Details

sample98.0ms

Algorithm

intervals

Results

29.0ms	668×	body	80	nan
10.0ms	195×	body	80	valid
8.0ms	26×	body	640	valid
6.0ms	8×	body	1280	valid
4.0ms	13×	body	160	valid
3.0ms	15×	body	320	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8
done	5001	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.2b	(* (- x 1.0) (log y))
5.2b	(log (- 1.0 y))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
21×	`log-prod`
20×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `prod-diff` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `associate-*l/` `flip--` `log1p-expm1-u`
3×	`fma-neg` `log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 114

Calls

4 calls:

89.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
29.0ms	(* (- z 1.0) (log (- 1.0 y)))
25.0ms	(* (- x 1.0) (log y))
6.0ms	(log (- 1.0 y))

series298.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
41.0ms	(* (- z 1.0) (log (- 1.0 y)))
58.0ms	(* (- x 1.0) (log y))
41.0ms	(log (- 1.0 y))

simplify57.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	587	1089
1	2183	902
2	5001	886
done	5001	886

prune332.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b	(* (- x 1.0) (log y))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
80×	`times-frac`
78×	`add-cube-cbrt` `associate-r`
56×	`unpow-prod-down`
48×	`prod-diff`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`pow1` `log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`frac-add`
14×	`log-pow`
13×	`associate-l` `add-cbrt-cube`
12×	`frac-times` `prod-exp` `associate--l+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 280

Calls

4 calls:

36.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
36.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
86.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
22.0ms	(* (- x 1.0) (log y))

series330.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
155.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
63.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
59.0ms	(* (- x 1.0) (log y))

simplify67.0ms

Counts

292 → 292

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1523	4510
1	5001	3592
done	5001	3592

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.2b	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
0.5b	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
58.4b	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`pow1`
18×	`prod-diff` `sqrt-prod`
12×	`sqrt-div`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
9×	`associate-l`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube`
6×	`flip3-+` `flip-+`
5×	`pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`sub-neg` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `fma-udef`
1×	`pow2` `flip3--` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

24.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.0ms	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
42.0ms	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
241.0ms	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
106.0ms	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
793.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify92.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	504	3017
1	2310	2593
2	5001	2522
done	5001	2522

prune649.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.2b	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
1.7b	(* (- z 1.0) (fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt 1) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
58.1b	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt 1) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `flip3--` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

22.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.0ms	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
24.0ms	(* (- z 1.0) (fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt 1) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt 1) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
242.0ms	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
216.0ms	(* (- z 1.0) (fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt 1) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
787.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt 1) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify67.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	410	2963
1	1812	2505
2	5001	2267
done	5001	2267

prune580.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes355.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	48
1	59	48
2	71	48
3	73	48
4	73	48
done	73	48

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	23584×	body	80	nan
307.0ms	5863×	body	80	valid
232.0ms	789×	body	640	valid
159.0ms	264×	body	1280	valid
122.0ms	682×	body	320	valid
48.0ms	434×	body	160	valid