Details

sample197.0ms

Algorithm

intervals

Results

80.0ms	364×	body	80	valid
47.0ms	402×	body	80	nan

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (260.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	92	23
3	265	23
4	934	22
5	4335	22
done	5000	22

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.2b	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
0.3b	(fma (- x 0.5) (log x) 0.91893853320467)
6.2b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

1.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
210.0ms	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
1.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
23.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
263.0ms	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
563.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
141.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	178	2316
1	407	2178
2	1360	1923
done	5001	1766

prune963.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.2b	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))) x)
0.3b	(fma (- x 0.5) (log x) 0.91893853320467)
6.4b	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

1.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
65.0ms	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))) x)
1.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
41.0ms	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

series1.0s

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
247.0ms	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))) x)
552.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
156.0ms	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

simplify2.2s

Counts

100 → 100

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	202	2400
1	500	2120
2	1974	1841
done	5001	1711

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
0.2b	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) (/ 1 x))) x)
0.3b	(fma (- x 0.5) (log x) 0.91893853320467)
6.4b	(* (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) (/ 1 x))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

98.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
73.0ms	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) (/ 1 x))) x)
1.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
196.0ms	(* (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) (/ 1 x))

series1.0s

Counts

4 → 12

Calls

4 calls:

66.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
218.0ms	(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) (/ 1 x))) x)
579.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
158.0ms	(* (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) (/ 1 x))

simplify2.8s

Counts

126 → 126

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	281	2978
1	740	2527
2	3710	2218
done	5000	2217

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (- x 0.5) (log x) 0.91893853320467)
0.3b	(fma (- x 0.5) (log x) 0.91893853320467)
0.5b	(* (sqrt (fma (- x 0.5) (log x) 0.91893853320467)) (sqrt (fma (- x 0.5) (log x) 0.91893853320467)))
6.2b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
18×	`sqrt-prod`
9×	`times-frac`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 100

Calls

4 calls:

1.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
1.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
29.0ms	(* (sqrt (fma (- x 0.5) (log x) 0.91893853320467)) (sqrt (fma (- x 0.5) (log x) 0.91893853320467)))
11.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series1.9s

Counts

4 → 12

Calls

4 calls:

569.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
575.0ms	(fma (- x 0.5) (log x) 0.91893853320467)
577.0ms	(* (sqrt (fma (- x 0.5) (log x) 0.91893853320467)) (sqrt (fma (- x 0.5) (log x) 0.91893853320467)))
158.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify5.6s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	151	2056
1	303	1560
2	840	1399
3	4595	1332
done	5000	1332

prune951.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.2b

regimes774.0ms

Accuracy

87.3% (0.3b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 5.8b

bsearch198.0ms

Steps

Iters	Range		Point
9	132261263930.07881	7.385247819399577e+18	5383194378760586.0

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	56
1	33	56
done	33	56

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	11619×	body	80	nan
1.9s	11683×	body	80	valid