Details

sample94.0ms

Algorithm

intervals

Results

36.0ms	395×	body	80	valid
24.0ms	406×	body	80	nan

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (242.0ms)

Iter	Nodes	Cost
0	20	518
1	40	493
2	91	493
3	260	493
4	687	468
5	1555	468
6	2777	468
done	5001	468

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))
0.1b	(- (fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
5.5b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
1.0ms	(fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))
12.0ms	(- (fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
8.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series550.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
195.0ms	(fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x))
178.0ms	(- (fma (log x) (- x 0.5) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
109.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify3.5s

Counts

90 → 90

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	158	40426
1	343	36883
2	904	35118
3	3448	34583
done	5000	34438

prune699.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

100.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
31.0ms	(* (- x 0.5) (log x))
16.0ms	(- (* (- x 0.5) (log x)) x)
42.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

724.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
445.0ms	(* (- x 0.5) (log x))
703.0ms	(- (* (- x 0.5) (log x)) x)
122.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.4s

Counts

128 → 128

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	241	39878
1	628	35873
2	1899	34452
done	5002	33974

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.3b	(fma (log x) (- x 0.5) (- 0.91893853320467 x))
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`flip3-+` `associate-*l/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3--` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

35.0ms	(+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- 0.91893853320467 x))
47.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series571.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)
52.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
354.0ms	(fma (log x) (- x 0.5) (- 0.91893853320467 x))
102.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.8s

Counts

89 → 89

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	171	29858
1	407	25762
2	1228	25411
done	5001	25221

prune844.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma x (log x) 0.91893853320467)
0.3b	(- (fma x (log x) 0.91893853320467) (fma 0.5 (log x) x))
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

60.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma x (log x) 0.91893853320467)
10.0ms	(- (fma x (log x) 0.91893853320467) (fma 0.5 (log x) x))
77.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
353.0ms	(fma x (log x) 0.91893853320467)
724.0ms	(- (fma x (log x) 0.91893853320467) (fma 0.5 (log x) x))
128.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.9s

Counts

105 → 105

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	211	37531
1	500	33337
2	1502	31392
done	5000	31177

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes601.0ms

Accuracy

87.5% (0.3b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 5.9b

bsearch40.0ms

Steps

Iters	Range		Point
3	8.99513475934388e+21	1.2982871237097387e+22	9.411134885982841e+21

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	38	1364
1	50	1364
done	50	1364

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	11597×	body	80	nan
1.5s	11601×	body	80	valid