Details

sample91.0ms

Algorithm

intervals

Results

21.0ms	37×	body	1280	valid
17.0ms	34×	body	10240	exit
15.0ms	51×	body	640	valid
7.0ms	127×	body	80	valid
4.0ms	4×	body	2560	valid
4.0ms	20×	body	320	valid
3.0ms	75×	body	80	nan
2.0ms	17×	body	160	valid
1.0ms	6×	body	640	nan
1.0ms	5×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	2×	body	160	nan

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

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: 23.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.7b	(log (+ (- 1.0 y) (* y (exp z))))
3.5b	(+ (- 1.0 y) (* y (exp z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`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` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
8.0ms	(log (+ (- 1.0 y) (* y (exp z))))
8.0ms	(+ (- 1.0 y) (* y (exp z)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
152.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
93.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune332.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 3.8b

Counts

115 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
3.5b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
6.3b	(* (pow z 2) y)
6.9b	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
50×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
11×	`add-exp-log`
8×	`associate-l` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`fma-neg` `associate-r` `prod-exp` `associate-/r` `associate-/l`
2×	`unpow2` `difference-of-squares` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `pow-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--`

Counts

4 → 127

Calls

4 calls:

8.0ms	(- x (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
1.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.0ms	(* (pow z 2) y)
3.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)

series296.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- x (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
64.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
18.0ms	(* (pow z 2) y)
95.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)

simplify80.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	546	3031
1	1897	1985
2	5001	1748

prune370.0ms

Filtered

139 candidates to 82 candidates (59.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	129	10	139
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	130	16	146

Merged error: 3.7b

Counts

146 → 16

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.3b	(/ (* z y) t)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`times-frac` `fma-neg` `associate-/r*`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `diff-log` `div-exp` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 53

Calls

2 calls:

11.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
5.0ms	(/ (* z y) t)

series110.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
20.0ms	(/ (* z y) t)

simplify40.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	261	704
1	1021	433
2	5001	422

prune179.0ms

Filtered

59 candidates to 40 candidates (67.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	53	6	59
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	60	15	75

Merged error: 2.9b

Counts

75 → 15

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (* (* z y) (/ 1 t))) (/ (log 1.0) t)))
4.4b	(* (* z y) (/ 1 t))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
18×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`add-cbrt-cube`
13×	`associate-r`
12×	`prod-exp`
9×	`times-frac` `prod-diff`
7×	`pow1` `add-log-exp`
6×	`cbrt-unprod`
4×	`div-exp`
3×	`fma-neg` `pow-prod-down`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `diff-log` `1-exp` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `associate-r/` `associate-l` `sum-log` `un-div-inv` `-commutative` `flip--` `div-inv` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 70

Calls

2 calls:

13.0ms	(- x (+ (* 1.0 (* (* z y) (/ 1 t))) (/ (log 1.0) t)))
8.0ms	(* (* z y) (/ 1 t))

series110.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- x (+ (* 1.0 (* (* z y) (/ 1 t))) (/ (log 1.0) t)))
20.0ms	(* (* z y) (/ 1 t))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	407	866
1	1824	513
2	5001	488

prune134.0ms

Filtered

76 candidates to 44 candidates (57.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	75	16	91

Merged error: 2.9b

Counts

91 → 16

regimes645.0ms

Accuracy

63.3% (4.9b remaining)

Error of 8.6b against oracle of 3.7b and baseline of 17.1b

bsearch25.0ms

Steps

Iters	Range		Point
2	-8.328242841637719	-7.218583477017294	-7.33677571999249

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

765.0ms	1436×	body	1280	valid
751.0ms	1511×	body	10240	exit
481.0ms	1601×	body	640	valid
214.0ms	3545×	body	80	valid
159.0ms	867×	body	320	valid
99.0ms	77×	body	2560	valid
93.0ms	2423×	body	80	nan
55.0ms	492×	body	160	valid
47.0ms	232×	body	640	nan
34.0ms	113×	body	1280	nan
25.0ms	173×	body	320	nan
9.0ms	111×	body	160	nan

Details

sample91.0ms

simplify211.0ms

prune3.0ms

localize10.0ms

rewrite32.0ms

series302.0ms

simplify62.0ms

prune332.0ms

localize12.0ms

rewrite21.0ms

series296.0ms

simplify80.0ms

prune370.0ms

localize14.0ms

rewrite17.0ms

series110.0ms

simplify40.0ms

prune179.0ms

localize11.0ms

rewrite24.0ms

series110.0ms

simplify57.0ms

prune134.0ms

regimes645.0ms

bsearch25.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling