Details

sample108.0ms

Algorithm

intervals

Results

40.0ms	822×	body	80	nan
10.0ms	182×	body	80	valid
9.0ms	15×	body	1280	valid
7.0ms	23×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	15×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 10.9b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.1b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.2b	(log (- 1.0 y))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`log-div`
1×	`flip3--` `*-commutative` `flip--` `fma-udef`

Counts

3 → 4

Calls

3 calls:

3.0ms	(* z (log (- 1.0 y)))
1.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
2.0ms	(log (- 1.0 y))

series226.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* z (log (- 1.0 y)))
113.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
45.0ms	(log (- 1.0 y))

simplify62.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	225	101
1	687	96
2	2359	93
3	5001	92

prune55.0ms

Filtered

13 candidates to 13 candidates (100.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.2b

Counts

15 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.0b	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.1b	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
9.7b	(* z (pow y 2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-r`
9×	`associate-*r/` `unpow2` `sqr-pow`
8×	`times-frac`
5×	`*-commutative`
4×	`associate-/l*`
2×	`clear-num` `associate-/r*` `fma-udef`
1×	`frac-2neg` `un-div-inv` `div-inv`

Counts

4 → 25

Calls

4 calls:

1.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
6.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
1.0ms	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
3.0ms	(* z (pow y 2))

series358.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
61.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
158.0ms	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
32.0ms	(* z (pow y 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	135	105
1	457	102
2	2222	102
3	5001	102

prune147.0ms

Filtered

37 candidates to 27 candidates (73.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	37	2	39

Merged error: 0.2b

Counts

39 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
0.0b	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.2b	(* (log y) x)
9.7b	(* z (pow y 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-r`
9×	`associate-*r/` `unpow2` `sqr-pow`
8×	`times-frac`
7×	`*-commutative`
4×	`associate-/l*`
3×	`associate-+r+`
2×	`fma-def` `clear-num` `associate-/r*`
1×	`+-commutative` `associate-+r-` `sub-neg` `frac-2neg` `flip3-+` `associate--l+` `un-div-inv` `flip-+` `fma-udef` `div-inv`

Counts

4 → 33

Calls

4 calls:

5.0ms	(+ (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
6.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
2.0ms	(* (log y) x)
3.0ms	(* z (pow y 2))

series316.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(+ (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
57.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
65.0ms	(* (log y) x)
33.0ms	(* z (pow y 2))

simplify122.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	227	228
1	775	223
2	3973	218
3	5001	218

prune180.0ms

Filtered

45 candidates to 34 candidates (75.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	43	4	47

Merged error: 0.2b

Counts

47 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

9.7b	(* z (pow y 2))
9.7b	(* z (pow y 2))
9.7b	(* z (pow y 2))
31.7b	(/ (* (- (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)) (fma x (log y) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))) (- (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-r`
4×	`*-commutative`
3×	`unpow2` `sqr-pow`
2×	`flip3--` `associate-l/` `associate-/r/` `flip--` `associate-/l/` `associate-/l`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 18

Calls

4 calls:

3.0ms	(* z (pow y 2))
3.0ms	(* z (pow y 2))
3.0ms	(* z (pow y 2))
9.0ms	(/ (* (- (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)) (fma x (log y) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))) (- (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* z (pow y 2))
33.0ms	(* z (pow y 2))
28.0ms	(* z (pow y 2))
168.0ms	(/ (* (- (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)) (fma x (log y) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))) (- (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t)))

simplify115.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	171	324
1	705	264
2	3919	264
3	5001	263

prune131.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	26	4	30
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	27	7	34

Merged error: 0.1b

Counts

34 → 7

regimes209.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	14
1	26	14

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	23996×	body	80	nan
296.0ms	5550×	body	80	valid
266.0ms	872×	body	640	valid
244.0ms	408×	body	1280	valid
138.0ms	758×	body	320	valid
51.0ms	444×	body	160	valid