to 906 computations (22.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	10
1	10	10

end0.0ms (0%)

sample623.0ms (23.9%)

Algorithm

1×

intervals

Results

192.0ms	8000×	body	128	valid
4.0ms	158×	body	128	invalid

Compiler

Compiled 248 to 194 computations (21.8% saved)

Details

analyze173.0ms (6.6%)

sample12.0ms (0.5%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite10.0ms (0.4%)

series61.0ms (2.3%)

simplify62.0ms (2.4%)

prune38.0ms (1.5%)

localize7.0ms (0.3%)

rewrite34.0ms (1.3%)

series119.0ms (4.6%)

simplify96.0ms (3.7%)

prune94.0ms (3.6%)

localize9.0ms (0.3%)

rewrite32.0ms (1.2%)

series257.0ms (9.8%)

simplify73.0ms (2.8%)

prune118.0ms (4.5%)

localize8.0ms (0.3%)

rewrite68.0ms (2.6%)

series256.0ms (9.8%)

simplify85.0ms (3.3%)

prune223.0ms (8.6%)

regimes131.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample623.0ms (23.9%)

Profiling