Details

analyze1.2s (31.6%)

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)

sample36.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.4%)

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

prune5.0ms (0.1%)

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

4.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	4.2b	(/.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))
4.2b	(/.f64 x (-.f64 y (*.f64 z t)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

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:

3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
2.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 631 to 143 computations (77.3% saved)

series61.0ms (1.7%)

Error

4.2b

Counts

2 → 39

Calls

2 calls:

38.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
21.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 971 to 645 computations (33.6% saved)

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

344×	`div-sub_binary64`
314×	`associate-/r/_binary64`
305×	`distribute-rgt-in_binary64`
258×	`cancel-sign-sub-inv_binary64`
257×	`distribute-lft-in_binary64`

Counts

80 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1117
1	220	1060
2	618	1006
3	2095	1006
4	4588	1006
5	5201	1006

prune28.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	6	57

Error

4.1b

Counts

57 → 6

Alt Table

Status	Error	Program
	5.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 t z)) (cbrt.f64 x)))
▶	4.3b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	4.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
✓	4.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))
	5.1b	(.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)))))

Compiler

Compiled 743 to 232 computations (68.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
0.1b	(/.f64 1 (-.f64 y (*.f64 t z)))
4.3b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))

rewrite72.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

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:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
2.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1405 to 540 computations (61.6% saved)

series96.0ms (2.6%)

Error

4.1b

Counts

3 → 61

Calls

3 calls:

36.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
34.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
19.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1823 to 1269 computations (30.4% saved)

simplify112.0ms (3%)

Algorithm

1×	egg-herbie

Rules

421×	`times-frac_binary64`
395×	`cancel-sign-sub-inv_binary64`
314×	`associate-/l*_binary64`
287×	`associate-l_binary64`
285×	`unswap-sqr_binary64`

Counts

144 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2030
1	279	1882
2	877	1804
3	3106	1804
4	4914	1804
5	4948	1804

prune28.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Error

4.1b

Counts

92 → 6

Alt Table

Status	Error	Program
	5.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 1 (cbrt.f64 (-.f64 y (*.f64 t z)))))
	5.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 t z)) (cbrt.f64 x)))
✓	4.3b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
▶	4.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
✓	4.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 790 to 284 computations (64.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
0.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
4.0b	(/.f64 (-.f64 y (*.f64 t z)) x)

rewrite86.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

3 → 118

Calls

3 calls:

5.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
4.0ms	(/.f64 (-.f64 y (*.f64 t z)) x)
2.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 2282 to 715 computations (68.7% saved)

series104.0ms (2.8%)

Error

4.1b

Counts

3 → 60

Calls

3 calls:

40.0ms	(/.f64 (-.f64 y (*.f64 t z)) x)
38.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
20.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1525 to 1037 computations (32% saved)

simplify150.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

467×	`times-frac_binary64`
360×	`associate-l_binary64`
328×	`associate-r_binary64`
315×	`associate-/l*_binary64`
281×	`div-sub_binary64`

Counts

178 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	3020
1	324	2762
2	1044	2683
3	4103	2683
4	4912	2683
5	4971	2683

prune30.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	116	6	122

Error

4.1b

Counts

122 → 6

Alt Table

Status	Error	Program
▶	5.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 1 (cbrt.f64 (-.f64 y (*.f64 t z)))))
	5.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 t z)) (cbrt.f64 x)))
✓	4.3b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
✓	4.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
✓	4.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 949 to 282 computations (70.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
10.5b	(cbrt.f64 (-.f64 y (*.f64 t z)))
10.5b	(cbrt.f64 (-.f64 y (*.f64 t z)))
10.5b	(cbrt.f64 (-.f64 y (*.f64 t z)))

rewrite58.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

18×	`cbrt-div_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`
9×	`flip--_binary64`

Counts

4 → 68

Calls

4 calls:

9.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))

Compiler

Compiled 2337 to 459 computations (80.4% saved)

series312.0ms (8.5%)

Error

4.1b

Counts

4 → 70

Calls

4 calls:

126.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
51.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
48.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
45.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))

Compiler

Compiled 6978 to 4536 computations (35% saved)

simplify176.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

736×	`associate-/l*_binary64`
595×	`associate-/r*_binary64`
176×	`associate-/r/_binary64`
167×	`times-frac_binary64`
148×	`distribute-rgt-neg-in_binary64`

Counts

138 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3423
1	616	3180
2	1768	3062
3	4800	2983
4	4974	2983
5	4999	2983
6	4963	2983

prune50.0ms (1.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	95	6	101

Error

4.1b

Counts

101 → 6

Alt Table

Status	Error	Program
	5.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 1 (cbrt.f64 (-.f64 y (*.f64 t z)))))
	5.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 t z)) (cbrt.f64 x)))
	4.3b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	4.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
	4.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 2207 to 836 computations (62.1% saved)

regimes297.0ms (8.1%)

Accuracy

Total 0.1b remaining (2.1%)

Threshold costs 0.1b (2.1%)

Compiler

Compiled 6345 to 3351 computations (47.2% saved)

simplify4.0ms (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

end7.0ms (0.2%)

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

sample642.0ms (17.5%)

Algorithm

1×

intervals

Results

284.0ms	8000×	body	128	valid
11.0ms	366×	body	128	invalid

Compiler

Compiled 131 to 75 computations (42.7% 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

analyze1.2s (31.6%)

sample36.0ms (1%)

simplify14.0ms (0.4%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

rewrite34.0ms (0.9%)

series61.0ms (1.7%)

simplify82.0ms (2.2%)

prune28.0ms (0.8%)

localize6.0ms (0.2%)

rewrite72.0ms (2%)

series96.0ms (2.6%)

simplify112.0ms (3%)

prune28.0ms (0.8%)

localize6.0ms (0.2%)

rewrite86.0ms (2.3%)

series104.0ms (2.8%)

simplify150.0ms (4.1%)

prune30.0ms (0.8%)

localize11.0ms (0.3%)

rewrite58.0ms (1.6%)

series312.0ms (8.5%)

simplify176.0ms (4.8%)

prune50.0ms (1.4%)

regimes297.0ms (8.1%)

simplify4.0ms (0.1%)

end7.0ms (0.2%)

sample642.0ms (17.5%)

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