Details

sample162.0ms

Algorithm

intervals

Results

53.0ms	684×	body	80	nan
15.0ms	19×	body	1280	valid
15.0ms	176×	body	80	valid
9.0ms	22×	body	640	valid
7.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid

simplify951.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	13
1	22	12
2	38	12
3	53	12
4	61	12
5	78	12
6	113	12
7	238	12
8	767	12
done	5000	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
0.0b	(* z (log (- 1.0 y)))
0.2b	(fma x (log y) (* z (log (- 1.0 y))))
5.0b	(log (- 1.0 y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
26.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma x (log y) (* z (log (- 1.0 y))))
7.0ms	(log (- 1.0 y))

series468.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
131.0ms	(* z (log (- 1.0 y)))
126.0ms	(fma x (log y) (* z (log (- 1.0 y))))
76.0ms	(log (- 1.0 y))

simplify994.0ms

Counts

100 → 100

Iterations

Useful iterations: done (991.0ms)

Iter	Nodes	Cost
0	204	1528
1	488	1381
2	1552	1220
done	5000	1128

prune521.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.0b	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.2b	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
8.1b	(* z (pow y 2))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
25×	`prod-exp`
24×	`associate--l+`
23×	`add-sqr-sqrt`
20×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`div-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `prod-diff`
8×	`pow1` `pow-to-exp` `times-frac` `pow-exp`
7×	`unpow-prod-down`
6×	`log-prod` `associate-l` `add-log-exp`
5×	`associate-*r/` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `unpow2` `sqr-pow`
2×	`cbrt-undiv` `flip3--` `log-pow` `*-commutative` `frac-sub` `flip--`
1×	`fma-neg` `diff-log` `pow-prod-down` `fma-udef` `div-inv`

Counts

4 → 119

Calls

4 calls:

32.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
22.0ms	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.0ms	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
22.0ms	(* z (pow y 2))

series486.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
149.0ms	(- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
213.0ms	(fma x (log y) (- (* z (- (log 1.0) (* 1.0 y))) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
38.0ms	(* z (pow y 2))

simplify2.0s

Counts

131 → 131

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	230	2280
1	614	2088
2	2736	1903
done	5000	1897

prune811.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

8.1b	(* z (pow y 2))
13.8b	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
13.8b	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
13.8b	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-r`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow1/3` `associate-l` `prod-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 68

Calls

4 calls:

13.0ms	(* z (pow y 2))
1.0ms	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
1.0ms	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
1.0ms	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* z (pow y 2))
444.0ms	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
405.0ms	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))
499.0ms	(cbrt (fma z (- (log 1.0) (* 1.0 y)) (* -1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))

simplify887.0ms

Counts

80 → 80

Iterations

Useful iterations: done (880.0ms)

Iter	Nodes	Cost
0	152	2302
1	359	2228
2	1326	2042
done	5000	1919

prune762.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma x (log y) (+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y))))))
12.1b	(+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y)))))
15.1b	(log (- (sqrt 1.0) (sqrt y)))
15.2b	(log (+ (sqrt 1.0) (sqrt y)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
34×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`sqrt-prod`
18×	`associate-+r+`
14×	`distribute-rgt-in` `distribute-lft-in`
12×	`difference-of-squares`
10×	`add-cube-cbrt` `associate-+l+`
7×	`distribute-lft-out`
6×	`pow1` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`+-commutative` `flip3--` `fma-def` `sum-log` `flip--` `fma-udef`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma x (log y) (+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y))))))
71.0ms	(+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y)))))
18.0ms	(log (- (sqrt 1.0) (sqrt y)))
18.0ms	(log (+ (sqrt 1.0) (sqrt y)))

series1.4s

Counts

4 → 12

Calls

4 calls:

484.0ms	(fma x (log y) (+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y))))))
538.0ms	(+ (* z (log (+ (sqrt 1.0) (sqrt y)))) (* z (log (- (sqrt 1.0) (sqrt y)))))
199.0ms	(log (- (sqrt 1.0) (sqrt y)))
202.0ms	(log (+ (sqrt 1.0) (sqrt y)))

simplify1.4s

Counts

105 → 105

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	213	2061
1	544	1854
2	2042	1431
done	5000	1417

prune589.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes292.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	26
1	24	26
done	24	26

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.9s	24081×	body	80	nan
808.0ms	880×	body	640	valid
505.0ms	5553×	body	80	valid
360.0ms	421×	body	1280	valid
238.0ms	733×	body	320	valid
114.0ms	445×	body	160	valid