Details

sample254.0ms

Algorithm

intervals

Results

94.0ms	116×	body	1280	valid
93.0ms	73×	body	2560	valid
19.0ms	37×	body	640	valid
13.0ms	326×	pre	80	true
10.0ms	70×	body	80	overflowed
4.0ms	10×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	4×	body	160	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: 59.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.9b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite42.0ms

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:

28.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series163.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
39.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune363.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.5b

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
12.6b	(* (pow a 2) (pow eps 2))
15.2b	(* (pow a 3) (pow eps 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

4.0ms	(- (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))

series178.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	470	772
1	2119	679
2	5002	636

prune619.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.7b

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
12.6b	(* (pow a 2) (pow eps 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

23.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
36.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow a 2) (pow eps 2))

simplify63.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	452	731
1	2002	601
2	5003	597

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 48.7b

localize37.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2)) (pow (cbrt eps) 2))) (* a eps)))
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
11.5b	(* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
23×	`add-sqr-sqrt`
16×	`unswap-sqr`
15×	`prod-exp`
13×	`add-log-exp`
12×	`unpow-prod-down`
11×	`*-un-lft-identity`
10×	`pow-exp` `unpow2` `sqr-pow`
8×	`associate-l`
7×	`pow-to-exp` `add-cube-cbrt`
6×	`associate-r` `add-cbrt-cube`
4×	`pow1`
3×	`sum-log`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 93

Calls

4 calls:

80.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2)) (pow (cbrt eps) 2))) (* a eps)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2))

series323.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2)) (pow (cbrt eps) 2))) (* a eps)))
31.0ms	(- (exp (* b eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
113.0ms	(* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2))

simplify70.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	498	988
1	2175	877
2	5001	860

prune549.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.7b

regimes270.0ms

Accuracy

48.1% (4.3b remaining)

Error of 53.3b against oracle of 49.0b and baseline of 57.2b

bsearch548.0ms

Steps

Iters	Range		Point
9	1.64577538054275e-40	6.465754957999803e-34	7.604732750432952e-35
9	-3.2189945075889483e+120	-1.936652528360916e+115	-2.140357494799946e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	58
1	81	58
2	81	58

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.5s	2586×	body	2560	valid
2.7s	3461×	body	1280	valid
538.0ms	1023×	body	640	valid
287.0ms	2044×	body	80	overflowed
233.0ms	10045×	pre	80	true
141.0ms	355×	body	320	valid
64.0ms	450×	body	80	valid
33.0ms	126×	body	160	valid