Details

analyze238.0ms (4.1%)

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
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify238.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	1363	18
1	1363	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.2b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_12807`
12×	`log-prod_binary64_12893`
11×	`add-sqr-sqrt_binary64_12829`
10×	`add-log-exp_binary64_12846`
9×	`add-cube-cbrt_binary64_12842`
6×	`pow1_binary64_12868` `distribute-rgt-in_binary64_12757` `distribute-lft-in_binary64_12756` `associate--r+_binary64_12743`
5×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
4×	`associate-l_binary64_12748` `associate-r_binary64_12747`
2×	`flip3-+_binary64_12810` `associate-*l/_binary64_12750` `associate-+l+_binary64_12740` `diff-log_binary64_12899` `sum-log_binary64_12898` `flip-+_binary64_12781` `distribute-lft-out_binary64_12758` `cancel-sign-sub-inv_binary64_12773` `sub-neg_binary64_12800`
1×	`pow-prod-down_binary64_12878` `associate-+l-_binary64_12742` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `*-commutative_binary64_12738` `flip--_binary64_12782` `flip3--_binary64_12811` `log-pow_binary64_12896` `+-commutative_binary64_12737` `unswap-sqr_binary64_12775`

Counts

3 → 62

Calls

3 calls:

8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
7.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
5.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series312.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

170.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
74.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
68.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5136	1135

prune165.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Merged error: 0.0b

Counts

72 → 6

Compiler

Compiled 2841 to 1929 computations (32.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`log-prod_binary64_12893`
18×	`*-un-lft-identity_binary64_12807` `cbrt-prod_binary64_12838` `add-sqr-sqrt_binary64_12829`
16×	`add-cube-cbrt_binary64_12842`
12×	`distribute-rgt-in_binary64_12757` `associate-+r+_binary64_12739` `distribute-lft-in_binary64_12756`
10×	`associate-*l/_binary64_12750`
7×	`pow1_binary64_12868`
6×	`add-cbrt-cube_binary64_12843` `flip3-+_binary64_12810` `add-exp-log_binary64_12845` `flip-+_binary64_12781` `add-log-exp_binary64_12846`
5×	`associate-r_binary64_12747`
4×	`associate-l_binary64_12748` `frac-add_binary64_12815`
3×	`pow1/3_binary64_12889`
2×	`log-pow_binary64_12896` `distribute-lft-out_binary64_12758`
1×	`pow-prod-down_binary64_12878` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `*-commutative_binary64_12738` `sum-log_binary64_12898` `+-commutative_binary64_12737` `unswap-sqr_binary64_12775`

Counts

4 → 85

Calls

4 calls:

13.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
9.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series1.5s (25.1%)

Counts

4 → 12

Calls

4 calls:

745.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
419.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
152.0ms	(cbrt.f64 y)
136.0ms	(cbrt.f64 y)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4899	1460
1	4899	1460

prune174.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	99	4	103

Merged error: 0b

Counts

103 → 4

Compiler

Compiled 3463 to 2120 computations (38.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
0.0b	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
0.1b	(+.f64 (-.f64 x (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) y)
0.3b	(*.f64 y (log.f64 y))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_12807`
20×	`add-log-exp_binary64_12846`
18×	`log-prod_binary64_12893` `add-sqr-sqrt_binary64_12829`
14×	`add-cube-cbrt_binary64_12842`
11×	`associate-+l+_binary64_12740`
9×	`distribute-rgt-in_binary64_12757` `distribute-lft-in_binary64_12756`
8×	`cancel-sign-sub-inv_binary64_12773`
7×	`pow1_binary64_12868`
6×	`add-cbrt-cube_binary64_12843` `associate-+r+_binary64_12739` `add-exp-log_binary64_12845` `sum-log_binary64_12898`
4×	`diff-log_binary64_12899` `associate-r_binary64_12747`
3×	`distribute-rgt-out_binary64_12760` `associate-l_binary64_12748`
2×	`flip3-+_binary64_12810` `distribute-lft-out--_binary64_12759` `flip-+_binary64_12781` `distribute-lft-out_binary64_12758` `sub-neg_binary64_12800` `+-commutative_binary64_12737`
1×	`pow-prod-down_binary64_12878` `associate-+l-_binary64_12742` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `*-commutative_binary64_12738` `flip--_binary64_12782` `flip3--_binary64_12811` `log-pow_binary64_12896` `unswap-sqr_binary64_12775` `associate--r+_binary64_12743` `difference-of-squares_binary64_12776`

Counts

4 → 89

Calls

4 calls:

11.0ms	(+.f64 (-.f64 x (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) y)
7.0ms	(-.f64 x (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
6.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
5.0ms	(*.f64 y (log.f64 y))

series565.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
126.0ms	(*.f64 y (log.f64 y))
75.0ms	(-.f64 x (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
75.0ms	(+.f64 (-.f64 x (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) y)

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4945	1434
1	4945	1434

prune99.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	101	4	105

Merged error: 0b

Counts

105 → 4

Compiler

Compiled 2007 to 1020 computations (49.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3))))
0.1b	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
0.3b	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
0.6b	(cbrt.f64 (neg.f64 y))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_12807` `add-sqr-sqrt_binary64_12829` `add-log-exp_binary64_12846`
10×	`cbrt-prod_binary64_12838`
9×	`pow1_binary64_12868` `add-cube-cbrt_binary64_12842`
6×	`add-cbrt-cube_binary64_12843` `associate-l_binary64_12748` `add-exp-log_binary64_12845`
3×	`pow1/3_binary64_12889` `pow-prod-down_binary64_12878` `distribute-rgt-neg-in_binary64_12765` `distribute-lft-neg-in_binary64_12764` `log-pow_binary64_12896` `associate-r_binary64_12747`
2×	`distribute-rgt-in_binary64_12757` `associate-*r/_binary64_12749` `flip3-+_binary64_12810` `associate-+l+_binary64_12740` `diff-log_binary64_12899` `sum-log_binary64_12898` `flip-+_binary64_12781` `cancel-sign-sub-inv_binary64_12773` `sub-neg_binary64_12800` `distribute-lft-in_binary64_12756` `associate--r+_binary64_12743`
1×	`associate-+l-_binary64_12742` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `*-commutative_binary64_12738` `flip--_binary64_12782` `flip3--_binary64_12811` `distribute-lft-out_binary64_12758` `+-commutative_binary64_12737` `unswap-sqr_binary64_12775` `neg-mul-1_binary64_12803`

Counts

4 → 73

Calls

4 calls:

12.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
7.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
5.0ms	(-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3))))
2.0ms	(cbrt.f64 (neg.f64 y))

series1.2s (19.9%)

Counts

4 → 12

Calls

4 calls:

565.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
224.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
195.0ms	(-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3))))
168.0ms	(cbrt.f64 (neg.f64 y))

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4749	2040
1	4749	2040

prune118.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	85	4	89

Merged error: 0b

Counts

89 → 4

Compiler

Compiled 2276 to 1527 computations (32.9% saved)

regimes39.0ms (0.7%)

Compiler: Compiled 249 to 207 computations (16.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	76	23
1	76	23

end0.0ms (0%)

sample712.0ms (12.3%)

Algorithm

1×

intervals

Results

384.0ms	8000×	body	128	valid
2.0ms	33×	body	128	invalid

Compiler

Compiled 121 to 98 computations (19% saved)

Details

analyze238.0ms (4.1%)

sample20.0ms (0.3%)

simplify238.0ms (4.1%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite25.0ms (0.4%)

series312.0ms (5.4%)

simplify68.0ms (1.2%)

prune165.0ms (2.9%)

localize15.0ms (0.3%)

rewrite35.0ms (0.6%)

series1.5s (25.1%)

simplify85.0ms (1.5%)

prune174.0ms (3%)

localize11.0ms (0.2%)

rewrite39.0ms (0.7%)

series565.0ms (9.8%)

simplify66.0ms (1.1%)

prune99.0ms (1.7%)

localize15.0ms (0.3%)

rewrite32.0ms (0.6%)

series1.2s (19.9%)

simplify94.0ms (1.6%)

prune118.0ms (2%)

regimes39.0ms (0.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample712.0ms (12.3%)

Profiling