Details

sample220.0ms

Algorithm

intervals

Results

70.0ms	70×	body	2560	valid
60.0ms	125×	body	1280	valid
54.0ms	58×	body	10240	exit
10.0ms	37×	body	640	valid
5.0ms	314×	pre	80	true
3.0ms	14×	body	320	valid
1.0ms	10×	body	80	valid

simplify96.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.0b	(- (exp (* b eps)) 1.0)
3.6b	(- (exp (* a eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite38.0ms

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)

series167.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
33.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

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

prune326.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.7b

localize31.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
5.1b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 3))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
25×	`associate-r`
23×	`associate-l`
20×	`*-un-lft-identity` `sqr-pow`
19×	`prod-exp`
16×	`add-cube-cbrt`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`add-cbrt-cube` `unpow2`
6×	`pow1` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`
2×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 156

Calls

4 calls:

130.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))
11.0ms	(* (pow a 3) (pow eps 3))

series263.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
66.0ms	(* (pow a 3) (pow eps 3))

simplify123.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	674	1563
1	3675	1373
2	5002	1366

prune636.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.4b

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
2.7b	(* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
5.1b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow a 2) (pow eps 2))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

35.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
102.0ms	(* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))

series960.0ms

Counts

4 → 12

Calls

4 calls:

757.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
122.0ms	(* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow a 2) (pow eps 2))

simplify140.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	839	2225
1	4666	1895
2	5001	1895

prune588.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite16.0ms

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))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify67.0ms

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

prune36.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (3.0b remaining)

Error of 3.3b against oracle of 0.3b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2566×	body	2560	valid
1.7s	1920×	body	10240	exit
1.7s	3422×	body	1280	valid
286.0ms	1040×	body	640	valid
172.0ms	9920×	pre	80	true
70.0ms	373×	body	320	valid
23.0ms	445×	body	80	valid
17.0ms	154×	body	160	valid