Details

analyze1.3s (29%)

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
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample27.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	13×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`cancel-sign-sub-inv_binary64`
21×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`
13×	`neg-mul-1_binary64`
12×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

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

2.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	2.7b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 y (*.f64 z t))
2.7b	(/.f64 x (-.f64 y (*.f64 z t)))

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
3.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 631 to 143 computations (77.3% saved)

series80.0ms (1.7%)

Error

2.7b

Counts

2 → 39

Calls

2 calls:

51.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
23.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 971 to 645 computations (33.6% saved)

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Rules

320×	`div-sub_binary64`
311×	`associate-/r/_binary64`
308×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
258×	`cancel-sign-sub-inv_binary64`

Counts

80 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1117
1	221	1060
2	619	1018
3	2076	1006
4	4563	1006
5	5125	1006

prune45.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	8	57

Error

2.6b

Counts

57 → 8

Alt Table

Status	Error	Program
	23.2b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	34.7b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	3.5b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 t z))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	3.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.7b	(/.f64 x (-.f64 y (*.f64 z t)))
▶	2.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	34.7b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y (.f64 t z))) (sqrt.f64 (-.f64 y (*.f64 t z)))))
	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 837 to 269 computations (67.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
0.4b	(/.f64 1 (-.f64 y (*.f64 t z)))
2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))

rewrite109.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

26×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 83

Calls

3 calls:

10.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
5.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
3.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1405 to 540 computations (61.6% saved)

series123.0ms (2.7%)

Error

2.6b

Counts

3 → 57

Calls

3 calls:

51.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
36.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
25.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1634 to 1133 computations (30.7% saved)

simplify121.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

582×	`div-sub_binary64`
386×	`cancel-sign-sub-inv_binary64`
301×	`distribute-rgt-neg-in_binary64`
296×	`times-frac_binary64`
286×	`associate-l_binary64`

Counts

140 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1894
1	273	1746
2	794	1704
3	2661	1704
4	4620	1704
5	5612	1704

prune45.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	81	9	90

Error

2.6b

Counts

90 → 9

Alt Table

Status	Error	Program
	23.2b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	34.7b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	3.5b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 t z))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	3.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.7b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 y (.f64 t z))) 3)))
✓	2.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	34.7b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y (.f64 t z))) (sqrt.f64 (-.f64 y (*.f64 t z)))))
▶	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 901 to 332 computations (63.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
10.0b	(cbrt.f64 (-.f64 y (*.f64 t z)))
10.0b	(cbrt.f64 (-.f64 y (*.f64 t z)))
10.0b	(cbrt.f64 (-.f64 y (*.f64 t z)))

rewrite119.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

60×	`cbrt-div_binary64`
30×	`flip--_binary64`
30×	`flip3--_binary64`
28×	`frac-times_binary64`
26×	`associate-/r/_binary64`

Counts

4 → 88

Calls

4 calls:

17.0ms	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
4.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
3.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
3.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))

Compiler

Compiled 3484 to 529 computations (84.8% saved)

series287.0ms (6.3%)

Error

2.6b

Counts

4 → 69

Calls

4 calls:

64.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
60.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
60.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
59.0ms	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 5146 to 3069 computations (40.4% saved)

simplify143.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-l_binary64`
425×	`times-frac_binary64`
390×	`associate-/r*_binary64`
382×	`associate-/l*_binary64`
183×	`distribute-rgt-neg-in_binary64`

Counts

157 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	3539
1	499	3441
2	1408	3380
3	4689	3272
4	5061	3272

prune79.0ms (1.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	118	9	127

Error

2.6b

Counts

127 → 9

Alt Table

Status	Error	Program
	23.2b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	34.7b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	27.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z))))))) (cbrt.f64 (+.f64 y (.f64 t z))))
▶	3.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.7b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 y (.f64 t z))) 3)))
✓	2.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	34.7b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y (.f64 t z))) (sqrt.f64 (-.f64 y (*.f64 t z)))))
✓	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 2520 to 681 computations (73% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.1b	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
2.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))

rewrite140.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
28×	`cbrt-prod_binary64`

Counts

4 → 110

Calls

4 calls:

15.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
5.0ms	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 2549 to 383 computations (85% saved)

series191.0ms (4.2%)

Error

2.6b

Counts

4 → 48

Calls

4 calls:

85.0ms	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
56.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
18.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)

Compiler

Compiled 2172 to 1451 computations (33.2% saved)

simplify123.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

518×	`associate-/r*_binary64`
471×	`*-commutative_binary64`
419×	`associate-/l/_binary64`
314×	`div-sub_binary64`
223×	`associate-l_binary64`

Counts

158 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	2867
1	441	2529
2	1764	2415
3	4249	2401
4	5181	2401

prune56.0ms (1.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	110	9	119

Error

2.6b

Counts

119 → 9

Alt Table

Status	Error	Program
	23.2b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	34.7b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	27.1b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z))))))) (cbrt.f64 (+.f64 y (.f64 t z))))
	3.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	2.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.7b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 y (.f64 t z))) 3)))
	2.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	34.7b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y (.f64 t z))) (sqrt.f64 (-.f64 y (*.f64 t z)))))
	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))) (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 1392 to 390 computations (72% saved)

regimes672.0ms (14.7%)

Accuracy

Total 0.1b remaining (2.3%)

Threshold costs 0.1b (2.3%)

Compiler

Compiled 12015 to 6158 computations (48.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end6.0ms (0.1%)

Remove: (sort z t)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample684.0ms (14.9%)

Algorithm

1×

intervals

Results

231.0ms	8000×	body	128	valid
9.0ms	343×	body	128	invalid

Compiler

Compiled 205 to 111 computations (45.9% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

Details

analyze1.3s (29%)

sample27.0ms (0.6%)

simplify14.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite54.0ms (1.2%)

series80.0ms (1.7%)

simplify93.0ms (2%)

prune45.0ms (1%)

localize7.0ms (0.1%)

rewrite109.0ms (2.4%)

series123.0ms (2.7%)

simplify121.0ms (2.6%)

prune45.0ms (1%)

localize11.0ms (0.2%)

rewrite119.0ms (2.6%)

series287.0ms (6.3%)

simplify143.0ms (3.1%)

prune79.0ms (1.7%)

localize10.0ms (0.2%)

rewrite140.0ms (3.1%)

series191.0ms (4.2%)

simplify123.0ms (2.7%)

prune56.0ms (1.2%)

regimes672.0ms (14.7%)

simplify6.0ms (0.1%)

end6.0ms (0.1%)

sample684.0ms (14.9%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10