Details

sample100.0ms

Algorithm

intervals

Results

32.0ms	58×	body	1280	valid
16.0ms	50×	body	640	valid
7.0ms	109×	body	80	valid
6.0ms	27×	body	320	valid
3.0ms	72×	body	80	nan
3.0ms	2×	body	2560	valid
3.0ms	52×	body	80	overflowed
1.0ms	11×	body	160	valid
1.0ms	4×	body	640	nan
1.0ms	6×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	3×	body	160	nan

simplify214.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	628	7
9	935	7
10	1028	7
11	1354	7
12	3968	7
13	5002	7

prune9.0ms

Filtered

1 candidates to 0 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: 24.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
0.8b	(log (+ (- 1.0 y) (* y (exp z))))
3.3b	(+ (- 1.0 y) (* y (exp z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

9.0ms	(* y (exp z))
10.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
6.0ms	(+ (- 1.0 y) (* y (exp z)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* y (exp z))
190.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
99.0ms	(log (+ (- 1.0 y) (* y (exp z))))
63.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5002	726

prune646.0ms

Filtered

92 candidates to 68 candidates (26.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 2.3b

Counts

93 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
4.2b	(/ (* z y) t)
7.9b	(/ (* (pow z 2) y) t)
8.9b	(* (pow z 2) y)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `unpow-prod-down` `associate-*r/` `frac-add` `unswap-sqr`
3×	`associate-r` `sum-log` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`+-commutative` `associate-+r+` `*-commutative`

Counts

4 → 87

Calls

4 calls:

12.0ms	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
4.0ms	(/ (* z y) t)
5.0ms	(/ (* (pow z 2) y) t)
7.0ms	(* (pow z 2) y)

series192.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
27.0ms	(/ (* z y) t)
22.0ms	(/ (* (pow z 2) y) t)
22.0ms	(* (pow z 2) y)

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	492	659
1	2299	586
2	5001	586

prune655.0ms

Filtered

99 candidates to 66 candidates (33.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 1.9b

Counts

104 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (pow z 2) y)
20.7b	(cbrt (/ (* z y) t))
20.7b	(cbrt (/ (* z y) t))
20.7b	(cbrt (/ (* z y) t))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
19×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `times-frac`
8×	`associate-l`
6×	`add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `add-log-exp` `unswap-sqr`
3×	`cbrt-div` `pow1/3` `associate-r` `prod-exp` `div-inv`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

5.0ms	(* (pow z 2) y)
3.0ms	(cbrt (/ (* z y) t))
3.0ms	(cbrt (/ (* z y) t))
3.0ms	(cbrt (/ (* z y) t))

series337.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (pow z 2) y)
103.0ms	(cbrt (/ (* z y) t))
104.0ms	(cbrt (/ (* z y) t))
108.0ms	(cbrt (/ (* z y) t))

simplify112.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	198	453
1	585	418
2	3234	403
3	5002	376

prune692.0ms

Filtered

87 candidates to 64 candidates (26.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	87	8	95

Merged error: 1.9b

Counts

95 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 1.0 (/ z (/ t y))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
5.9b	(/ z (/ t y))
7.9b	(/ (* (pow z 2) y) t)
8.9b	(* (pow z 2) y)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
57×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log`
16×	`associate-/r*` `add-cbrt-cube`
9×	`add-log-exp`
8×	`associate-l`
7×	`div-exp`
6×	`prod-exp` `div-inv`
5×	`cbrt-undiv`
4×	`pow1` `unpow-prod-down` `associate-r/` `frac-add` `associate-/l` `unswap-sqr`
3×	`associate-r` `sum-log`
2×	`pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `associate-+r+` `associate-/r/` `*-commutative`

Counts

4 → 136

Calls

4 calls:

14.0ms	(+ (* 1.0 (/ z (/ t y))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
6.0ms	(/ z (/ t y))
5.0ms	(/ (* (pow z 2) y) t)
5.0ms	(* (pow z 2) y)

series192.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (* 1.0 (/ z (/ t y))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
26.0ms	(/ z (/ t y))
25.0ms	(/ (* (pow z 2) y) t)
22.0ms	(* (pow z 2) y)

simplify91.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	721	1014
1	3666	937
2	5001	937

prune1.8s

Filtered

148 candidates to 112 candidates (24.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	149	7	156

Merged error: 1.9b

Counts

156 → 7

regimes721.0ms

Accuracy

74.2% (4.4b remaining)

Error of 8.2b against oracle of 3.8b and baseline of 20.7b

bsearch272.0ms

Steps

Iters	Range		Point
5	4.5898364893588405e-34	1.720946338532426e-33	7.255051022077384e-34
8	1.3022887670696334e-138	2.554760771555832e-135	1.2038363056561298e-136
8	-1.289397842534223e-10	-3.6387519926632435e-14	-9.98191876129602e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	54
1	69	54

end0.0ms

sample3.0s

Algorithm

intervals

Results

839.0ms	1420×	body	1280	valid
534.0ms	1582×	body	640	valid
248.0ms	3553×	body	80	valid
202.0ms	922×	body	320	valid
108.0ms	78×	body	2560	valid
107.0ms	2355×	body	80	nan
79.0ms	1545×	body	80	overflowed
66.0ms	264×	body	640	nan
61.0ms	463×	body	160	valid
42.0ms	126×	body	1280	nan
36.0ms	193×	body	320	nan
11.0ms	109×	body	160	nan

Details

sample100.0ms

simplify214.0ms

prune9.0ms

localize10.0ms

rewrite34.0ms

series380.0ms

simplify53.0ms

prune646.0ms

localize15.0ms

rewrite31.0ms

series192.0ms

simplify64.0ms

prune655.0ms

localize20.0ms

rewrite15.0ms

series337.0ms

simplify112.0ms

prune692.0ms

localize15.0ms

rewrite36.0ms

series192.0ms

simplify91.0ms

prune1.8s

regimes721.0ms

bsearch272.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling