Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

268×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	8
1	35	8
2	60	8
3	103	8
4	183	8
5	416	8
6	1194	8
7	5001	8

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: 7.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
10.5b	(/ (- (* y z) x) (- (* t z) x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r` `associate-/l`
4×	`pow1` `div-sub` `associate-/r/` `associate-/l/`
3×	`flip3--` `flip3-+` `flip--` `flip-+`
2×	`cbrt-undiv` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 98

Calls

4 calls:

3.0ms	(- (* t z) x)
14.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
10.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
11.0ms	(/ (- (* y z) x) (- (* t z) x))

series270.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (* t z) x)
116.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
75.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
56.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify45.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	397	1011
1	1388	948
2	5001	947

prune243.0ms

Filtered

110 candidates to 80 candidates (72.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Merged error: 0.3b

Counts

111 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
0.0b	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
0.3b	(/ 1 (- (* t z) x))
10.3b	(* (- (* y z) x) (/ 1 (- (* t z) x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
29×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`flip3--` `prod-exp` `flip--` `distribute-lft-out`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 121

Calls

4 calls:

7.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
3.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
6.0ms	(/ 1 (- (* t z) x))
16.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
82.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
28.0ms	(/ 1 (- (* t z) x))
54.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	469	1203
1	2114	1077
2	5003	1046

prune251.0ms

Filtered

133 candidates to 90 candidates (67.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	133	7	140

Merged error: 0.3b

Counts

140 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
0.0b	(+ x (/ 1 (/ (- (* t z) x) (- (* y z) x))))
0.2b	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
10.4b	(/ (- (* t z) x) (- (* y z) x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

110×	`times-frac`
97×	`*-un-lft-identity`
67×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
19×	`add-exp-log`
18×	`distribute-lft-out`
13×	`associate-/r/` `add-cbrt-cube` `div-inv`
11×	`associate-/l*`
9×	`div-exp`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`associate-/l/`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`rec-exp` `1-exp`
1×	`+-commutative` `pow-flip` `div-sub` `sum-log` `inv-pow`

Counts

4 → 174

Calls

4 calls:

22.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
21.0ms	(+ x (/ 1 (/ (- (* t z) x) (- (* y z) x))))
10.0ms	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
10.0ms	(/ (- (* t z) x) (- (* y z) x))

series388.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
99.0ms	(+ x (/ 1 (/ (- (* t z) x) (- (* y z) x))))
83.0ms	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
61.0ms	(/ (- (* t z) x) (- (* y z) x))

simplify87.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	633	2103
1	2900	1864
2	5001	1852

prune318.0ms

Filtered

186 candidates to 108 candidates (58.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	186	7	193

Merged error: 0.3b

Counts

193 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

2.9b	(cbrt (/ (- (* y z) x) (- (* t z) x)))
10.5b	(/ (- (* y z) x) (- (* t z) x))
10.5b	(/ (- (* y z) x) (- (* t z) x))
10.5b	(/ (- (* y z) x) (- (* t z) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`cbrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
8×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`associate-/l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num`
1×	`cbrt-div` `pow1/3`

Counts

4 → 120

Calls

4 calls:

7.0ms	(cbrt (/ (- (* y z) x) (- (* t z) x)))
9.0ms	(/ (- (* y z) x) (- (* t z) x))
10.0ms	(/ (- (* y z) x) (- (* t z) x))
9.0ms	(/ (- (* y z) x) (- (* t z) x))

series343.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (/ (- (* y z) x) (- (* t z) x)))
58.0ms	(/ (- (* y z) x) (- (* t z) x))
54.0ms	(/ (- (* y z) x) (- (* t z) x))
59.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify89.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	273	1193
1	811	1114
2	2922	1112
3	5001	1107

prune426.0ms

Filtered

132 candidates to 111 candidates (84.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	132	7	139

Merged error: 0.3b

Counts

139 → 7

regimes194.0ms

Accuracy

63.8% (2.3b remaining)

Error of 3.1b against oracle of 0.8b and baseline of 7.1b

bsearch81.0ms

Steps

Iters	Range		Point
8	2.921594920859903e+75	1.0050562596883415e+79	4.470179030476853e+77
7	-6.26121931620902e+157	-1.588426443043857e+156	-2.580925602273766e+157

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	13
1	34	13

end0.0ms

sample553.0ms

Algorithm

intervals

Results

333.0ms

8312×

body

valid