Details

sample231.0ms

Algorithm

intervals

Results

81.0ms	1168×	body	80	nan
31.0ms	379×	body	80	valid
7.0ms	15×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	11×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	58	10
2	129	10
3	318	10
4	1073	10
5	5001	10

prune5.0ms

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: 1.8b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.7b	(log (- 1.0 z))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`pow1`
7×	`add-exp-log` `sub-neg` `flip3--` `flip--` `distribute-lft-out--` `add-log-exp`
6×	`associate-r` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`frac-add`
3×	`associate-l` `log-pow`
2×	`log-div`
1×	`+-commutative` `flip3-+` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

4.0ms	(- (log z) t)
7.0ms	(* y (- (log z) t))
11.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series68.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (log z) t)
14.0ms	(* y (- (log z) t))
40.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

simplify62.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	615	897
1	2222	843
2	5001	813

prune173.0ms

Filtered

83 candidates to 118 candidates (-42.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Merged error: 0.3b

Counts

119 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

47×	`associate--l+`
30×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `log-prod`
24×	`distribute-rgt-in` `distribute-lft-in`
17×	`add-cube-cbrt`
14×	`associate-+r+`
13×	`sub-neg` `associate-r`
12×	`associate-*r/`
11×	`pow1`
10×	`associate-+l+`
9×	`distribute-lft-out--`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3--` `flip--` `add-log-exp`
6×	`associate-l`
4×	`frac-add`
3×	`log-pow` `difference-of-squares`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 128

Calls

4 calls:

4.0ms	(- (log z) t)
18.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
7.0ms	(* y (- (log z) t))
20.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (log z) t)
35.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
24.0ms	(* y (- (log z) t))
70.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify98.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	616	1574
1	2486	1490
2	5001	1463

prune277.0ms

Filtered

89 candidates to 140 candidates (-57.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Merged error: 0.0b

Counts

142 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (+ (* y (- (log z) t)) (* (log 1.0) a))))
0.0b	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-r`
9×	`log-prod` `associate--l+`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log`
6×	`associate-l`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`distribute-lft-out--`
3×	`sub-neg` `exp-prod`
2×	`flip3--` `associate-r/` `exp-sum` `pow-prod-down` `prod-exp` `log-pow` `-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`
1×	`diff-log` `sum-log`

Counts

4 → 83

Calls

4 calls:

18.0ms	(* x (exp (+ (* y (- (log z) t)) (* (log 1.0) a))))
12.0ms	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
7.0ms	(- (log z) t)
12.0ms	(* y (- (log z) t))

series99.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* x (exp (+ (* y (- (log z) t)) (* (log 1.0) a))))
24.0ms	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
13.0ms	(- (log z) t)
23.0ms	(* y (- (log z) t))

simplify109.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	351	647
1	1274	561
2	4303	519
3	5001	517

prune138.0ms

Filtered

66 candidates to 95 candidates (-43.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	4	97

Merged error: 0.0b

Counts

97 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow E (+ (* y (- (log z) t)) (* (log 1.0) a)))
0.0b	(* x (pow E (+ (* y (- (log z) t)) (* (log 1.0) a))))
0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
14×	`add-cube-cbrt` `associate-r`
13×	`add-exp-log`
9×	`pow1` `log-prod` `associate--l+`
8×	`add-cbrt-cube`
7×	`unpow-prod-down`
6×	`associate-l`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `add-log-exp`
4×	`pow-exp` `distribute-lft-out--` `unswap-sqr`
3×	`sub-neg` `pow-unpow` `sqr-pow`
2×	`unpow-prod-up` `pow-to-exp` `e-exp-1` `flip3--` `associate-r/` `log-pow` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`pow-pow` `diff-log` `pow-prod-down`

Counts

4 → 97

Calls

4 calls:

6.0ms	(pow E (+ (* y (- (log z) t)) (* (log 1.0) a)))
6.0ms	(* x (pow E (+ (* y (- (log z) t)) (* (log 1.0) a))))
4.0ms	(- (log z) t)
7.0ms	(* y (- (log z) t))

series92.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow E (+ (* y (- (log z) t)) (* (log 1.0) a)))
45.0ms	(* x (pow E (+ (* y (- (log z) t)) (* (log 1.0) a))))
9.0ms	(- (log z) t)
13.0ms	(* y (- (log z) t))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	415	813
1	1560	742
2	5002	712

prune125.0ms

Filtered

71 candidates to 109 candidates (-53.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Merged error: 0.0b

Counts

113 → 4

regimes551.0ms

Accuracy

53.1% (7.5b remaining)

Error of 7.6b against oracle of 0.1b and baseline of 16.1b

bsearch364.0ms

Steps

Iters	Range		Point
6	5.2166811733135343e-73	2.1648507840991104e-72	2.1465531428141075e-72
9	-6.580007695244171e+62	-1.7470351819595298e+56	-2.2357795218145826e+57

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	19
1	68	19
2	80	19
3	90	19
4	90	19

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.0s	41543×	body	80	nan
1.0s	12577×	body	80	valid
151.0ms	353×	body	640	valid
118.0ms	438×	body	320	valid
60.0ms	73×	body	1280	valid
43.0ms	255×	body	160	valid

Details

sample231.0ms

simplify37.0ms

prune5.0ms

localize16.0ms

rewrite29.0ms

series68.0ms

simplify62.0ms

prune173.0ms

localize22.0ms

rewrite53.0ms

series148.0ms

simplify98.0ms

prune277.0ms

localize12.0ms

rewrite52.0ms

series99.0ms

simplify109.0ms

prune138.0ms

localize15.0ms

rewrite25.0ms

series92.0ms

simplify48.0ms

prune125.0ms

regimes551.0ms

bsearch364.0ms

simplify3.0ms

end0.0ms

sample7.9s

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