Details

analyze247.0ms (4%)

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)

sample21.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify261.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	1363	18
1	1363	18

prune2.0ms (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)

localize9.0ms (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)
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_11198`
12×	`log-prod_binary64_11281`
11×	`add-sqr-sqrt_binary64_11219`
10×	`add-log-exp_binary64_11234`
9×	`add-cube-cbrt_binary64_11230`
6×	`distribute-rgt-in_binary64_11150` `associate--r+_binary64_11136` `pow1_binary64_11256` `distribute-lft-in_binary64_11149`
5×	`add-exp-log_binary64_11233` `add-cbrt-cube_binary64_11231`
4×	`associate-r_binary64_11140` `associate-l_binary64_11141`
2×	`sum-log_binary64_11286` `associate-*l/_binary64_11143` `distribute-lft-out_binary64_11151` `sub-neg_binary64_11191` `flip3-+_binary64_11201` `diff-log_binary64_11287` `flip-+_binary64_11172`
1×	`+-commutative_binary64_11130` `prod-exp_binary64_11244` `flip--_binary64_11173` `associate-+l-_binary64_11135` `pow-prod-down_binary64_11266` `flip3--_binary64_11202` `unswap-sqr_binary64_11166` `associate-+l+_binary64_11133` `cbrt-unprod_binary64_11228` `log-pow_binary64_11284` `*-commutative_binary64_11131`

Counts

3 → 60

Calls

3 calls:

8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
6.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
5.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series319.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

178.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
75.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
66.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4953	1122
1	4953	1122

prune79.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	8	70

Merged error: 0.0b

Counts

70 → 8

Compiler

Compiled 1418 to 823 computations (42% saved)

localize18.0ms (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 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`log-prod_binary64_11281`
36×	`distribute-rgt-in_binary64_11150` `distribute-lft-in_binary64_11149`
30×	`cbrt-prod_binary64_11226`
26×	`add-sqr-sqrt_binary64_11219` `*-un-lft-identity_binary64_11198`
24×	`add-cube-cbrt_binary64_11230` `associate-+l+_binary64_11133`
12×	`associate-+r+_binary64_11132`
10×	`associate-*l/_binary64_11143`
7×	`pow1_binary64_11256`
6×	`add-exp-log_binary64_11233` `add-log-exp_binary64_11234` `add-cbrt-cube_binary64_11231` `flip3-+_binary64_11201` `flip-+_binary64_11172`
5×	`associate-r_binary64_11140`
4×	`frac-add_binary64_11206` `associate-l_binary64_11141`
3×	`pow1/3_binary64_11277`
2×	`distribute-lft-out_binary64_11151` `log-pow_binary64_11284`
1×	`+-commutative_binary64_11130` `prod-exp_binary64_11244` `sum-log_binary64_11286` `pow-prod-down_binary64_11266` `unswap-sqr_binary64_11166` `cbrt-unprod_binary64_11228` `*-commutative_binary64_11131`

Counts

4 → 109

Calls

4 calls:

16.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series1.4s (23%)

Counts

4 → 12

Calls

4 calls:

728.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
404.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
154.0ms	(cbrt.f64 y)
147.0ms	(cbrt.f64 y)

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4933	1851
1	4933	1851

prune174.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	121	8	129

Merged error: 0b

Counts

129 → 8

Compiler

Compiled 3496 to 1995 computations (42.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (+.f64 y 1/2) 1/3)
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 (.f64 (+.f64 y 1/2) 1/3) (log.f64 y)))
0.4b	(.f64 (.f64 (+.f64 y 1/2) 1/3) (log.f64 y))
0.6b	(cbrt.f64 y)

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64_11281`
30×	`distribute-rgt-in_binary64_11150` `distribute-lft-in_binary64_11149`
24×	`associate-+l+_binary64_11133`
22×	`add-sqr-sqrt_binary64_11219` `*-un-lft-identity_binary64_11198`
20×	`add-cube-cbrt_binary64_11230`
18×	`associate-*l/_binary64_11143`
15×	`cbrt-prod_binary64_11226`
12×	`pow1_binary64_11256`
11×	`add-exp-log_binary64_11233` `add-cbrt-cube_binary64_11231`
7×	`associate-r_binary64_11140` `flip3-+_binary64_11201` `flip-+_binary64_11172`
6×	`add-log-exp_binary64_11234` `associate-+r+_binary64_11132`
5×	`associate-l_binary64_11141`
4×	`frac-add_binary64_11206` `prod-exp_binary64_11244` `pow-prod-down_binary64_11266` `cbrt-unprod_binary64_11228`
2×	`*-commutative_binary64_11131`
1×	`+-commutative_binary64_11130` `sum-log_binary64_11286` `pow1/3_binary64_11277` `distribute-lft-out_binary64_11151` `unswap-sqr_binary64_11166` `log-pow_binary64_11284`

Counts

4 → 104

Calls

4 calls:

20.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 (.f64 (+.f64 y 1/2) 1/3) (log.f64 y)))
9.0ms	(.f64 (.f64 (+.f64 y 1/2) 1/3) (log.f64 y))
7.0ms	(*.f64 (+.f64 y 1/2) 1/3)
1.0ms	(cbrt.f64 y)

series1.4s (22.4%)

Counts

4 → 12

Calls

4 calls:

1.0s	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 (.f64 (+.f64 y 1/2) 1/3) (log.f64 y)))
191.0ms	(.f64 (.f64 (+.f64 y 1/2) 1/3) (log.f64 y))
156.0ms	(cbrt.f64 y)
38.0ms	(*.f64 (+.f64 y 1/2) 1/3)

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4915	1731
1	4915	1731

prune153.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	116	8	124

Merged error: 0b

Counts

124 → 8

Compiler

Compiled 3397 to 2033 computations (40.2% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 y))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64_11226`
9×	`add-cube-cbrt_binary64_11230` `add-sqr-sqrt_binary64_11219` `*-un-lft-identity_binary64_11198`
4×	`add-exp-log_binary64_11233` `add-log-exp_binary64_11234` `add-cbrt-cube_binary64_11231` `pow1_binary64_11256` `pow1/3_binary64_11277`

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt.f64 (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series662.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt.f64 (cbrt.f64 y))
165.0ms	(cbrt.f64 y)
154.0ms	(cbrt.f64 y)
150.0ms	(cbrt.f64 y)

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4793	391
1	4793	391

prune96.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	59	8	67

Merged error: 0b

Counts

67 → 8

Compiler

Compiled 2254 to 1266 computations (43.8% saved)

regimes64.0ms (1%)

Compiler: Compiled 597 to 474 computations (20.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	134	37
1	134	37

end0.0ms (0%)

sample857.0ms (13.7%)

Algorithm

1×

intervals

Results

413.0ms	7997×	body	128	valid
2.0ms	38×	body	128	invalid
0.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 246 to 196 computations (20.3% saved)

Details

analyze247.0ms (4%)

sample21.0ms (0.3%)

simplify261.0ms (4.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite23.0ms (0.4%)

series319.0ms (5.1%)

simplify58.0ms (0.9%)

prune79.0ms (1.3%)

localize18.0ms (0.3%)

rewrite41.0ms (0.7%)

series1.4s (23%)

simplify86.0ms (1.4%)

prune174.0ms (2.8%)

localize18.0ms (0.3%)

rewrite50.0ms (0.8%)

series1.4s (22.4%)

simplify72.0ms (1.2%)

prune153.0ms (2.4%)

localize22.0ms (0.4%)

rewrite11.0ms (0.2%)

series662.0ms (10.6%)

simplify68.0ms (1.1%)

prune96.0ms (1.5%)

regimes64.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample857.0ms (13.7%)

Profiling