Details

sample66.0ms

Algorithm

intervals

Results

29.0ms	244×	body	80	valid
8.0ms	16×	body	640	valid
4.0ms	7×	body	1280	valid
3.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify932.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
6	989
5	406
4	195
3	103
2	50
1	22
0	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.7b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 66

Calls

2 calls:

18.0ms	(/ (- t z) (- a t))
1.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series234.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- t z) (- a t))
181.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify554.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
2	645
1	265
0	116

prune354.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
6.4b	(fma y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) (+ y x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 65

Calls

4 calls:

3.0ms	(cbrt (- a t))
7.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
0.0ms	(fma y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) (+ y x))

series842.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (- a t))
209.0ms	(cbrt (- a t))
209.0ms	(cbrt (- a t))
171.0ms	(fma y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))) (+ y x))

simplify604.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	2000
3	984
2	406
1	193
0	96

prune469.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma y (/ (- t z) (- a t)) (+ y x)))
2.2b	(fma y (/ (- t z) (- a t)) (+ y x))
2.2b	(fma y (/ (- t z) (- a t)) (+ y x))
2.2b	(fma y (/ (- t z) (- a t)) (+ y x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (fma y (/ (- t z) (- a t)) (+ y x)))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.3s	(cbrt (fma y (/ (- t z) (- a t)) (+ y x)))
179.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
179.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
162.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify773.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2000
3	1414
2	408
1	164
0	79

prune396.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.3b

localize45.0ms

Local error

Found 4 expressions with local error:

2.2b	(fma y (/ (- t z) (- a t)) (+ y x))
2.2b	(fma y (/ (- t z) (- a t)) (+ y x))
2.2b	(fma y (/ (- t z) (- a t)) (+ y x))
2.2b	(fma y (/ (- t z) (- a t)) (+ y x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series746.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
202.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
187.0ms	(fma y (/ (- t z) (- a t)) (+ y x))
148.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify758.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
4	1402
3	250
2	81
1	41
0	25

prune424.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.3b

regimes505.0ms

Accuracy

36.5% (5.0b remaining)

Error of 8.1b against oracle of 3.1b and baseline of 11.0b

bsearch101.0ms

Steps

Iters	Range		Point
2	1.0488449087684188e+108	1.124400183306477e+108	1.0771781367201906e+108
9	-3.891955142222253e+180	-6.0792118571536216e+172	-6.157437085390881e+172

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	7419×	body	80	valid
249.0ms	400×	body	320	valid
140.0ms	428×	body	640	valid
130.0ms	237×	body	1280	valid
97.0ms	245×	body	160	valid
6.0ms	13×	body	2560	valid