Details

sample217.0ms

Algorithm

intervals

Results

64.0ms	72×	body	2560	valid
61.0ms	118×	body	1280	valid
55.0ms	55×	body	10240	exit
9.0ms	32×	body	640	valid
6.0ms	311×	pre	80	true
3.0ms	15×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	3×	body	160	valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.8b	(- (exp (* b eps)) 1.0)
3.4b	(- (exp (* a eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

24.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series166.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune347.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 47.4b

localize32.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.5b	(- (exp (* (+ a b) eps)) 1.0)
12.4b	(* (pow eps 2) (pow b 2))
15.2b	(* (pow eps 3) (pow b 3))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`add-log-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1`
3×	`sum-log`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

34.0ms	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))
11.0ms	(* (pow eps 3) (pow b 3))

series430.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))
61.0ms	(* (pow eps 3) (pow b 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	510	927
1	2493	815
2	5002	772

prune544.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 47.2b

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* a eps)) 1.0)
3.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.5b	(- (exp (* (+ a b) eps)) 1.0)
12.4b	(* (pow eps 2) (pow b 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
8×	`add-cube-cbrt` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `associate-*l/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 110

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
24.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
6.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))

series982.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (exp (* a eps)) 1.0)
865.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))

simplify110.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	738	1419
1	4138	1141
2	5001	1141

prune425.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

16.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify69.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90

prune34.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes81.0ms

Accuracy

0% (3.0b remaining)

Error of 3.5b against oracle of 0.5b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2546×	body	2560	valid
1.7s	1962×	body	10240	exit
1.7s	3434×	body	1280	valid
292.0ms	1050×	body	640	valid
172.0ms	9966×	pre	80	true
70.0ms	370×	body	320	valid
25.0ms	470×	body	80	valid
16.0ms	134×	body	160	valid