Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify70.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6
done	5001	6

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
22.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
31.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series95.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* x x) (* y y))
66.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify46.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	322	380
1	1875	324
2	5001	308
done	5001	308

prune129.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune9.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.3b	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
22.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
0.0ms	(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.0ms	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
29.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
112.0ms	(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
94.0ms	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
66.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify47.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	352	600
1	1919	513
2	5003	494
done	5003	494

prune208.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(expm1 (log1p (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
2.4b	(log1p (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
22.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
0.0ms	(expm1 (log1p (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.0ms	(log1p (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
31.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
168.0ms	(expm1 (log1p (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
128.0ms	(log1p (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
68.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify50.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	367	614
1	1963	525
2	5001	506
done	5001	506

prune216.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes79.0ms

Accuracy

76.5% (5.0b remaining)

Error of 5.5b against oracle of 0.5b and baseline of 21.9b

bsearch94.0ms

Steps

Iters	Range		Point
2	1.3208852066059225e-166	1.5408131166191686e-166	1.336866892806928e-166
10	2.7636474607770915e-218	6.51746038965982e-208	6.45195923821976e-208
10	-1.2064467384309053e-161	-8.786774377342885e-175	-1.6940632468089707e-162
8	-2.4426674496164293e+154	-2.3894100003351086e+151	-3.8474348794431934e+151

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	20
1	31	20
done	31	20

end0.0ms

sample507.0ms

Algorithm

intervals

Results

232.0ms	8000×	body	80	valid
96.0ms	8000×	pre	80	true