Details

sample47.0ms

Algorithm

intervals

Results

23.0ms

343×

body

valid

simplify9.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	8	9
1	14	9
2	28	9
3	51	8
4	89	8
5	149	8
6	198	8
7	222	8
8	252	8
9	305	8
10	433	8
11	549	8
12	617	8
13	663	8
14	792	8
15	930	8
16	1243	8
17	1732	8
18	2338	8
19	2508	8
20	2515	8
done	2515	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) t)
5.5b	(fma (/ (- y x) t) z x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/r*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 50

Calls

2 calls:

25.0ms	(/ (- y x) t)
0.0ms	(fma (/ (- y x) t) z x)

series95.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- y x) t)
55.0ms	(fma (/ (- y x) t) z x)

simplify2.2s

Counts

56 → 56

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	93	570
1	194	548
2	455	512
3	1240	497
4	3730	496
done	5000	496

prune172.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
5.5b	(fma (* (* (cbrt (- y x)) (cbrt (- y x))) (/ (cbrt (- y x)) t)) z x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

11.0ms	(cbrt (- y x))
6.0ms	(cbrt (- y x))
7.0ms	(cbrt (- y x))
1.0ms	(fma (* (* (cbrt (- y x)) (cbrt (- y x))) (/ (cbrt (- y x)) t)) z x)

series602.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (- y x))
168.0ms	(cbrt (- y x))
183.0ms	(cbrt (- y x))
42.0ms	(fma (* (* (cbrt (- y x)) (cbrt (- y x))) (/ (cbrt (- y x)) t)) z x)

simplify2.3s

Counts

73 → 73

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	93	885
1	193	867
2	413	717
3	988	645
4	3012	597
done	5001	585

prune245.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

5.5b	(fma (* (* (cbrt (/ (- y x) t)) (cbrt (/ (- y x) t))) (cbrt (/ (- y x) t))) z x)
8.8b	(cbrt (/ (- y x) t))
8.8b	(cbrt (/ (- y x) t))
8.8b	(cbrt (/ (- y x) t))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

0.0ms	(fma (* (* (cbrt (/ (- y x) t)) (cbrt (/ (- y x) t))) (cbrt (/ (- y x) t))) z x)
6.0ms	(cbrt (/ (- y x) t))
6.0ms	(cbrt (/ (- y x) t))
6.0ms	(cbrt (/ (- y x) t))

series582.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma (* (* (cbrt (/ (- y x) t)) (cbrt (/ (- y x) t))) (cbrt (/ (- y x) t))) z x)
157.0ms	(cbrt (/ (- y x) t))
167.0ms	(cbrt (/ (- y x) t))
178.0ms	(cbrt (/ (- y x) t))

simplify3.0s

Counts

112 → 112

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	139	1735
1	254	1681
2	506	1461
3	1251	1398
4	3633	1323
done	5001	1317

prune520.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt t) (cbrt t))))
5.5b	(fma (* (* (cbrt (/ (- y x) t)) (cbrt (/ (- y x) t))) (* (cbrt (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt t) (cbrt t)))) (cbrt (/ (cbrt (- y x)) (cbrt t))))) z x)
8.8b	(cbrt (/ (- y x) t))
8.8b	(cbrt (/ (- y x) t))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
35×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 86

Calls

4 calls:

26.0ms	(cbrt (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt t) (cbrt t))))
0.0ms	(fma (* (* (cbrt (/ (- y x) t)) (cbrt (/ (- y x) t))) (* (cbrt (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt t) (cbrt t)))) (cbrt (/ (cbrt (- y x)) (cbrt t))))) z x)
13.0ms	(cbrt (/ (- y x) t))
10.0ms	(cbrt (/ (- y x) t))

series854.0ms

Counts

4 → 12

Calls

4 calls:

426.0ms	(cbrt (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt t) (cbrt t))))
72.0ms	(fma (* (* (cbrt (/ (- y x) t)) (cbrt (/ (- y x) t))) (* (cbrt (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt t) (cbrt t)))) (cbrt (/ (cbrt (- y x)) (cbrt t))))) z x)
181.0ms	(cbrt (/ (- y x) t))
174.0ms	(cbrt (/ (- y x) t))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	198	1972
1	403	1923
2	887	1754
3	2369	1719
done	5000	1656

prune731.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

73.8% (1.7b remaining)

Error of 1.7b against oracle of 0.0b and baseline of 6.4b

bsearch84.0ms

Steps

Iters	Range		Point
8	1.988857617426115e+39	5.4352915068142585e+42	3.2712300343252506e+39
7	-7.289001802915994e-67	-1.0993416426332305e-68	-7.148917450038407e-67

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	33
1	21	26
done	21	26

end0.0ms

sample1.3s

Algorithm

intervals

Results

561.0ms

10642×

body

valid