Details

sample258.0ms

Algorithm

intervals

Results

113.0ms	784×	body	80	nan
22.0ms	178×	body	80	valid
15.0ms	27×	body	640	valid
14.0ms	13×	body	1280	valid
10.0ms	30×	body	320	valid
2.0ms	11×	body	160	valid

simplify668.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	21	13
2	30	13
3	38	13
4	44	13
5	59	13
6	90	13
7	187	13
8	611	13
done	5000	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.0b	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
0.3b	(* x (log y))
5.8b	(log (- 1.0 y))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

30.0ms	(* z (log (- 1.0 y)))
82.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
26.0ms	(* x (log y))
10.0ms	(log (- 1.0 y))

series448.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* z (log (- 1.0 y)))
174.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
71.0ms	(* x (log y))
79.0ms	(log (- 1.0 y))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	209	1141
1	470	1103
2	1490	987
done	5000	966

prune837.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.3b	(* x (log y))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `log-prod`
21×	`*-un-lft-identity`
16×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
13×	`associate--l+`
11×	`add-log-exp`
10×	`pow1` `associate-+r+` `associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-l`
5×	`sub-neg`
3×	`distribute-lft-out--`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 101

Calls

4 calls:

126.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
89.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
33.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
17.0ms	(* x (log y))

series831.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
345.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
236.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
66.0ms	(* x (log y))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	201	2374
1	470	2239
2	1538	2120
done	5000	2075

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (log (cbrt y)))
0.3b	(+ (* (* 2 (log (cbrt y))) x) (* x (log (cbrt y))))
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
18×	`cbrt-prod` `add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-r`
3×	`pow1/3` `associate-l`
2×	`log-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

20.0ms	(* x (log (cbrt y)))
45.0ms	(+ (* (* 2 (log (cbrt y))) x) (* x (log (cbrt y))))
2.0ms	(cbrt y)
2.0ms	(cbrt y)

series1.1s

Counts

4 → 12

Calls

4 calls:

169.0ms	(* x (log (cbrt y)))
238.0ms	(+ (* (* 2 (log (cbrt y))) x) (* x (log (cbrt y))))
334.0ms	(cbrt y)
371.0ms	(cbrt y)

simplify1.6s

Counts

89 → 89

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	119	909
1	305	849
2	1321	721
done	5000	711

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (* 3 x) (log (* (cbrt (- y)) (cbrt -1)))) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* (* 3 x) (log (* (cbrt (- y)) (cbrt -1)))) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.4b	(* (* 3 x) (log (* (cbrt (- y)) (cbrt -1))))
0.7b	(cbrt (- y))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-sqr-sqrt` `*-un-lft-identity`
11×	`add-log-exp`
10×	`cbrt-prod` `add-cube-cbrt` `associate-+r+` `log-prod`
9×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
6×	`associate-r`
5×	`pow-prod-down`
3×	`distribute-lft-neg-in` `sub-neg` `distribute-rgt-neg-in` `pow1/3` `prod-exp` `log-pow` `cbrt-unprod`
2×	`associate-+l+` `diff-log` `sum-log`
1×	`+-commutative` `neg-mul-1` `flip3--` `flip3-+` `associate-l` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

336.0ms	(- (+ (* (* 3 x) (log (* (cbrt (- y)) (cbrt -1)))) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
66.0ms	(+ (* (* 3 x) (log (* (cbrt (- y)) (cbrt -1)))) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
78.0ms	(* (* 3 x) (log (* (cbrt (- y)) (cbrt -1))))
4.0ms	(cbrt (- y))

series1.9s

Counts

4 → 12

Calls

4 calls:

709.0ms	(- (+ (* (* 3 x) (log (* (cbrt (- y)) (cbrt -1)))) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
497.0ms	(+ (* (* 3 x) (log (* (cbrt (- y)) (cbrt -1)))) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
342.0ms	(* (* 3 x) (log (* (cbrt (- y)) (cbrt -1))))
398.0ms	(cbrt (- y))

simplify2.1s

Counts

92 → 92

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	186	2147
1	451	2012
2	2157	1876
done	5001	1840

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes649.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	32
1	35	32
done	35	32

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.9s	23483×	body	80	nan
1.1s	5544×	body	80	valid
640.0ms	868×	body	640	valid
528.0ms	397×	body	1280	valid
315.0ms	779×	body	320	valid
234.0ms	443×	body	160	valid