Details

sample181.0ms

Algorithm

intervals

Results

74.0ms	1324×	body	80	nan
26.0ms	413×	body	80	valid
5.0ms	13×	body	640	valid
2.0ms	3×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify38.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (- (log z) t))
0.3b	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.8b	(log (- 1.0 z))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

12.0ms	(* y (- (log z) t))
50.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
13.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
2.0ms	(log (- 1.0 z))

series471.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* y (- (log z) t))
158.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
198.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
46.0ms	(log (- 1.0 z))

simplify69.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	675	1085
1	2724	1003
2	5001	985

prune431.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite816.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

400.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
12.0ms	(* y (- (log z) t))
301.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
98.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
74.0ms	(* y (- (log z) t))
224.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
248.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify89.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	677	1907
1	3019	1768
2	5001	1757

prune599.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (exp (+ (* t y) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
0.4b	(* (pow z y) (exp (* a (- (log 1.0) b))))
0.5b	(* (/ x (exp (+ (* t y) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))) (* (pow z y) (exp (* a (- (log 1.0) b)))))
6.5b	(* a (pow z 2))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log` `associate-l`
24×	`times-frac`
22×	`associate-r` `add-cbrt-cube`
20×	`prod-exp`
17×	`exp-sum`
8×	`unpow-prod-down` `cbrt-unprod`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate--l+`
5×	`distribute-rgt-in` `distribute-lft-in` `div-exp`
4×	`pow-to-exp` `pow-exp` `associate-/r*` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `-commutative` `associate-/l`
2×	`sub-neg` `div-inv` `unpow2`
1×	`frac-2neg` `pow-prod-down` `associate-*l/` `clear-num`

Counts

4 → 132

Calls

4 calls:

65.0ms	(/ x (exp (+ (* t y) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
16.0ms	(* (pow z y) (exp (* a (- (log 1.0) b))))
222.0ms	(* (/ x (exp (+ (* t y) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))) (* (pow z y) (exp (* a (- (log 1.0) b)))))
6.0ms	(* a (pow z 2))

series636.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ x (exp (+ (* t y) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
135.0ms	(* (pow z y) (exp (* a (- (log 1.0) b))))
346.0ms	(* (/ x (exp (+ (* t y) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))) (* (pow z y) (exp (* a (- (log 1.0) b)))))
32.0ms	(* a (pow z 2))

simplify86.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	601	1799
1	2593	1539
2	5002	1528

prune653.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
0.0b	(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
0.2b	(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
6.5b	(* a (pow z 2))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

13.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
101.0ms	(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
325.0ms	(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
6.0ms	(* a (pow z 2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
53.0ms	(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
89.0ms	(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
31.0ms	(* a (pow z 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	335	842
1	1386	740
2	5002	730

prune305.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes164.0ms

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

sample5.3s

Algorithm

intervals

Results

2.2s	41113×	body	80	nan
785.0ms	12663×	body	80	valid
126.0ms	361×	body	640	valid
87.0ms	406×	body	320	valid
56.0ms	78×	body	1280	valid
34.0ms	258×	body	160	valid