Details

sample116.0ms

Algorithm

intervals

Results

35.0ms	374×	body	80	valid
27.0ms	333×	body	80	nan

simplify5.7s

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.5b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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` `insert-posit16` `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` `div-inv` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
10.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
1.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
7.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
490.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
419.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
163.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify5.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	3664
2	1020
1	369
0	174

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize97.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
0.2b	(- x (fma (log x) (- x 0.5) 0.91893853320467))
0.2b	(fma (log x) (- x 0.5) 0.91893853320467)
7.0b	(* (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (/ 1 x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
19×	`add-cube-cbrt`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube` `prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `fma-udef` `unswap-sqr`
2×	`div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

2.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
20.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
2.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
25.0ms	(* (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (/ 1 x))

series1.1s

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333)
503.0ms	(- x (fma (log x) (- x 0.5) 0.91893853320467))
449.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
133.0ms	(* (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) (/ 1 x))

simplify5.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
3	3675
2	1168
1	457
0	197

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize188.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log x) (- x 0.5) 0.91893853320467)
0.2b	(fma (log x) (- x 0.5) 0.91893853320467)
0.4b	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
6.9b	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-prod`
72×	`add-sqr-sqrt` `prod-diff`
70×	`*-un-lft-identity`
62×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac` `associate-r`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `flip3-+` `flip3--` `flip-+` `flip--` `associate-/l`
2×	`sub-neg` `associate-l/` `associate-r/` `fma-udef` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

1.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
2.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
158.0ms	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
15.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

series2.2s

Counts

4 → 12

Calls

4 calls:

500.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
489.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
1.1s	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))
135.0ms	(/ (fma z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) 0.083333333333333) x)

simplify9.5s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
1	1457
0	479

prune3.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize171.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.0027777777777778 (/ z x))
0.2b	(fma (log x) (- x 0.5) 0.91893853320467)
0.2b	(fma (log x) (- x 0.5) 0.91893853320467)
0.4b	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-prod`
77×	`add-sqr-sqrt`
72×	`prod-diff`
70×	`*-un-lft-identity`
62×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac`
8×	`pow1` `associate-l`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `flip3--` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`
2×	`sub-neg` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-undiv` `div-exp` `div-inv`

Counts

4 → 170

Calls

4 calls:

26.0ms	(* 0.0027777777777778 (/ z x))
2.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
2.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
149.0ms	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))

series1.9s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 0.0027777777777778 (/ z x))
363.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
460.0ms	(fma (log x) (- x 0.5) 0.91893853320467)
1.1s	(* (+ (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))) (- (sqrt x) (sqrt (fma (log x) (- x 0.5) 0.91893853320467))))

simplify6.9s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
1	1497
0	479

prune2.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes1.7s

Accuracy

96.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 6.6b

bsearch102.0ms

Steps

Iters	Range		Point
5	1.9756105794475683e+22	5.350792530299976e+22	2.0160595213046038e+22

simplify25.0ms

Iterations

Iter	Nodes
done	40
1	40
0	35

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	11652×	body	80	nan
1.7s	11631×	body	80	valid