Details

analyze433.0ms (9.7%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.6%	0.1%	6
12.5%	87.4%	0.1%	7
15.6%	84.3%	0.1%	8
18.7%	71.8%	9.5%	9
23.4%	56%	20.6%	10
26.3%	52.2%	21.5%	11
31%	40.1%	28.9%	12
35.6%	28.9%	35.5%	13
36.8%	27.5%	35.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	68×	body	80	nan

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

prune5.0ms (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: 19.1b

Counts

2 → 2

Compiler

Compiled 38 to 31 computations (18.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.6b	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
0.8b	(+.f64 (.f64 x y) (.f64 x z))
18.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_1542`
5×	`add-sqr-sqrt_binary64_1562`
4×	`sum-log_binary64_1487` `pow1_binary64_1519` `add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
3×	`add-exp-log_binary64_1541` `flip3-+_binary64_1575` `sqrt-prod_binary64_1556` `flip-+_binary64_1602` `add-cbrt-cube_binary64_1549`
2×	`sqrt-div_binary64_1557` `+-commutative_binary64_1644`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `rem-sqrt-square_binary64_1565` `distribute-lft-out_binary64_1621` `associate-+l+_binary64_1629`

Counts

3 → 40

Calls

3 calls:

11.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))
9.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
5.0ms	(+.f64 (.f64 x y) (.f64 x z))

series321.0ms (7.2%)

Counts

3 → 9

Calls

3 calls:

221.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))
54.0ms	(+.f64 (.f64 x y) (.f64 x z))
46.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))

simplify115.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4982	871
1	4982	871

prune55.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 19.0b

Counts

51 → 7

Compiler

Compiled 1122 to 373 computations (66.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 z (+.f64 x y))
0.8b	(+.f64 (.f64 x y) (.f64 z (+.f64 x y)))
18.0b	(sqrt.f64 (+.f64 (.f64 x y) (.f64 z (+.f64 x y))))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1562`
8×	`*-un-lft-identity_binary64_1577`
6×	`pow1_binary64_1519` `add-cube-cbrt_binary64_1548`
5×	`add-exp-log_binary64_1541` `add-log-exp_binary64_1542` `add-cbrt-cube_binary64_1549`
4×	`associate-r_binary64_1636`
3×	`associate-l_binary64_1637` `flip3-+_binary64_1575` `sqrt-prod_binary64_1556` `flip-+_binary64_1602`
2×	`distribute-lft-in_binary64_1619` `distribute-rgt-in_binary64_1620` `sqrt-div_binary64_1557` `associate-*r/_binary64_1638` `associate-+r+_binary64_1628`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `*-commutative_binary64_1645` `prod-exp_binary64_1524` `sum-log_binary64_1487` `rem-sqrt-square_binary64_1565` `pow-prod-down_binary64_1500` `unswap-sqr_binary64_1605` `distribute-lft-out_binary64_1621` `cbrt-unprod_binary64_1546` `+-commutative_binary64_1644`

Counts

3 → 51

Calls

3 calls:

8.0ms	(*.f64 z (+.f64 x y))
6.0ms	(+.f64 (.f64 x y) (.f64 z (+.f64 x y)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x y) (.f64 z (+.f64 x y))))

series319.0ms (7.1%)

Counts

3 → 9

Calls

3 calls:

229.0ms	(sqrt.f64 (+.f64 (.f64 x y) (.f64 z (+.f64 x y))))
48.0ms	(*.f64 z (+.f64 x y))
42.0ms	(+.f64 (.f64 x y) (.f64 z (+.f64 x y)))

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4960	932
1	4960	932

prune58.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Merged error: 19.0b

Counts

67 → 7

Compiler

Compiled 1223 to 414 computations (66.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

14.8b	(cbrt.f64 (*.f64 x (+.f64 y z)))
14.8b	(cbrt.f64 (*.f64 x (+.f64 y z)))
14.8b	(cbrt.f64 (*.f64 x (+.f64 y z)))
18.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (+.f64 y z))) (cbrt.f64 (.f64 x (+.f64 y z)))) (cbrt.f64 (.f64 x (+.f64 y z)))) (.f64 y z)))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-div_binary64_1545` `add-sqr-sqrt_binary64_1562` `associate-*r/_binary64_1638`
5×	`pow1_binary64_1519` `add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
4×	`add-exp-log_binary64_1541` `flip3-+_binary64_1575` `add-log-exp_binary64_1542` `flip-+_binary64_1602` `add-cbrt-cube_binary64_1549`
3×	`cbrt-prod_binary64_1544` `pow1/3_binary64_1511` `sqrt-prod_binary64_1556`
2×	`sqrt-div_binary64_1557`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `rem-sqrt-square_binary64_1565`

Counts

4 → 48

Calls

4 calls:

18.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (+.f64 y z))) (cbrt.f64 (.f64 x (+.f64 y z)))) (cbrt.f64 (.f64 x (+.f64 y z)))) (.f64 y z)))
6.0ms	(cbrt.f64 (*.f64 x (+.f64 y z)))
6.0ms	(cbrt.f64 (*.f64 x (+.f64 y z)))
6.0ms	(cbrt.f64 (*.f64 x (+.f64 y z)))

series861.0ms (19.3%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (+.f64 y z))) (cbrt.f64 (.f64 x (+.f64 y z)))) (cbrt.f64 (.f64 x (+.f64 y z)))) (.f64 y z)))
207.0ms	(cbrt.f64 (*.f64 x (+.f64 y z)))
205.0ms	(cbrt.f64 (*.f64 x (+.f64 y z)))
203.0ms	(cbrt.f64 (*.f64 x (+.f64 y z)))

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4990	919
1	4990	919

prune67.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	59	8	67

Merged error: 19.0b

Counts

67 → 8

Compiler

Compiled 1916 to 529 computations (72.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 z)
0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.8b	(+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (+.f64 x y) (cbrt.f64 z))))
18.0b	(sqrt.f64 (+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (+.f64 x y) (cbrt.f64 z)))))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1562`
19×	`cbrt-prod_binary64_1544`
14×	`add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
12×	`pow1_binary64_1519`
7×	`pow1/3_binary64_1511`
6×	`swap-sqr_binary64_1604` `add-exp-log_binary64_1541` `associate-l_binary64_1637` `associate-r_binary64_1636` `add-log-exp_binary64_1542`
4×	`unswap-sqr_binary64_1605` `add-cbrt-cube_binary64_1549`
3×	`sqrt-prod_binary64_1556`
2×	`pow-sqr_binary64_1610` `pow-prod-down_binary64_1500` `flip3-+_binary64_1575` `pow-prod-up_binary64_1499` `flip-+_binary64_1602` `sqrt-div_binary64_1557`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `*-commutative_binary64_1645` `prod-exp_binary64_1524` `sum-log_binary64_1487` `rem-sqrt-square_binary64_1565` `pow-plus_binary64_1514` `cbrt-unprod_binary64_1546` `pow2_binary64_1510` `+-commutative_binary64_1644`

Counts

4 → 77

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
7.0ms	(+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (+.f64 x y) (cbrt.f64 z))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (+.f64 x y) (cbrt.f64 z)))))
1.0ms	(cbrt.f64 z)

series648.0ms (14.5%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt.f64 (+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (+.f64 x y) (cbrt.f64 z)))))
186.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
154.0ms	(cbrt.f64 z)
59.0ms	(+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (+.f64 x y) (cbrt.f64 z))))

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5036	1117

prune80.0ms (1.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	88	9	97

Merged error: 19.0b

Counts

97 → 9

Compiler

Compiled 1931 to 608 computations (68.5% saved)

regimes68.0ms (1.5%)

Compiler: Compiled 684 to 390 computations (43% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms (0%)

sample931.0ms (20.8%)

Algorithm

1×

intervals

Results

362.0ms	8000×	body	80	valid
104.0ms	2320×	body	80	nan

Compiler

Compiled 318 to 196 computations (38.4% saved)

Details

analyze433.0ms (9.7%)

sample23.0ms (0.5%)

simplify21.0ms (0.5%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite26.0ms (0.6%)

series321.0ms (7.2%)

simplify115.0ms (2.6%)

prune55.0ms (1.2%)

localize8.0ms (0.2%)

rewrite20.0ms (0.4%)

series319.0ms (7.1%)

simplify119.0ms (2.7%)

prune58.0ms (1.3%)

localize12.0ms (0.3%)

rewrite38.0ms (0.9%)

series861.0ms (19.3%)

simplify105.0ms (2.4%)

prune67.0ms (1.5%)

localize15.0ms (0.3%)

rewrite24.0ms (0.5%)

series648.0ms (14.5%)

simplify83.0ms (1.9%)

prune80.0ms (1.8%)

regimes68.0ms (1.5%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample931.0ms (20.8%)

Profiling