Details

sample208.0ms

Algorithm

intervals

Results

91.0ms	1421×	body	80	nan
30.0ms	428×	body	80	valid
5.0ms	12×	body	640	valid
2.0ms	2×	body	1280	valid
2.0ms	7×	body	320	valid
1.0ms	10×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 2.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
0.2b	(* y (- (log z) t))
6.5b	(log (- 1.0 z))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-*r/`
8×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
7×	`flip3--` `flip--`
4×	`associate-+l+` `associate-+r+` `frac-add`
3×	`*-commutative`
2×	`log-div` `fma-def`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 33

Calls

4 calls:

4.0ms	(* a (- (log (- 1.0 z)) b))
8.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(* y (- (log z) t))
2.0ms	(log (- 1.0 z))

series374.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* a (- (log (- 1.0 z)) b))
184.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
68.0ms	(* y (- (log z) t))
46.0ms	(log (- 1.0 z))

simplify47.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	489	416
1	1801	406
2	5001	402

prune174.0ms

Filtered

45 candidates to 33 candidates (73.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	1	46

Merged error: 0.0b

Counts

46 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a b (* 1.0 (* a z)))
0.0b	(* x (exp (+ (* y (- (log z) t)) (fma a (log 1.0) (- (fma a b (* 1.0 (* a z))))))))
0.0b	(+ (* y (- (log z) t)) (fma a (log 1.0) (- (fma a b (* 1.0 (* a z))))))
0.2b	(* y (- (log z) t))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-+l+`
7×	`associate-r` `exp-sum`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
3×	`*-commutative` `fma-udef`
2×	`+-commutative` `associate-+r+` `fma-def` `associate-*r/`
1×	`flip3--` `flip3-+` `flip--` `flip-+`

Counts

4 → 26

Calls

4 calls:

1.0ms	(fma a b (* 1.0 (* a z)))
6.0ms	(* x (exp (+ (* y (- (log z) t)) (fma a (log 1.0) (- (fma a b (* 1.0 (* a z))))))))
5.0ms	(+ (* y (- (log z) t)) (fma a (log 1.0) (- (fma a b (* 1.0 (* a z))))))
4.0ms	(* y (- (log z) t))

series439.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(fma a b (* 1.0 (* a z)))
169.0ms	(* x (exp (+ (* y (- (log z) t)) (fma a (log 1.0) (- (fma a b (* 1.0 (* a z))))))))
149.0ms	(+ (* y (- (log z) t)) (fma a (log 1.0) (- (fma a b (* 1.0 (* a z))))))
72.0ms	(* y (- (log z) t))

simplify69.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	225	232
1	708	214
2	2866	211
3	5002	211

prune124.0ms

Filtered

38 candidates to 24 candidates (63.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	2	39

Merged error: 0.0b

Counts

39 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a b (* 1.0 (* a z)))
0.0b	(* x (* (pow z y) (pow 1.0 a)))
0.0b	(fma t y (fma a b (* 1.0 (* a z))))
1.0b	(/ (* x (* (pow z y) (pow 1.0 a))) (exp (fma t y (fma a b (* 1.0 (* a z))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-r`
12×	`sqr-pow`
10×	`fma-udef`
8×	`exp-sum`
7×	`times-frac` `associate-/l*`
6×	`*-commutative`
3×	`associate-l` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 26

Calls

4 calls:

1.0ms	(fma a b (* 1.0 (* a z)))
4.0ms	(* x (* (pow z y) (pow 1.0 a)))
1.0ms	(fma t y (fma a b (* 1.0 (* a z))))
7.0ms	(/ (* x (* (pow z y) (pow 1.0 a))) (exp (fma t y (fma a b (* 1.0 (* a z))))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma a b (* 1.0 (* a z)))
133.0ms	(* x (* (pow z y) (pow 1.0 a)))
54.0ms	(fma t y (fma a b (* 1.0 (* a z))))
286.0ms	(/ (* x (* (pow z y) (pow 1.0 a))) (exp (fma t y (fma a b (* 1.0 (* a z))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	207	278
1	580	278
2	3400	264
3	5001	260

prune152.0ms

Filtered

38 candidates to 30 candidates (78.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	38	2	40

Merged error: 0b

Counts

40 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a b (* 1.0 (* a z)))
0.0b	(/ x (/ (exp (fma t y (fma a b (* 1.0 (* a z))))) (* (pow z y) (pow 1.0 a))))
0.0b	(fma t y (fma a b (* 1.0 (* a z))))
0.8b	(/ (exp (fma t y (fma a b (* 1.0 (* a z))))) (* (pow z y) (pow 1.0 a)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-/r*` `sqr-pow`
14×	`fma-udef`
12×	`exp-sum`
10×	`times-frac`
9×	`associate-/r/`
4×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`pow-to-exp` `associate-/l*`
1×	`div-exp` `prod-exp`

Counts

4 → 35

Calls

4 calls:

1.0ms	(fma a b (* 1.0 (* a z)))
5.0ms	(/ x (/ (exp (fma t y (fma a b (* 1.0 (* a z))))) (* (pow z y) (pow 1.0 a))))
1.0ms	(fma t y (fma a b (* 1.0 (* a z))))
5.0ms	(/ (exp (fma t y (fma a b (* 1.0 (* a z))))) (* (pow z y) (pow 1.0 a)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma a b (* 1.0 (* a z)))
261.0ms	(/ x (/ (exp (fma t y (fma a b (* 1.0 (* a z))))) (* (pow z y) (pow 1.0 a))))
54.0ms	(fma t y (fma a b (* 1.0 (* a z))))
208.0ms	(/ (exp (fma t y (fma a b (* 1.0 (* a z))))) (* (pow z y) (pow 1.0 a)))

simplify114.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	235	375
1	742	374
2	4136	359
3	5001	354

prune191.0ms

Filtered

47 candidates to 38 candidates (80.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	47	2	49

Merged error: 0b

Counts

49 → 2

regimes133.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	40968×	body	80	nan
862.0ms	12457×	body	80	valid
139.0ms	366×	body	640	valid
104.0ms	422×	body	320	valid
60.0ms	80×	body	1280	valid
39.0ms	265×	body	160	valid