Details

sample208.0ms

Algorithm

intervals

Results

80.0ms	85×	body	2560	valid
51.0ms	108×	body	1280	valid
40.0ms	48×	body	10240	exit
7.0ms	26×	body	640	valid
6.0ms	304×	pre	80	true
3.0ms	14×	body	320	valid
1.0ms	18×	body	80	valid
1.0ms	5×	body	160	valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.7b	(- (exp (* a eps)) 1.0)
3.5b	(- (exp (* b eps)) 1.0)
4.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 117

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series307.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
33.0ms	(- (exp (* a eps)) 1.0)
30.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	608	1462
1	2778	1079
2	5002	1072

prune429.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

14.0ms

(+ (/ 1 b) (/ 1 a))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(+ (/ 1 b) (/ 1 a))

simplify71.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune88.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize4.0ms

Local error

Found 1 expressions with local error:

15.0b

(/ (+ b a) (* b a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

7.0ms

(/ (+ b a) (* b a))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(/ (+ b a) (* b a))

simplify50.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	149	142
1	531	120
2	2110	120
3	5001	120

prune67.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ b a) a)
6.5b	(* (/ 1 b) (/ (+ b a) a))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`times-frac`
26×	`add-exp-log` `add-cube-cbrt`
16×	`associate-r` `add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp`
7×	`distribute-lft-out`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`pow1` `cbrt-unprod` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip-+`

Counts

2 → 96

Calls

2 calls:

6.0ms	(/ (+ b a) a)
14.0ms	(* (/ 1 b) (/ (+ b a) a))

series56.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(/ (+ b a) a)
35.0ms	(* (/ 1 b) (/ (+ b a) a))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	402	559
1	2036	499
2	5001	482

prune169.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes150.0ms

Accuracy

93.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	46
1	50	46

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2604×	body	2560	valid
1.7s	1968×	body	10240	exit
1.6s	3383×	body	1280	valid
283.0ms	1033×	body	640	valid
166.0ms	9970×	pre	80	true
67.0ms	374×	body	320	valid
25.0ms	463×	body	80	valid
17.0ms	145×	body	160	valid