Details

sample175.0ms

Algorithm

intervals

Results

68.0ms	1245×	body	80	nan
26.0ms	395×	body	80	valid
7.0ms	20×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	2×	body	1280	valid
0.0ms	3×	body	160	valid

simplify39.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.1b	(* y (- (log z) t))
1.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.9b	(log (- 1.0 z))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

9.0ms	(* a (- (log (- 1.0 z)) b))
10.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series370.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* a (- (log (- 1.0 z)) b))
71.0ms	(* y (- (log z) t))
183.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
41.0ms	(log (- 1.0 z))

simplify75.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	678	1058
1	2743	995
2	5002	986

prune479.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

15.0ms	(* x (exp (+ (* y (- (log z) t)) (- (* a (log 1.0)) (+ (* a b) (* 1.0 (* a z)))))))
4.0ms	(+ (* a b) (* 1.0 (* a z)))
8.0ms	(* y (- (log z) t))
14.0ms	(+ (* y (- (log z) t)) (- (* a (log 1.0)) (+ (* a b) (* 1.0 (* a z)))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* x (exp (+ (* y (- (log z) t)) (- (* a (log 1.0)) (+ (* a b) (* 1.0 (* a z)))))))
43.0ms	(+ (* a b) (* 1.0 (* a z)))
70.0ms	(* y (- (log z) t))
148.0ms	(+ (* y (- (log z) t)) (- (* a (log 1.0)) (+ (* a b) (* 1.0 (* a z)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	648	1279
1	3012	1167
2	5002	1153

prune419.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a b) (* 1.0 (* a z)))
0.1b	(* y (- (log z) t))
2.7b	(+ (* y (- (log z) t)) (- (* a (log 1.0)) (log (exp (+ (* a b) (* 1.0 (* a z)))))))
3.1b	(log (exp (+ (* a b) (* 1.0 (* a z)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

4.0ms	(+ (* a b) (* 1.0 (* a z)))
10.0ms	(* y (- (log z) t))
15.0ms	(+ (* y (- (log z) t)) (- (* a (log 1.0)) (log (exp (+ (* a b) (* 1.0 (* a z)))))))
4.0ms	(log (exp (+ (* a b) (* 1.0 (* a z)))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* a b) (* 1.0 (* a z)))
72.0ms	(* y (- (log z) t))
151.0ms	(+ (* y (- (log z) t)) (- (* a (log 1.0)) (log (exp (+ (* a b) (* 1.0 (* a z)))))))
43.0ms	(log (exp (+ (* a b) (* 1.0 (* a z)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	569	1085
1	2526	1022
2	5001	1014

prune442.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-log-exp`
13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
8×	`add-cbrt-cube`
7×	`add-exp-log` `associate-l`
6×	`exp-sum`
4×	`diff-log`
3×	`sub-neg` `exp-prod` `associate--l+` `rem-exp-log`
2×	`exp-diff` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `associate-*r/` `log-pow` `flip--`

Counts

4 → 72

Calls

4 calls:

6.0ms	(exp (- (+ (* (log z) y) (* a (log 1.0))) (* t y)))
6.0ms	(- (+ (* (log z) y) (* a (log 1.0))) (* t y))
9.0ms	(* x (exp (- (+ (* (log z) y) (* a (log 1.0))) (* t y))))
4.0ms	(* (log z) y)

series437.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(exp (- (+ (* (log z) y) (* a (log 1.0))) (* t y)))
108.0ms	(- (+ (* (log z) y) (* a (log 1.0))) (* t y))
156.0ms	(* x (exp (- (+ (* (log z) y) (* a (log 1.0))) (* t y))))
63.0ms	(* (log z) y)

simplify152.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	299	699
1	1132	596
2	4817	548
3	5001	548

prune266.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes188.0ms

Accuracy

61.2% (1.8b remaining)

Error of 1.9b against oracle of 0.1b and baseline of 4.8b

bsearch493.0ms

Steps

Iters	Range		Point
11	3.697422422313879e-16	10036.896206933432	39.48835808714443
9	-7.926672511512008e+126	-2.2890933192576946e+117	-7.424562313903535e+126

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	31
1	55	31

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	40219×	body	80	nan
778.0ms	12447×	body	80	valid
142.0ms	403×	body	640	valid
79.0ms	364×	body	320	valid
58.0ms	82×	body	1280	valid
36.0ms	268×	body	160	valid