Details

analyze244.0ms (15.2%)

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 (1.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify178.0ms (11.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	4927	18
1	4927	18

prune4.0ms (0.3%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize9.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`log-prod_binary64`
10×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate--r+_binary64` `diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
3×	`sub-neg_binary64` `distribute-lft-out_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-+l-_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
6.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
4.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series51.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
14.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
11.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
10.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify96.0ms (6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5015	1613

prune78.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

Compiler

Compiled 1763 to 1002 computations (43.2% saved)

localize16.0ms (1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2))
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))))
0.5b	(cbrt.f64 y)
0.5b	(cbrt.f64 y)

rewrite27.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`log-prod_binary64` `associate-+r+_binary64` `cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`associate-*l/_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `associate-l_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`distribute-lft-out_binary64` `pow1/3_binary64`
1×	`associate-r_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 71

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))))
8.0ms	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2))
2.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series175.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
55.0ms	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2))
15.0ms	(cbrt.f64 y)
15.0ms	(cbrt.f64 y)

simplify77.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4956	1277
1	4956	1277

prune78.0ms (4.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 0b

Counts

90 → 7

Compiler

Compiled 2327 to 1363 computations (41.4% saved)

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (cbrt.f64 y))
0.1b	(+.f64 (-.f64 x (.f64 (log.f64 (cbrt.f64 y)) (+.f64 (.f64 y 3) 3/2))) y)
0.4b	(.f64 (log.f64 (cbrt.f64 y)) (+.f64 (.f64 y 3) 3/2))
0.5b	(cbrt.f64 y)

rewrite20.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
7×	`add-exp-log_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
5×	`associate-l_binary64`
4×	`log-pow_binary64`
3×	`associate-r_binary64` `pow1/3_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-+l-_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

8.0ms	(.f64 (log.f64 (cbrt.f64 y)) (+.f64 (.f64 y 3) 3/2))
6.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (cbrt.f64 y)) (+.f64 (.f64 y 3) 3/2))) y)
2.0ms	(log.f64 (cbrt.f64 y))
2.0ms	(cbrt.f64 y)

series129.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 (log.f64 (cbrt.f64 y)) (+.f64 (.f64 y 3) 3/2))
32.0ms	(log.f64 (cbrt.f64 y))
29.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (cbrt.f64 y)) (+.f64 (.f64 y 3) 3/2))) y)
15.0ms	(cbrt.f64 y)

simplify93.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5009	970

prune62.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	78	7	85

Merged error: 0b

Counts

85 → 7

Compiler

Compiled 1525 to 878 computations (42.4% saved)

localize21.0ms (1.3%)

Local error

Found 4 expressions with local error:

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

rewrite20.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`log-prod_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64` `associate-+r+_binary64`
7×	`pow1_binary64`
6×	`associate-+l+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`add-log-exp_binary64`
4×	`associate-r_binary64`
3×	`associate-l_binary64`
2×	`pow1/3_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

8.0ms	(+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))
5.0ms	(*.f64 2/3 (log.f64 y))
2.0ms	(cbrt.f64 (sqrt.f64 y))
2.0ms	(cbrt.f64 (sqrt.f64 y))

series61.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))
12.0ms	(cbrt.f64 (sqrt.f64 y))
12.0ms	(cbrt.f64 (sqrt.f64 y))
9.0ms	(*.f64 2/3 (log.f64 y))

simplify85.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4872	1160
1	4872	1160

Details

analyze244.0ms (15.2%)

sample20.0ms (1.2%)

simplify178.0ms (11.1%)

prune4.0ms (0.3%)

localize9.0ms (0.6%)

rewrite31.0ms (2%)

series51.0ms (3.2%)

simplify96.0ms (6%)

prune78.0ms (4.9%)

localize16.0ms (1%)

rewrite27.0ms (1.7%)

series175.0ms (10.9%)

simplify77.0ms (4.8%)

prune78.0ms (4.9%)

localize12.0ms (0.7%)

rewrite20.0ms (1.3%)

series129.0ms (8.1%)

simplify93.0ms (5.8%)

prune62.0ms (3.9%)

localize21.0ms (1.3%)

rewrite20.0ms (1.2%)

series61.0ms (3.8%)

simplify85.0ms (5.3%)

prune12.0ms (0.7%)

Profiling