Details

analyze2.4s (29.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.2%	98.5%	0.3%	13
1.8%	97.9%	0.3%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample76.0ms (0.9%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
7.0ms	138×	body	128	invalid

Compiler

Compiled 56 to 42 computations (25% saved)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

258×	`cancel-sign-sub-inv_binary64`
149×	`sub-neg_binary64`
148×	`distribute-rgt-in_binary64`
133×	`unsub-neg_binary64`
120×	`associate--r+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	33	25
2	73	25
3	138	25
4	266	25
5	499	25
6	678	25
7	867	25
8	1013	25
9	1033	25
10	1043	25
11	1044	25
12	1044	25
13	1044	25
14	937	25

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
0.0b	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
0.0b	(/.f64 (*.f64 a b) 4)
0.0b	(+.f64 (.f64 x y) (/.f64 (.f64 z t) 16))

rewrite136.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-log-exp_binary64`
17×	`*-un-lft-identity_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 81

Calls

4 calls:

13.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
10.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
5.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 z t) 16))
4.0ms	(/.f64 (*.f64 a b) 4)

Compiler

Compiled 2172 to 1040 computations (52.1% saved)

series319.0ms (3.9%)

Error

0.0b

Counts

4 → 108

Calls

4 calls:

126.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
99.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
51.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 z t) 16))
15.0ms	(/.f64 (*.f64 a b) 4)

Compiler

Compiled 3739 to 2629 computations (29.7% saved)

simplify134.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

440×	`distribute-rgt-in_binary64`
413×	`distribute-lft-in_binary64`
378×	`associate-*l/_binary64`
370×	`associate-/l*_binary64`
130×	`cancel-sign-sub-inv_binary64`

Counts

189 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	3409
1	472	3342
2	1428	3291
3	4811	3291
4	5012	3291

prune67.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
▶	28.0b	(+.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))) (/.f64 (.f64 a b) 4)) c)
	29.9b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)) (/.f64 (*.f64 a b) 4)) c)
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
	28.2b	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))

Compiler

Compiled 1643 to 808 computations (50.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))
1.1b	(sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))
1.1b	(sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))

rewrite153.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 100

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))
8.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
5.0ms	(sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))

Compiler

Compiled 3610 to 1708 computations (52.7% saved)

series229.0ms (2.8%)

Error

Counts

4 → 80

Calls

4 calls:

58.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
54.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))
52.0ms	(sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))
51.0ms	(sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))

Compiler

Compiled 4738 to 3158 computations (33.3% saved)

simplify122.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

612×	`distribute-rgt-in_binary64`
584×	`distribute-lft-in_binary64`
481×	`associate-l_binary64`
372×	`associate-r_binary64`
175×	`distribute-rgt-out_binary64`

Counts

180 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	3360
1	224	3107
2	654	3011
3	2132	2928
4	4997	2928

prune64.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Error

Counts

121 → 4

Alt Table

Status	Error	Program
✓	28.0b	(+.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))) (/.f64 (.f64 a b) 4)) c)
	29.9b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)) (/.f64 (*.f64 a b) 4)) c)
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
▶	28.2b	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))

Compiler

Compiled 1882 to 917 computations (51.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
0.1b	(sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))))
0.1b	(sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))))
0.3b	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))

rewrite177.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`sqrt-prod_binary64`
32×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

28.0ms	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))
10.0ms	(sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))))
9.0ms	(sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))))
5.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))

Compiler

Compiled 4914 to 2361 computations (52% saved)

series502.0ms (6.1%)

Error

Counts

4 → 128

Calls

4 calls:

139.0ms	(sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))))
136.0ms	(sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))))
128.0ms	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))
62.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))

Compiler

Compiled 9939 to 6260 computations (37% saved)

simplify217.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

684×	`distribute-rgt-in_binary64`
648×	`distribute-lft-in_binary64`
212×	`cancel-sign-sub-inv_binary64`
129×	`distribute-rgt-neg-in_binary64`
123×	`associate-r_binary64`

Counts

235 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	7052
1	429	6641
2	1373	6488
3	4825	6457
4	4966	6457

prune72.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	116	4	120

Error

Counts

120 → 4

Alt Table

Status	Error	Program
✓	28.0b	(+.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))) (/.f64 (.f64 a b) 4)) c)
▶	29.9b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)) (/.f64 (*.f64 a b) 4)) c)
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
✓	28.2b	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))

Compiler

Compiled 2777 to 1367 computations (50.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 a b) 4)
0.0b	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
0.3b	(pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)
35.3b	(cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3))

rewrite109.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`add-cube-cbrt_binary64` `cbrt-prod_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow1_binary64`
4×	`cube-div_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)
6.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3))
5.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
4.0ms	(/.f64 (*.f64 a b) 4)

Compiler

Compiled 2136 to 1133 computations (47% saved)

series268.0ms (3.2%)

Error

Counts

4 → 102

Calls

4 calls:

120.0ms	(pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)
57.0ms	(+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))
52.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3))
17.0ms	(/.f64 (*.f64 a b) 4)

Compiler

Compiled 4552 to 3361 computations (26.2% saved)

simplify171.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

433×	`*-commutative_binary64`
305×	`unswap-sqr_binary64`
252×	`associate-/l*_binary64`
242×	`distribute-rgt-in_binary64`
238×	`associate-*l/_binary64`

Counts

182 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	4058
1	405	3764
2	1336	3739
3	3899	3739
4	4939	3739
5	4981	3739

prune51.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
	28.0b	(+.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))) (sqrt.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)))) (/.f64 (.f64 a b) 4)) c)
	29.9b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16)) 3)) (/.f64 (*.f64 a b) 4)) c)
	0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
	28.2b	(.f64 (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (.f64 t z) 16))))) (sqrt.f64 (+.f64 c (+.f64 (.f64 (.f64 a b) -1/4) (+.f64 (.f64 x y) (/.f64 (*.f64 t z) 16))))))

Compiler

Compiled 1324 to 668 computations (49.5% saved)

regimes1.3s (16.1%)

Accuracy

Total 0.0b remaining (2.9%)

Threshold costs 0.0b (2.9%)

Compiler

Compiled 23549 to 16581 computations (29.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64` `+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
1×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	25	25
2	32	25
3	42	25
4	49	25
5	54	25
6	56	25
7	56	25

end49.0ms (0.6%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 168 to 119 computations (29.2% saved)

sample1.5s (17.6%)

Algorithm

1×

intervals

Results

463.0ms	8000×	body	128	valid
212.0ms	3996×	body	128	invalid

Compiler

Compiled 187 to 129 computations (31% saved)

Details

analyze2.4s (29.2%)

sample76.0ms (0.9%)

simplify74.0ms (0.9%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite136.0ms (1.6%)

series319.0ms (3.9%)

simplify134.0ms (1.6%)

prune67.0ms (0.8%)

localize16.0ms (0.2%)

rewrite153.0ms (1.9%)

series229.0ms (2.8%)

simplify122.0ms (1.5%)

prune64.0ms (0.8%)

localize17.0ms (0.2%)

rewrite177.0ms (2.2%)

series502.0ms (6.1%)

simplify217.0ms (2.6%)

prune72.0ms (0.9%)

localize16.0ms (0.2%)

rewrite109.0ms (1.3%)

series268.0ms (3.2%)

simplify171.0ms (2.1%)

prune51.0ms (0.6%)

regimes1.3s (16.1%)

simplify4.0ms (0%)

end49.0ms (0.6%)

sample1.5s (17.6%)

Profiling