Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample12.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	224×	body	80	valid
2.0ms	15×	body	1280	valid
1.0ms	11×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify37.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	406	10
1	406	10

prune4.0ms (0.2%)

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: 0.2b

Counts

2 → 2

Compiler

Compiled 23 to 20 computations (13% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 6 (*.f64 x -9))
0.1b	(.f64 x (+.f64 6 (.f64 x -9)))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 33

Calls

2 calls:

6.0ms	(.f64 x (+.f64 6 (.f64 x -9)))
3.0ms	(+.f64 6 (*.f64 x -9))

series10.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(.f64 x (+.f64 6 (.f64 x -9)))
3.0ms	(+.f64 6 (*.f64 x -9))

simplify122.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4887	455
1	4887	455

prune40.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	30	9	39
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	31	10	41

Merged error: 0.0b

Counts

41 → 10

Compiler

Compiled 616 to 476 computations (22.7% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 6 (*.f64 x -9))
0.1b	(.f64 x (/.f64 (-.f64 36 (.f64 x (.f64 x 81))) (-.f64 6 (.f64 x -9))))
0.2b	(/.f64 (-.f64 36 (.f64 x (.f64 x 81))) (-.f64 6 (*.f64 x -9)))
0.2b	(.f64 x (.f64 x 81))

rewrite28.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
16×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 95

Calls

4 calls:

10.0ms	(.f64 x (/.f64 (-.f64 36 (.f64 x (.f64 x 81))) (-.f64 6 (.f64 x -9))))
7.0ms	(/.f64 (-.f64 36 (.f64 x (.f64 x 81))) (-.f64 6 (*.f64 x -9)))
5.0ms	(.f64 x (.f64 x 81))
3.0ms	(-.f64 6 (*.f64 x -9))

series29.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 x (/.f64 (-.f64 36 (.f64 x (.f64 x 81))) (-.f64 6 (.f64 x -9))))
9.0ms	(/.f64 (-.f64 36 (.f64 x (.f64 x 81))) (-.f64 6 (*.f64 x -9)))
3.0ms	(-.f64 6 (*.f64 x -9))
3.0ms	(.f64 x (.f64 x 81))

simplify80.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4886	2102
1	4886	2102

prune102.0ms (5.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	105	12	117

Merged error: 0b

Counts

117 → 12

Compiler

Compiled 2538 to 1949 computations (23.2% saved)

localize10.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 6 (*.f64 x -9))
0.1b	(.f64 x (/.f64 (-.f64 36 (.f64 (.f64 x x) 81)) (-.f64 6 (.f64 x -9))))
0.2b	(/.f64 (-.f64 36 (.f64 (.f64 x x) 81)) (-.f64 6 (*.f64 x -9)))
0.3b	(.f64 (.f64 x x) 81)

rewrite32.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`associate-r_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `flip3--_binary64` `associate-/r/_binary64` `associate-l_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 x (/.f64 (-.f64 36 (.f64 (.f64 x x) 81)) (-.f64 6 (.f64 x -9))))
7.0ms	(/.f64 (-.f64 36 (.f64 (.f64 x x) 81)) (-.f64 6 (*.f64 x -9)))
7.0ms	(.f64 (.f64 x x) 81)
3.0ms	(-.f64 6 (*.f64 x -9))

series31.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 x (/.f64 (-.f64 36 (.f64 (.f64 x x) 81)) (-.f64 6 (.f64 x -9))))
10.0ms	(/.f64 (-.f64 36 (.f64 (.f64 x x) 81)) (-.f64 6 (*.f64 x -9)))
4.0ms	(-.f64 6 (*.f64 x -9))
4.0ms	(.f64 (.f64 x x) 81)

simplify54.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4928	2109
1	4928	2109

prune94.0ms (5.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	108	12	120

Merged error: 0b

Counts

120 → 12

Compiler

Compiled 2536 to 1825 computations (28% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9)))) (cbrt.f64 (.f64 x (+.f64 6 (*.f64 x -9)))))
0.6b	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))
0.6b	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))
0.6b	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))

rewrite22.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9)))) (cbrt.f64 (.f64 x (+.f64 6 (*.f64 x -9)))))
4.0ms	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))
4.0ms	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))
4.0ms	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))

series41.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9)))) (cbrt.f64 (.f64 x (+.f64 6 (*.f64 x -9)))))
10.0ms	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))
10.0ms	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))
9.0ms	(cbrt.f64 (.f64 x (+.f64 6 (.f64 x -9))))

simplify67.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4938	1793
1	4938	1793

prune98.0ms (5.6%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	84	12	96

Merged error: 0b

Counts

96 → 12

Compiler

Compiled 2667 to 2113 computations (20.8% saved)

regimes33.0ms (1.9%)

Compiler: Compiled 214 to 173 computations (19.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	10
1	10	10

end0.0ms (0%)

sample779.0ms (44.1%)

Algorithm

1×

intervals

Results

161.0ms	7225×	body	80	valid
36.0ms	338×	body	1280	valid
25.0ms	236×	body	640	valid
8.0ms	137×	body	320	valid
3.0ms	64×	body	160	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 238 to 194 computations (18.5% saved)

Details

analyze3.0ms (0.2%)

sample12.0ms (0.7%)

simplify37.0ms (2.1%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

rewrite10.0ms (0.5%)

series10.0ms (0.6%)

simplify122.0ms (6.9%)

prune40.0ms (2.3%)

localize9.0ms (0.5%)

rewrite28.0ms (1.6%)

series29.0ms (1.6%)

simplify80.0ms (4.6%)

prune102.0ms (5.8%)

localize10.0ms (0.6%)

rewrite32.0ms (1.8%)

series31.0ms (1.7%)

simplify54.0ms (3.1%)

prune94.0ms (5.3%)

localize11.0ms (0.6%)

rewrite22.0ms (1.2%)

series41.0ms (2.3%)

simplify67.0ms (3.8%)

prune98.0ms (5.6%)

regimes33.0ms (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample779.0ms (44.1%)

Profiling