Details

analyze324.0ms (0.8%)

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%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
21.8%	78%	0.1%	8
33.5%	66.3%	0.1%	9
49.1%	50.7%	0.1%	10
56.2%	43.7%	0.1%	11
64.1%	35.8%	0.1%	12
73%	26.8%	0.1%	13
79.5%	20.3%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample38.0ms (0.1%)

Algorithm

1×

intervals

Results

16.0ms	129×	body	2048	valid
10.0ms	95×	body	1024	valid
2.0ms	26×	body	512	valid
0.0ms	1×	body	4096	valid
0.0ms	3×	body	256	valid
0.0ms	2×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify475.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (378.0ms)

Iter	Nodes	Cost
0	5284	1

prune5.0ms (0%)

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

Error

Counts

2 → 2

Compiler

Compiled 1 to 4 computations (-300% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 y z))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 x (+.f64 y z))
0.0b	(+.f64 (+.f64 x y) z)

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`associate-+l+_binary64` `associate-+r+_binary64`

Counts

2 → 30

Calls

4 calls:

8.0ms	(+.f64 (+.f64 x y) z)
6.0ms	(+.f64 x (+.f64 y z))
0.0ms	(+.f64 (+.f64 x y) z)
0.0ms	(+.f64 x (+.f64 y z))

series130.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

73.0ms	(+.f64 (+.f64 x y) z)
56.0ms	(+.f64 x (+.f64 y z))

Compiler

Compiled 534 to 401 computations (24.9% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4966	494
1	4966	494

prune135.0ms (0.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	50	16	66
Fresh	0	1	1
Picked	0	0	0
Done	0	1	1
Total	50	18	68

Error

Counts

68 → 18

Compiler

Compiled 737 to 249 computations (66.2% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 y z))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 x (+.f64 y z))
0.0b	(+.f64 (+.f64 x y) z)

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`associate-+l+_binary64` `associate-+r+_binary64`

Counts

2 → 30

Calls

4 calls:

6.0ms	(+.f64 (+.f64 x y) z)
6.0ms	(+.f64 x (+.f64 y z))
0.0ms	(+.f64 (+.f64 x y) z)
0.0ms	(+.f64 x (+.f64 y z))

series124.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

64.0ms	(+.f64 (+.f64 x y) z)
60.0ms	(+.f64 x (+.f64 y z))

Compiler

Compiled 642 to 509 computations (20.7% saved)

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4966	494
1	4966	494

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 y (+.f64 x (+.f64 y z)))
0.0b	(+.f64 x (+.f64 y z))
0.0b	(+.f64 x (+.f64 y z))
2.0b	(-.f64 y (+.f64 x (+.f64 y z)))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
16×	`add-log-exp_binary64`
9×	`distribute-lft-out_binary64`
6×	`sum-log_binary64`
5×	`cancel-sign-sub-inv_binary64` `add-sqr-sqrt_binary64`
3×	`diff-log_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

2 → 38

Calls

4 calls:

11.0ms	(-.f64 y (+.f64 x (+.f64 y z)))
6.0ms	(+.f64 x (+.f64 y z))
0.0ms	(+.f64 x (+.f64 y z))
0.0ms	(-.f64 y (+.f64 x (+.f64 y z)))

series74.0ms (0.2%)

Counts

2 → 23

Calls

2 calls:

45.0ms	(+.f64 x (+.f64 y z))
29.0ms	(-.f64 y (+.f64 x (+.f64 y z)))

Compiler

Compiled 203 to 219 computations (-7.9% saved)

simplify89.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4912	519
1	4912	519

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

3.1b	(-.f64 (+.f64 (+.f64 x y) z) (+.f64 x z))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 (+.f64 x y) z)
3.1b	(-.f64 (+.f64 (+.f64 x y) z) (+.f64 x z))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
28×	`add-log-exp_binary64`
13×	`distribute-lft-out_binary64`
12×	`sum-log_binary64`
6×	`diff-log_binary64` `distribute-lft-out--_binary64`
5×	`flip3-+_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64`
4×	`cancel-sign-sub-inv_binary64` `frac-sub_binary64`
3×	`add-cube-cbrt_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `associate-+l+_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 48

Calls

4 calls:

13.0ms	(-.f64 (+.f64 (+.f64 x y) z) (+.f64 x z))
6.0ms	(+.f64 (+.f64 x y) z)
0.0ms	(+.f64 (+.f64 x y) z)
0.0ms	(-.f64 (+.f64 (+.f64 x y) z) (+.f64 x z))

series80.0ms (0.2%)

Counts

2 → 26

Calls

2 calls:

59.0ms	(+.f64 (+.f64 x y) z)
21.0ms	(-.f64 (+.f64 (+.f64 x y) z) (+.f64 x z))

Compiler

Compiled 222 to 220 computations (0.9% saved)

simplify31.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5120	770

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

5.2b	(-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z))
0.2b	(-.f64 (/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z)) (+.f64 x (+.f64 y z)))
0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.0b	(+.f64 x (+.f64 y z))
0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.2b	(-.f64 (/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z)) (+.f64 x (+.f64 y z)))
5.2b	(-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z))
30.3b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z))

rewrite88.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
17×	`distribute-lft-out_binary64`
15×	`add-log-exp_binary64` `difference-of-squares_binary64`
13×	`distribute-lft-out--_binary64`
11×	`pow1_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-/r*_binary64` `swap-sqr_binary64` `cancel-sign-sub-inv_binary64`
4×	`flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip--_binary64` `frac-times_binary64`
3×	`sum-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `frac-sub_binary64` `associate--l+_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate--r+_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 133

Calls

8 calls:

36.0ms	(-.f64 (/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z)) (+.f64 x (+.f64 y z)))
18.0ms	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z))
10.0ms	(-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z))
9.0ms	(*.f64 (+.f64 x y) (+.f64 x y))
0.0ms	(+.f64 x (+.f64 y z))

series5.1s (12.5%)

Counts

4 → 56

Calls

4 calls:

4.6s	(-.f64 (/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z)) (+.f64 x (+.f64 y z)))
326.0ms	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (-.f64 (+.f64 x y) z))
143.0ms	(-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z))
58.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

Compiler

Compiled 2291 to 1560 computations (31.9% saved)

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4880	3494
1	4880	3494

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y))))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 z (+.f64 x y))
0.3b	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y))))
16.1b	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y)))))

rewrite61.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64`
38×	`sqrt-prod_binary64`
36×	`sqrt-div_binary64`
30×	`distribute-lft-out_binary64`
28×	`flip3-+_binary64` `flip-+_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`add-log-exp_binary64`
19×	`pow1_binary64`
16×	`swap-sqr_binary64` `frac-sub_binary64`
12×	`add-cube-cbrt_binary64` `frac-times_binary64`
9×	`sum-log_binary64`
8×	`pow1/2_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64`
6×	`associate-r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l/_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `diff-log_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `sqr-abs_binary64` `flip--_binary64` `pow2_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 132

Calls

8 calls:

18.0ms	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y))))
12.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y)))))
9.0ms	(+.f64 z (+.f64 x y))
6.0ms	(+.f64 z (+.f64 x y))
0.0ms	(+.f64 z (+.f64 x y))

series205.0ms (0.5%)

Counts

4 → 63

Calls

4 calls:

62.0ms	(+.f64 z (+.f64 x y))
62.0ms	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y))))
62.0ms	(+.f64 z (+.f64 x y))
19.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (+.f64 z (+.f64 x y)))))

Compiler

Compiled 1251 to 888 computations (29% saved)

simplify88.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4624	3115
1	4624	3115

prune5.5s (13.5%)

Pruning

177 alts after pruning (174 fresh and 3 done)

	Pruned	Kept	Total
New	415	170	585
Fresh	8	4	12
Picked	0	0	0
Done	3	3	6
Total	426	177	603

Error

Counts

603 → 177

Compiler

Compiled 11209 to 4048 computations (63.9% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 z (+.f64 x y))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

1 → 15

Calls

2 calls:

6.0ms	(+.f64 z (+.f64 x y))
0.0ms	(+.f64 z (+.f64 x y))

series24.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

23.0ms

(+.f64 z (+.f64 x y))

Compiler

Compiled 132 to 147 computations (-11.4% saved)

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5052	184

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

3.0b	(-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (+.f64 y z) 1))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 (+.f64 x y) z)
3.0b	(-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (+.f64 y z) 1))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
16×	`add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`distribute-lft-out_binary64`
6×	`sum-log_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`
3×	`diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`pow1_binary64` `sqr-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `associate-+l+_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate--l+_binary64`

Counts

2 → 43

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (+.f64 y z) 1))
6.0ms	(+.f64 (+.f64 x y) z)
0.0ms	(+.f64 (+.f64 x y) z)
0.0ms	(-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (+.f64 y z) 1))

series80.0ms (0.2%)

Counts

2 → 26

Calls

2 calls:

59.0ms	(+.f64 (+.f64 x y) z)
21.0ms	(-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (+.f64 y z) 1))

Compiler

Compiled 274 to 273 computations (0.4% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4900	562
1	4900	562

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

6.8b	(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3))
1.0b	(+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))
0.0b	(*.f64 (+.f64 x y) (+.f64 y (-.f64 x z)))
0.0b	(pow.f64 (+.f64 x y) 3)
1.0b	(+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))
6.8b	(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3))
7.5b	(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))) (+.f64 x z))
43.7b	(/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z)))))

rewrite106.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`*-un-lft-identity_binary64`
67×	`distribute-lft-out_binary64`
40×	`unpow-prod-down_binary64` `cube-prod_binary64` `times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
13×	`add-log-exp_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `sum-cubes_binary64` `flip-+_binary64`
4×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
3×	`associate-/r*_binary64` `sum-log_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `associate-+r+_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

4 → 128

Calls

8 calls:

39.0ms	(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))) (+.f64 x z))
25.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z)))))
16.0ms	(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3))
5.0ms	(+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))
0.0ms	(pow.f64 (+.f64 x y) 3)

series4.7s (11.7%)

Counts

4 → 68

Calls

4 calls:

3.2s	(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))) (+.f64 x z))
948.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3)) (+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z)))))
388.0ms	(+.f64 (.f64 z z) (.f64 (+.f64 x y) (+.f64 y (-.f64 x z))))
225.0ms	(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 z 3))

Compiler

Compiled 5734 to 4095 computations (28.6% saved)

simplify99.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5097	8159

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (+.f64 z (+.f64 x y)))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 z (+.f64 x y))
0.0b	(exp.f64 (+.f64 z (+.f64 x y)))
0.0b	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (exp.f64 (+.f64 z (+.f64 x y))))))
0.8b	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (exp.f64 (+.f64 z (+.f64 x y)))))))
3.3b	(log.f64 (exp.f64 (+.f64 z (+.f64 x y))))

rewrite55.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`add-log-exp_binary64`
18×	`sqrt-prod_binary64`
15×	`exp-prod_binary64`
12×	`distribute-lft-out_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `log-pow_binary64`
10×	`pow1_binary64`
8×	`associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `associate-*l/_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`log-prod_binary64` `unswap-sqr_binary64` `frac-sub_binary64`
3×	`pow-prod-down_binary64` `diff-log_binary64` `rem-exp-log_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `exp-sum_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `sqrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64` `flip--_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

8 calls:

20.0ms	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (exp.f64 (+.f64 z (+.f64 x y))))))
10.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (exp.f64 (+.f64 z (+.f64 x y)))))))
7.0ms	(log.f64 (exp.f64 (+.f64 z (+.f64 x y))))
7.0ms	(exp.f64 (+.f64 z (+.f64 x y)))
0.0ms	(+.f64 z (+.f64 x y))

series838.0ms (2.1%)

Counts

4 → 46

Calls

4 calls:

294.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (exp.f64 (+.f64 z (+.f64 x y)))))))
276.0ms	(log.f64 (exp.f64 (+.f64 z (+.f64 x y))))
220.0ms	(*.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (exp.f64 (+.f64 z (+.f64 x y))))))
48.0ms	(exp.f64 (+.f64 z (+.f64 x y)))

Compiler

Compiled 2913 to 1679 computations (42.4% saved)

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4833	1853
1	4833	1853

prune8.2s (20.2%)

Pruning

286 alts after pruning (279 fresh and 7 done)

	Pruned	Kept	Total
New	295	133	428
Fresh	23	146	169
Picked	0	0	0
Done	1	7	8
Total	319	286	605

Error

Counts

605 → 286

Compiler

Compiled 16874 to 7380 computations (56.3% saved)

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

39.5b	(cbrt.f64 (pow.f64 (-.f64 (neg.f64 z) x) 3))
0.0b	(pow.f64 (-.f64 (neg.f64 z) x) 3)
0.0b	(pow.f64 (-.f64 (neg.f64 z) x) 3)
39.5b	(cbrt.f64 (pow.f64 (-.f64 (neg.f64 z) x) 3))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
18×	`cbrt-prod_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
4×	`cube-div_binary64` `distribute-rgt-neg-in_binary64` `difference-of-squares_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`cbrt-div_binary64` `add-log-exp_binary64` `flip3--_binary64` `sqr-pow_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

2 → 60

Calls

4 calls:

7.0ms	(cbrt.f64 (pow.f64 (-.f64 (neg.f64 z) x) 3))
7.0ms	(pow.f64 (-.f64 (neg.f64 z) x) 3)
0.0ms	(pow.f64 (-.f64 (neg.f64 z) x) 3)
0.0ms	(cbrt.f64 (pow.f64 (-.f64 (neg.f64 z) x) 3))

series57.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

33.0ms	(pow.f64 (-.f64 (neg.f64 z) x) 3)
25.0ms	(cbrt.f64 (pow.f64 (-.f64 (neg.f64 z) x) 3))

Compiler

Compiled 180 to 210 computations (-16.7% saved)

simplify55.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4908	829
1	4908	829

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

31.5b	(-.f64 (exp.f64 (log.f64 (+.f64 z (+.f64 x y)))) (pow.f64 (+.f64 x (+.f64 y z)) 1))
2.9b	(exp.f64 (log.f64 (+.f64 z (+.f64 x y))))
0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 x (+.f64 y z))
0.0b	(+.f64 z (+.f64 x y))
0.0b	(+.f64 x (+.f64 y z))
2.9b	(exp.f64 (log.f64 (+.f64 z (+.f64 x y))))
31.5b	(-.f64 (exp.f64 (log.f64 (+.f64 z (+.f64 x y)))) (pow.f64 (+.f64 x (+.f64 y z)) 1))

rewrite43.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-log-exp_binary64`
12×	`distribute-lft-out_binary64`
9×	`cancel-sign-sub-inv_binary64`
8×	`log-prod_binary64` `add-cube-cbrt_binary64` `exp-sum_binary64`
7×	`unpow-prod-down_binary64`
6×	`difference-of-squares_binary64` `sum-log_binary64`
5×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `sqr-pow_binary64` `flip-+_binary64`
2×	`exp-diff_binary64` `log-div_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `log-pow_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 76

Calls

8 calls:

19.0ms	(-.f64 (exp.f64 (log.f64 (+.f64 z (+.f64 x y)))) (pow.f64 (+.f64 x (+.f64 y z)) 1))
6.0ms	(exp.f64 (log.f64 (+.f64 z (+.f64 x y))))
6.0ms	(+.f64 z (+.f64 x y))
6.0ms	(+.f64 x (+.f64 y z))
0.0ms	(+.f64 x (+.f64 y z))

series803.0ms (2%)

Counts

4 → 56

Calls

4 calls:

467.0ms	(exp.f64 (log.f64 (+.f64 z (+.f64 x y))))
220.0ms	(-.f64 (exp.f64 (log.f64 (+.f64 z (+.f64 x y)))) (pow.f64 (+.f64 x (+.f64 y z)) 1))
64.0ms	(+.f64 z (+.f64 x y))
51.0ms	(+.f64 x (+.f64 y z))

Compiler

Compiled 1510 to 1217 computations (19.4% saved)

simplify39.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5065	1018

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))))
0.0b	(exp.f64 (+.f64 x y))
0.0b	(+.f64 (+.f64 x y) z)
0.0b	(+.f64 z (+.f64 x y))
0.0b	(.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))))
0.2b	(*.f64 (exp.f64 z) (exp.f64 (+.f64 x y)))
0.8b	(-.f64 (+.f64 (+.f64 x y) z) (.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y)))))))
3.3b	(log.f64 (*.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))

rewrite58.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64` `sqrt-prod_binary64`
14×	`associate-r_binary64`
13×	`add-log-exp_binary64`
12×	`exp-prod_binary64`
11×	`associate-l_binary64`
10×	`add-cube-cbrt_binary64`
8×	`log-pow_binary64` `add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `pow-prod-up_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
5×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`
4×	`frac-sub_binary64`
3×	`diff-log_binary64` `prod-exp_binary64` `sum-log_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `log-prod_binary64` `sqrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `exp-sum_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 92

Calls

8 calls:

20.0ms	(.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))))
10.0ms	(-.f64 (+.f64 (+.f64 x y) z) (.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y)))))))
10.0ms	(*.f64 (exp.f64 z) (exp.f64 (+.f64 x y)))
8.0ms	(log.f64 (*.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))
0.0ms	(+.f64 z (+.f64 x y))

series976.0ms (2.4%)

Counts

4 → 46

Calls

4 calls:

327.0ms	(log.f64 (*.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))
326.0ms	(-.f64 (+.f64 (+.f64 x y) z) (.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y)))))))
237.0ms	(.f64 (sqrt.f64 (+.f64 z (+.f64 x y))) (sqrt.f64 (log.f64 (.f64 (exp.f64 z) (exp.f64 (+.f64 x y))))))
85.0ms	(*.f64 (exp.f64 z) (exp.f64 (+.f64 x y)))

Compiler

Compiled 3055 to 1736 computations (43.2% saved)

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4847	1795
1	4847	1795

prune7.0s (17.1%)

Pruning

342 alts after pruning (330 fresh and 12 done)

	Pruned	Kept	Total
New	276	66	342
Fresh	10	264	274
Picked	0	0	0
Done	0	12	12
Total	286	342	628

Error

Counts

628 → 342

Compiler

Compiled 3415 to 935 computations (72.6% saved)

simplify291.0ms (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4986	22641
1	4986	22641

regimes2.8s (6.8%)

Compiler: Compiled 35466 to 19713 computations (44.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 1 to 4 computations (-300% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	1	1

end0.0ms (0%)

sample1.2s (2.9%)

Algorithm

1×

intervals

Results

501.0ms	4319×	body	2048	valid
261.0ms	2696×	body	1024	valid
54.0ms	757×	body	512	valid
8.0ms	180×	body	256	valid
4.0ms	15×	body	4096	valid
1.0ms	33×	body	128	valid

Compiler

Compiled 11834 to 6585 computations (44.4% saved)

Details

analyze324.0ms (0.8%)

sample38.0ms (0.1%)

simplify475.0ms (1.2%)

prune5.0ms (0%)

localize9.0ms (0%)

rewrite17.0ms (0%)

series130.0ms (0.3%)

simplify61.0ms (0.2%)

prune135.0ms (0.3%)

localize8.0ms (0%)

rewrite14.0ms (0%)

series124.0ms (0.3%)

simplify59.0ms (0.1%)

localize5.0ms (0%)

rewrite19.0ms (0%)

series74.0ms (0.2%)

simplify89.0ms (0.2%)

localize6.0ms (0%)

rewrite24.0ms (0.1%)

series80.0ms (0.2%)

simplify31.0ms (0.1%)

localize13.0ms (0%)

rewrite88.0ms (0.2%)

series5.1s (12.5%)

simplify108.0ms (0.3%)

localize9.0ms (0%)

rewrite61.0ms (0.2%)

series205.0ms (0.5%)

simplify88.0ms (0.2%)

prune5.5s (13.5%)

localize7.0ms (0%)

rewrite7.0ms (0%)

series24.0ms (0.1%)

simplify62.0ms (0.2%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

localize7.0ms (0%)

rewrite24.0ms (0.1%)

series80.0ms (0.2%)

simplify50.0ms (0.1%)

localize16.0ms (0%)

rewrite106.0ms (0.3%)

series4.7s (11.7%)

simplify99.0ms (0.2%)

localize12.0ms (0%)

rewrite55.0ms (0.1%)

series838.0ms (2.1%)

simplify64.0ms (0.2%)

prune8.2s (20.2%)

localize4.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0%)

localize6.0ms (0%)

rewrite18.0ms (0%)

series57.0ms (0.1%)

simplify55.0ms (0.1%)

localize11.0ms (0%)

rewrite43.0ms (0.1%)

series803.0ms (2%)

simplify39.0ms (0.1%)

localize14.0ms (0%)

rewrite58.0ms (0.1%)

series976.0ms (2.4%)

simplify64.0ms (0.2%)

prune7.0s (17.1%)

simplify291.0ms (0.7%)

regimes2.8s (6.8%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (2.9%)

Profiling