Details

analyze242.0ms (5.3%)

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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	80	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify163.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	1364	18
1	1364	18

prune2.0ms (0.1%)

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 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))

rewrite33.0ms (0.7%)

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` `insert-posit16` `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 → 82

Calls

4 calls:

10.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
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)))

series393.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
93.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
72.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
67.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify203.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	4877	1675
1	4877	1675

prune109.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	7	95

Merged error: 0b

Counts

95 → 7

Compiler

Compiled 1854 to 1056 computations (43% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
20×	`add-log-exp_binary64`
18×	`log-prod_binary64` `add-sqr-sqrt_binary64`
14×	`associate--l+_binary64`
12×	`add-cube-cbrt_binary64`
10×	`diff-log_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`pow1_binary64` `associate--r+_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64`
4×	`associate-r_binary64` `associate-l_binary64` `distribute-lft-out--_binary64` `insert-posit16`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate--r-_binary64` `difference-of-squares_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

14.0ms	(-.f64 (-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)) z)
11.0ms	(-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y))
9.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)
9.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

series636.0ms (13.9%)

Counts

4 → 12

Calls

4 calls:

286.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)
171.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
98.0ms	(-.f64 (-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)) z)
81.0ms	(-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y))

simplify131.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5367	1804

prune106.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Merged error: 0b

Counts

109 → 7

Compiler

Compiled 1975 to 1109 computations (43.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64`
24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `associate--l+_binary64`
20×	`add-cube-cbrt_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
18×	`sqrt-prod_binary64`
13×	`associate-+r+_binary64`
12×	`pow1_binary64`
11×	`add-log-exp_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-*r/_binary64` `log-pow_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `insert-posit16`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`
1×	`associate-+r-_binary64` `+-commutative_binary64`

Counts

4 → 121

Calls

4 calls:

19.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2)) (-.f64 (.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y))
10.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y)
10.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y)))
9.0ms	(*.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2))

series274.0ms (6%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2)) (-.f64 (.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y))
77.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y)
56.0ms	(*.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2))
51.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y)))

simplify191.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4908	2914
1	4908	2914

prune177.0ms (3.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	133	7	140

Merged error: 0b

Counts

140 → 7

Compiler

Compiled 3945 to 2065 computations (47.7% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `insert-posit16`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series644.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
159.0ms	(cbrt.f64 y)
155.0ms	(cbrt.f64 y)
153.0ms	(cbrt.f64 y)

simplify160.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4961	584
1	4961	584

prune109.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	90	6	96

Merged error: 0b

Counts

96 → 6

Compiler

Compiled 2366 to 1207 computations (49% saved)

regimes47.0ms (1%)

Compiler: Compiled 363 to 294 computations (19% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	80	18
1	80	18

end0.0ms (0%)

sample758.0ms (16.6%)

Algorithm

1×

intervals

Results

386.0ms	7999×	body	80	valid
2.0ms	36×	body	80	invalid
0.0ms	1×	body	1280	valid

Compiler

Compiled 156 to 126 computations (19.2% saved)

Details

analyze242.0ms (5.3%)

sample24.0ms (0.5%)

simplify163.0ms (3.6%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite33.0ms (0.7%)

series393.0ms (8.6%)

simplify203.0ms (4.4%)

prune109.0ms (2.4%)

localize9.0ms (0.2%)

rewrite46.0ms (1%)

series636.0ms (13.9%)

simplify131.0ms (2.9%)

prune106.0ms (2.3%)

localize15.0ms (0.3%)

rewrite54.0ms (1.2%)

series274.0ms (6%)

simplify191.0ms (4.2%)

prune177.0ms (3.9%)

localize17.0ms (0.4%)

rewrite14.0ms (0.3%)

series644.0ms (14.1%)

simplify160.0ms (3.5%)

prune109.0ms (2.4%)

regimes47.0ms (1%)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample758.0ms (16.6%)

Profiling