Details

analyze693.0ms (36.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
12.5%	85.6%	1.9%	11
19.8%	76.5%	3.7%	12
26.1%	64.4%	9.6%	13
31.7%	54.5%	13.7%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample23.0ms (1.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
2.0ms	73×	body	80	invalid

Compiler

Compiled 19 to 21 computations (-10.5% saved)

simplify140.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	1583	13
1	1583	13

prune10.0ms (0.5%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize12.0ms (0.6%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (-.f64 y z) (-.f64 t x)))
0.0b	(*.f64 (-.f64 y z) (-.f64 t x))

rewrite21.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-+r+_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 45

Calls

2 calls:

15.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (-.f64 t x)))

series27.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(+.f64 x (*.f64 (-.f64 y z) (-.f64 t x)))
10.0ms	(*.f64 (-.f64 y z) (-.f64 t x))

simplify70.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5068	846

prune39.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 875 to 246 computations (71.9% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x))) (+.f64 t x)))
1.9b	(-.f64 (.f64 t t) (.f64 x x))
5.5b	(.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x)))
21.6b	(/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x))) (+.f64 t x))

rewrite42.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
13×	`flip3--_binary64` `flip--_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `frac-times_binary64`
6×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`associate-/r_binary64` `associate-r_binary64` `associate-r/_binary64` `times-frac_binary64` `associate-*l/_binary64`
3×	`sub-neg_binary64` `distribute-lft-out_binary64` `difference-of-squares_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

14.0ms	(/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x))) (+.f64 t x))
11.0ms	(.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x)))
9.0ms	(+.f64 x (/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x))) (+.f64 t x)))
5.0ms	(-.f64 (.f64 t t) (.f64 x x))

series119.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x))) (+.f64 t x))
40.0ms	(+.f64 x (/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x))) (+.f64 t x)))
29.0ms	(.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 x x)))
6.0ms	(-.f64 (.f64 t t) (.f64 x x))

simplify88.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4986	1982
1	4986	1982

prune61.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	100	4	104

Merged error: 0b

Counts

104 → 4

Compiler

Compiled 2301 to 631 computations (72.6% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 1 (-.f64 t x))))
0.0b	(/.f64 1 (-.f64 t x))
0.3b	(/.f64 (-.f64 y z) (/.f64 1 (-.f64 t x)))

rewrite62.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
179×	`*-un-lft-identity_binary64`
177×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`
44×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
26×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
15×	`associate-/r/_binary64`
10×	`add-cbrt-cube_binary64`
8×	`flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 205

Calls

3 calls:

31.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 1 (-.f64 t x))))
13.0ms	(/.f64 (-.f64 y z) (/.f64 1 (-.f64 t x)))
6.0ms	(/.f64 1 (-.f64 t x))

series31.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

15.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 1 (-.f64 t x))))
10.0ms	(/.f64 (-.f64 y z) (/.f64 1 (-.f64 t x)))
5.0ms	(/.f64 1 (-.f64 t x))

simplify106.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5222	4597

prune103.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	214	4	218

Merged error: 0b

Counts

218 → 4

Compiler

Compiled 4088 to 1193 computations (70.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 y z))
0.0b	(+.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z)))))
0.1b	(*.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z)))
0.1b	(.f64 (sqrt.f64 (-.f64 y z)) (.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z))))

rewrite42.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-div_binary64`
34×	`flip3--_binary64` `flip--_binary64`
32×	`frac-times_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`associate-*r/_binary64` `sqrt-prod_binary64`
13×	`associate-l_binary64`
12×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `associate-*l/_binary64`
9×	`associate-r_binary64`
6×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 111

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (-.f64 y z)) (.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z))))
11.0ms	(*.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z)))
6.0ms	(sqrt.f64 (-.f64 y z))
4.0ms	(+.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z)))))

series55.0ms (3%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z)))
16.0ms	(+.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z)))))
11.0ms	(sqrt.f64 (-.f64 y z))
10.0ms	(.f64 (sqrt.f64 (-.f64 y z)) (.f64 (-.f64 t x) (sqrt.f64 (-.f64 y z))))

simplify103.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4964	2651
1	4964	2651

Details

analyze693.0ms (36.9%)

sample23.0ms (1.2%)

simplify140.0ms (7.4%)

prune10.0ms (0.5%)

localize12.0ms (0.6%)

rewrite21.0ms (1.1%)

series27.0ms (1.4%)

simplify70.0ms (3.7%)

prune39.0ms (2.1%)

localize11.0ms (0.6%)

rewrite42.0ms (2.2%)

series119.0ms (6.3%)

simplify88.0ms (4.7%)

prune61.0ms (3.3%)

localize8.0ms (0.4%)

rewrite62.0ms (3.3%)

series31.0ms (1.6%)

simplify106.0ms (5.6%)

prune103.0ms (5.5%)

localize8.0ms (0.4%)

rewrite42.0ms (2.2%)

series55.0ms (3%)

simplify103.0ms (5.5%)

prune5.0ms (0.3%)

Profiling