Details

sample200.0ms

Algorithm

intervals

Results

73.0ms	1348×	body	80	nan
24.0ms	403×	body	80	valid
2.0ms	11×	body	320	valid
2.0ms	5×	body	640	valid
1.0ms	9×	body	160	valid
1.0ms	1×	body	1280	valid

simplify41.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.2b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.3b	(log (- 1.0 z))

rewrite70.0ms

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:

7.0ms	(- (log z) t)
27.0ms	(* y (- (log z) t))
27.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

series411.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (log z) t)
75.0ms	(* y (- (log z) t))
226.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
44.0ms	(log (- 1.0 z))

simplify61.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	593	882
1	2248	832
2	5001	830

prune411.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

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))
0.2b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite801.0ms

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:

7.0ms	(- (log z) t)
607.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
26.0ms	(* y (- (log z) t))
155.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (log z) t)
106.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
78.0ms	(* y (- (log z) t))
245.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify78.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	598	1562
1	2537	1477
2	5002	1473

prune557.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
0.0b	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
0.0b	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
5.9b	(* a (pow z 2))

rewrite775.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`associate-r`
11×	`add-log-exp`
10×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-cbrt-cube`
6×	`pow1` `associate-l`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp` `sum-log`
2×	`+-commutative` `exp-neg` `flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`neg-sub0` `pow-to-exp` `associate-+r+` `distribute-neg-in` `exp-diff` `exp-sum` `pow-prod-down` `pow-exp` `un-div-inv`

Counts

4 → 73

Calls

4 calls:

707.0ms	(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
17.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
37.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
12.0ms	(* a (pow z 2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
89.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
65.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
33.0ms	(* a (pow z 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	362	710
1	1634	626
2	5001	613

prune252.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
0.0b	(/ x (exp (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
0.0b	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
5.9b	(* a (pow z 2))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

17.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
146.0ms	(/ x (exp (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
37.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
12.0ms	(* a (pow z 2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
118.0ms	(/ x (exp (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
70.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
31.0ms	(* a (pow z 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	382	935
1	1790	860
2	5001	860

prune292.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.2s	40450×	body	80	nan
754.0ms	12447×	body	80	valid
120.0ms	357×	body	640	valid
86.0ms	409×	body	320	valid
44.0ms	62×	body	1280	valid
38.0ms	286×	body	160	valid