Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	232×	body	80	valid
2.0ms	13×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify232.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (230.0ms)

Iter	Nodes	Cost
0	2838	13
1	2838	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: 5.4b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ y (* y (/ (- t z) (- a t)))))
0.0b	(/ (- t z) (- a t))
1.6b	(* y (/ (- t z) (- a t)))
2.2b	(+ y (* y (/ (- t z) (- a t))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`associate-/r` `associate-/l`
4×	`sum-log` `associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `+-commutative` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`associate-+r+` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 127

Calls

4 calls:

5.0ms	(+ x (+ y (* y (/ (- t z) (- a t)))))
8.0ms	(/ (- t z) (- a t))
13.0ms	(* y (/ (- t z) (- a t)))
3.0ms	(+ y (* y (/ (- t z) (- a t))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ x (+ y (* y (/ (- t z) (- a t)))))
9.0ms	(/ (- t z) (- a t))
15.0ms	(* y (/ (- t z) (- a t)))
26.0ms	(+ y (* y (/ (- t z) (- a t))))

simplify46.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5126	1617

prune164.0ms

Filtered

96 candidates to 139 candidates (-44.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	133	8	141

Merged error: 2.2b

Counts

141 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
1.6b	(* y (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))))
14.9b	(+ y (* y (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
23.0ms	(* y (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))))
4.0ms	(+ y (* y (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t))))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- a t))
26.0ms	(cbrt (- a t))
27.0ms	(* y (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t)))))
32.0ms	(+ y (* y (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- t z) (cbrt (- a t))))))

simplify84.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4936	892
1	4936	892

prune103.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	92	8	100

Merged error: 2.2b

Counts

100 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.0b	(+ x (+ y (* (* y (- t z)) (/ 1 (- a t)))))
6.5b	(+ y (* (* y (- t z)) (/ 1 (- a t))))
13.2b	(* (* y (- t z)) (/ 1 (- a t)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
30×	`add-exp-log` `times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-cbrt-cube`
12×	`prod-exp`
11×	`add-log-exp`
10×	`pow1`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`div-exp` `cbrt-unprod`
5×	`associate-r/` `associate-/r`
4×	`flip3--` `sum-log` `associate-/r/` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-/l*`
2×	`+-commutative` `frac-times` `flip3-+` `associate-*l/` `flip-+` `div-inv`
1×	`associate-+r+` `pow-flip` `frac-2neg` `associate-l` `clear-num` `un-div-inv` `*-commutative` `distribute-lft-out` `inv-pow`

Counts

4 → 116

Calls

4 calls:

5.0ms	(/ 1 (- a t))
5.0ms	(+ x (+ y (* (* y (- t z)) (/ 1 (- a t)))))
3.0ms	(+ y (* (* y (- t z)) (/ 1 (- a t))))
13.0ms	(* (* y (- t z)) (/ 1 (- a t)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (- a t))
37.0ms	(+ x (+ y (* (* y (- t z)) (/ 1 (- a t)))))
22.0ms	(+ y (* (* y (- t z)) (/ 1 (- a t))))
16.0ms	(* (* y (- t z)) (/ 1 (- a t)))

simplify40.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5418	1324

prune115.0ms

Filtered

76 candidates to 128 candidates (-68.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	128	8	136

Merged error: 2.2b

Counts

136 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.7b	(- (+ x y) (/ (* (- z t) y) (- a t)))
13.1b	(/ (* (- z t) y) (- a t))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-l` `associate-/r*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
9.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.0ms	(/ (* (- z t) y) (- a t))

series58.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* (- z t) y)
34.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
18.0ms	(/ (* (- z t) y) (- a t))

simplify36.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5418	873

prune67.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	79	8	87

Merged error: 2.2b

Counts

87 → 8

regimes499.0ms

Accuracy

4.2% (3.8b remaining)

Error of 7.3b against oracle of 3.4b and baseline of 7.4b

bsearch46.0ms

Steps

Iters	Range		Point
6	3.6996367263932858e-236	3.1169117684654473e-235	1.0308070344394694e-235
8	-5.037778411777015e-47	-1.7939509273298652e-50	-1.8179064860235673e-50

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	29
1	28	29

end0.0ms

sample931.0ms

Algorithm

intervals

Results

291.0ms	7406×	body	80	valid
67.0ms	450×	body	640	valid
48.0ms	260×	body	1280	valid
42.0ms	368×	body	320	valid
20.0ms	269×	body	160	valid
4.0ms	16×	body	2560	valid

Details

sample38.0ms

simplify232.0ms

prune12.0ms

localize9.0ms

rewrite33.0ms

series84.0ms

simplify46.0ms

prune164.0ms

localize15.0ms

rewrite36.0ms

series114.0ms

simplify84.0ms

prune103.0ms

localize13.0ms

rewrite29.0ms

series80.0ms

simplify40.0ms

prune115.0ms

localize9.0ms

rewrite25.0ms

series58.0ms

simplify36.0ms

prune67.0ms

regimes499.0ms

bsearch46.0ms

simplify1.0ms

end0.0ms

sample931.0ms

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