Details

analyze2.3s (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample99.0ms (0.3%)

Algorithm

1×

intervals

Results

40.0ms	425×	body	80	nan
25.0ms	256×	body	80	valid
4.0ms	39×	body	80	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify556.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5485	39

prune8.0ms (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

Merged error: 33.7b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.6b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
8.2b	(.f64 (/.f64 l Om) (-.f64 U U))
9.3b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
23.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_1519`
27×	`add-exp-log_binary64_1541` `add-cbrt-cube_binary64_1549`
21×	`add-sqr-sqrt_binary64_1562`
17×	`associate-l_binary64_1637`
16×	`pow-prod-down_binary64_1500` `*-un-lft-identity_binary64_1577`
14×	`add-cube-cbrt_binary64_1548`
13×	`prod-exp_binary64_1524` `associate-*r/_binary64_1638` `cbrt-unprod_binary64_1546`
10×	`times-frac_binary64_1572`
9×	`associate-r_binary64_1636`
6×	`sub-neg_binary64_1581` `distribute-lft-in_binary64_1619` `distribute-rgt-in_binary64_1620`
4×	`sqrt-pow1_binary64_1558` `flip--_binary64_1603` `add-log-exp_binary64_1542` `frac-times_binary64_1569` `flip3--_binary64_1576`
3×	`*-commutative_binary64_1645`
2×	`div-exp_binary64_1526` `flip3-+_binary64_1575` `cbrt-undiv_binary64_1547` `unswap-sqr_binary64_1605` `flip-+_binary64_1602` `sqrt-div_binary64_1557` `associate-*l/_binary64_1639`
1×	`pow1/2_binary64_1509` `distribute-lft-out--_binary64_1622` `sqrt-prod_binary64_1556` `difference-of-squares_binary64_1606` `div-inv_binary64_1578`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
12.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
12.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
9.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series4.9s (17%)

Counts

4 → 12

Calls

4 calls:

3.7s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
787.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
200.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
118.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify128.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5101	2919

prune188.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 26.4b

Counts

123 → 10

Compiler

Compiled 4441 to 1940 computations (56.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

14.0b	(cbrt.f64 (/.f64 l Om))
14.0b	(cbrt.f64 (/.f64 l Om))
14.0b	(cbrt.f64 (/.f64 l Om))
23.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (-.f64 U U) (cbrt.f64 (/.f64 l Om))))))))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_1544`
27×	`times-frac_binary64_1572`
25×	`add-sqr-sqrt_binary64_1562` `add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
14×	`pow1_binary64_1519`
6×	`pow-prod-down_binary64_1500`
4×	`add-exp-log_binary64_1541` `sqrt-pow1_binary64_1558` `add-log-exp_binary64_1542` `add-cbrt-cube_binary64_1549`
3×	`cbrt-div_binary64_1545` `pow1/3_binary64_1511` `div-inv_binary64_1578`
2×	`sqrt-div_binary64_1557` `associate-*r/_binary64_1638`
1×	`pow1/2_binary64_1509` `flip3-+_binary64_1575` `sqrt-prod_binary64_1556` `flip-+_binary64_1602`

Counts

4 → 81

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (-.f64 U U) (cbrt.f64 (/.f64 l Om))))))))))
3.0ms	(cbrt.f64 (/.f64 l Om))
3.0ms	(cbrt.f64 (/.f64 l Om))
3.0ms	(cbrt.f64 (/.f64 l Om))

series4.1s (14.4%)

Counts

4 → 12

Calls

4 calls:

3.8s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (-.f64 U U) (cbrt.f64 (/.f64 l Om))))))))))
103.0ms	(cbrt.f64 (/.f64 l Om))
102.0ms	(cbrt.f64 (/.f64 l Om))
101.0ms	(cbrt.f64 (/.f64 l Om))

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5830	1681

prune143.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 26.4b

Counts

103 → 10

Compiler

Compiled 4278 to 1612 computations (62.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

14.5b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
14.5b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
14.5b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
23.1b	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64_1545`
34×	`pow1_binary64_1519`
32×	`associate-*r/_binary64_1638`
30×	`flip3-+_binary64_1575` `flip-+_binary64_1602`
28×	`frac-times_binary64_1569`
26×	`sqrt-div_binary64_1557`
22×	`pow-prod-down_binary64_1500`
14×	`associate-*l/_binary64_1639`
9×	`cbrt-prod_binary64_1544`
8×	`sqrt-pow1_binary64_1558`
7×	`add-sqr-sqrt_binary64_1562` `add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
4×	`add-exp-log_binary64_1541` `add-log-exp_binary64_1542` `add-cbrt-cube_binary64_1549`
3×	`pow1/3_binary64_1511`
1×	`pow1/2_binary64_1509` `sqrt-prod_binary64_1556`

Counts

4 → 82

Calls

4 calls:

27.0ms	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))))
4.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
4.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
4.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))

series6.2s (21.6%)

Counts

4 → 12

Calls

4 calls:

3.9s	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))))
775.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
764.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
757.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))

simplify176.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4946	8475
1	4946	8475

prune310.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	94	10	104

Merged error: 26.4b

Counts

104 → 10

Compiler

Compiled 9260 to 3573 computations (61.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.6b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
8.2b	(.f64 (/.f64 l Om) (-.f64 U U))
23.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite54.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_1519`
30×	`add-exp-log_binary64_1541` `add-cbrt-cube_binary64_1549`
20×	`add-sqr-sqrt_binary64_1562` `pow-prod-down_binary64_1500`
17×	`associate-l_binary64_1637` `associate-*r/_binary64_1638`
15×	`prod-exp_binary64_1524` `*-un-lft-identity_binary64_1577` `cbrt-unprod_binary64_1546`
13×	`add-cube-cbrt_binary64_1548`
10×	`times-frac_binary64_1572`
9×	`distribute-lft-in_binary64_1619` `distribute-rgt-in_binary64_1620`
7×	`associate-r_binary64_1636`
6×	`sub-neg_binary64_1581`
5×	`sqrt-pow1_binary64_1558`
4×	`flip--_binary64_1603` `add-log-exp_binary64_1542` `frac-times_binary64_1569` `flip3--_binary64_1576`
3×	`*-commutative_binary64_1645`
2×	`div-exp_binary64_1526` `flip3-+_binary64_1575` `cbrt-undiv_binary64_1547` `unswap-sqr_binary64_1605` `flip-+_binary64_1602` `sqrt-div_binary64_1557` `associate-*l/_binary64_1639`
1×	`pow1/2_binary64_1509` `distribute-lft-out--_binary64_1622` `sqrt-prod_binary64_1556` `difference-of-squares_binary64_1606` `div-inv_binary64_1578`

Counts

4 → 113

Calls

4 calls:

15.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
13.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
12.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
9.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series5.0s (17.6%)

Counts

4 → 12

Calls

4 calls:

3.9s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
786.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
190.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
119.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5156	3001

prune153.0ms (0.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	121	14	135

Merged error: 21.8b

Counts

135 → 14

Compiler

Compiled 4105 to 1715 computations (58.2% saved)

regimes306.0ms (1.1%)

Compiler: Compiled 3696 to 2322 computations (37.2% saved)

bsearch62.0ms (0.2%)

Steps

Iters	Range		Point
8	1.0694518543511852e-283	7.413726955250895e-280	1.089601404599227e-283

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	104
1	64	104

end0.0ms (0%)

sample3.4s (12%)

Algorithm

1×

intervals

Results

1.3s	12976×	body	80	nan
774.0ms	8000×	body	80	valid
121.0ms	1181×	body	80	invalid

Compiler

Compiled 711 to 444 computations (37.6% saved)

Details

analyze2.3s (8.2%)

sample99.0ms (0.3%)

simplify556.0ms (2%)

prune8.0ms (0%)

localize17.0ms (0.1%)

rewrite51.0ms (0.2%)

series4.9s (17%)

simplify128.0ms (0.5%)

prune188.0ms (0.7%)

localize22.0ms (0.1%)

rewrite22.0ms (0.1%)

series4.1s (14.4%)

simplify102.0ms (0.4%)

prune143.0ms (0.5%)

localize23.0ms (0.1%)

rewrite47.0ms (0.2%)

series6.2s (21.6%)

simplify176.0ms (0.6%)

prune310.0ms (1.1%)

localize17.0ms (0.1%)

rewrite54.0ms (0.2%)

series5.0s (17.6%)

simplify128.0ms (0.4%)

prune153.0ms (0.5%)

regimes306.0ms (1.1%)

bsearch62.0ms (0.2%)

simplify6.0ms (0%)

end0.0ms (0%)

sample3.4s (12%)

Profiling