Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	239×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	10×	body	1280	valid
1.0ms	7×	body	160	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5503	13

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 12.3b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

3.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
31×	`associate-r`
26×	`times-frac`
14×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 67

Calls

2 calls:

4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
18.0ms	(* (- y z) (/ (- t x) (- a z)))

series101.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
43.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify33.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5049	949

prune134.0ms

Filtered

50 candidates to 73 candidates (-46.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	61	12	73
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	62	13	75

Merged error: 3.8b

Counts

75 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.5b	(* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))))
10.7b	(+ x (* (* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
14×	`add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
10×	`cbrt-prod`
9×	`pow1` `frac-times` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt`
6×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`associate-l` `associate-*l/`
4×	`cbrt-undiv` `cbrt-div` `div-exp`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

4.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
31.0ms	(* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))))
4.0ms	(+ x (* (* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (- t x))
30.0ms	(cbrt (- t x))
136.0ms	(* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))))
62.0ms	(+ x (* (* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5103	1482

prune147.0ms

Filtered

63 candidates to 91 candidates (-44.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	91	13	104

Merged error: 3.8b

Counts

104 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
10.2b	(+ x (* (* (* (- y z) (/ (cbrt (- t x)) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

4.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
4.0ms	(+ x (* (* (* (- y z) (/ (cbrt (- t x)) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (- t x))
32.0ms	(cbrt (- t x))
29.0ms	(cbrt (- t x))
60.0ms	(+ x (* (* (* (- y z) (/ (cbrt (- t x)) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4963	673
1	4963	673

prune125.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	67	14	81

Merged error: 3.1b

Counts

81 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
3.3b	(* (/ (- t x) (- a z)) (cbrt (- y z)))
3.4b	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (- t x) (- a z)) (cbrt (- y z))))
9.2b	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (- t x) (- a z)) (cbrt (- y z)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div`
84×	`frac-times`
58×	`flip3--` `flip--`
52×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
37×	`associate-*r/`
32×	`associate-l`
30×	`add-exp-log` `associate-*l/`
27×	`times-frac`
18×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
9×	`associate-r` `pow-prod-down`
6×	`add-log-exp`
4×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `div-inv`

Counts

4 → 166

Calls

4 calls:

3.0ms	(cbrt (- y z))
22.0ms	(* (/ (- t x) (- a z)) (cbrt (- y z)))
27.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (- t x) (- a z)) (cbrt (- y z))))
4.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (- t x) (- a z)) (cbrt (- y z)))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (- y z))
76.0ms	(* (/ (- t x) (- a z)) (cbrt (- y z)))
44.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (- t x) (- a z)) (cbrt (- y z))))
58.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (- t x) (- a z)) (cbrt (- y z)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5109	3791

prune161.0ms

Filtered

108 candidates to 178 candidates (-64.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	11	11
Picked	0	1	1
Done	1	1	2
Total	178	14	192

Merged error: 3.1b

Counts

192 → 14

regimes616.0ms

Accuracy

30.5% (8.1b remaining)

Error of 11.6b against oracle of 3.5b and baseline of 15.1b

bsearch63.0ms

Steps

Iters	Range		Point
9	9.429701348320305e-163	9.254042445292205e-157	9.140856060673767e-157
8	-3.8588599355435313e-113	-1.1315410796121785e-115	-4.4256913699412465e-114

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	31
1	28	31

end0.0ms

sample1.1s

Algorithm

intervals

Results

327.0ms	7840×	body	80	valid
69.0ms	462×	body	640	valid
55.0ms	293×	body	1280	valid
51.0ms	421×	body	320	valid
20.0ms	256×	body	160	valid
3.0ms	15×	body	2560	valid

Details

sample43.0ms

simplify95.0ms

prune12.0ms

localize9.0ms

rewrite26.0ms

series101.0ms

simplify33.0ms

prune134.0ms

localize17.0ms

rewrite45.0ms

series261.0ms

simplify37.0ms

prune147.0ms

localize15.0ms

rewrite17.0ms

series151.0ms

simplify38.0ms

prune125.0ms

localize13.0ms

rewrite68.0ms

series208.0ms

simplify41.0ms

prune161.0ms

regimes616.0ms

bsearch63.0ms

simplify1.0ms

end0.0ms

sample1.1s

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