Details

sample60.0ms

Algorithm

intervals

Results

19.0ms	397×	body	80	nan
18.0ms	357×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	91	23
3	213	23
4	493	22
5	1037	22
6	1785	22
7	4319	22
done	5001	22

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.2b	(fma (log x) (- x 0.5) (+ (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) x) 0.91893853320467))
6.9b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`prod-diff` `associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 67

Calls

4 calls:

5.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.0ms	(fma (log x) (- x 0.5) (+ (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) x) 0.91893853320467))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series255.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
34.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
118.0ms	(fma (log x) (- x 0.5) (+ (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) x) 0.91893853320467))
72.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify1.1s

Counts

79 → 79

Iterations

Useful iterations: 3 (417.0ms)

Iter	Nodes	Cost
0	161	1432
1	341	1375
2	883	1221
3	2967	1193
done	5000	1193

prune325.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`associate-l`
7×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`flip3--` `prod-diff` `associate-/r` `flip--` `associate-/l`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `clear-num` `log-pow` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
10.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series776.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
247.0ms	(* (- x 0.5) (log x))
406.0ms	(- (* (- x 0.5) (log x)) x)
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify660.0ms

Counts

120 → 120

Iterations

Useful iterations: done (657.0ms)

Iter	Nodes	Cost
0	238	1762
1	543	1631
2	1608	1486
done	5002	1453

prune410.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series624.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt x)
182.0ms	(cbrt x)
176.0ms	(cbrt x)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify802.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (294.0ms)

Iter	Nodes	Cost
0	101	939
1	225	870
2	611	794
3	1847	767
done	5001	767

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.9b	(pow x 1/3)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(pow x 1/3)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series805.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt x)
175.0ms	(cbrt x)
361.0ms	(pow x 1/3)
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify923.0ms

Counts

89 → 89

Iterations

Useful iterations: 3 (388.0ms)

Iter	Nodes	Cost
0	130	994
1	285	879
2	721	814
3	2165	783
done	5000	783

prune417.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

regimes380.0ms

Accuracy

87.7% (0.3b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 5.8b

bsearch88.0ms

Steps

Iters	Range		Point
8	22276.40736340321	15372542.567402918	8078075.0826568445

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	75
1	62	75
done	62	75

end0.0ms

sample1.7s

Algorithm

intervals

Results

616.0ms	11767×	body	80	valid
535.0ms	12076×	body	80	nan