Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	238×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	8×	body	160	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune2.0ms

Filtered

1 candidates to 0 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: 24.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.4b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.5b	(/ (* (- y z) (- t x)) (- a z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series313.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y z) (- t x))
150.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
129.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune214.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 4.6b

Counts

91 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
36.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series802.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
307.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune385.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	143	14	157

Merged error: 4.5b

Counts

157 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
1.6b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
9.6b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-div`
40×	`add-exp-log`
23×	`add-sqr-sqrt`
22×	`add-cbrt-cube`
19×	`flip3--` `flip--`
17×	`associate-l`
16×	`times-frac` `associate-r` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
13×	`frac-times` `*-un-lft-identity`
12×	`cbrt-undiv` `div-exp`
9×	`cbrt-prod` `add-cube-cbrt`
7×	`associate-r/` `associate-l/`
6×	`pow1` `add-log-exp` `unswap-sqr`
2×	`pow1/3` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 112

Calls

4 calls:

3.0ms	(cbrt (- a z))
11.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
31.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- a z))
124.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
303.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
154.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	871	2589
1	3428	2241
2	5001	2201

prune465.0ms

Filtered

124 candidates to 90 candidates (72.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	123	15	138

Merged error: 4.5b

Counts

138 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
2.5b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
2.5b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
11.1b	(+ x (* (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
16×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`frac-times`
10×	`add-cube-cbrt`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 89

Calls

4 calls:

12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
13.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
13.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

368.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
356.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
354.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
155.0ms	(+ x (* (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	389	2078
1	1090	1899
2	5001	1887

prune556.0ms

Filtered

101 candidates to 83 candidates (82.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	101	15	116

Merged error: 4.5b

Counts

116 → 15

regimes498.0ms

Accuracy

43.3% (4.6b remaining)

Error of 8.8b against oracle of 4.2b and baseline of 12.3b

bsearch5.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	46
1	46	46

end0.0ms

sample719.0ms

Algorithm

intervals

Results

269.0ms	7788×	body	80	valid
60.0ms	483×	body	640	valid
43.0ms	423×	body	320	valid
42.0ms	258×	body	1280	valid
18.0ms	277×	body	160	valid
3.0ms	18×	body	2560	valid