Details

sample230.0ms

Algorithm

intervals

Results

82.0ms	90×	body	2560	valid
62.0ms	64×	body	10240	exit
46.0ms	93×	body	1280	valid
11.0ms	31×	body	640	valid
5.0ms	320×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	29×	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: 57.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite109.0ms

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:

68.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series175.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
34.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
53.0ms	(- (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

prune329.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* eps b)) 1.0) (- (exp (* a eps)) 1.0))
2.3b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* eps b)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite111.0ms

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:

69.0ms	(* (- (exp (* eps b)) 1.0) (- (exp (* a eps)) 1.0))
12.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* eps b)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

series171.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- (exp (* eps b)) 1.0) (- (exp (* a eps)) 1.0))
34.0ms	(- (exp (* a eps)) 1.0)
34.0ms	(- (exp (* eps b)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	339	733
1	1373	674
2	5001	672

prune298.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 48.2b

localize25.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (exp (* eps b)) 1.0)
2.8b	(- (exp (* eps b)) 1.0)
2.8b	(- (exp (* eps b)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

15.0ms	(- (exp (* eps b)) 1.0)
12.0ms	(- (exp (* eps b)) 1.0)
12.0ms	(- (exp (* eps b)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

series155.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* eps b)) 1.0)
38.0ms	(- (exp (* eps b)) 1.0)
34.0ms	(- (exp (* eps b)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	170	420
1	477	383
2	1603	378
3	5001	375

prune288.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 48.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (exp a) (* 2 eps))
1.0b	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
2.8b	(- (exp (* eps b)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

5.0ms	(pow (exp a) (* 2 eps))
82.0ms	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
12.0ms	(- (exp (* eps b)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (exp a) (* 2 eps))
76.0ms	(* (+ (- (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (- (exp (* eps b)) 1.0))
33.0ms	(- (exp (* eps b)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	435	855
1	1842	790
2	5001	782

prune410.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 48.0b

regimes187.0ms

Accuracy

52% (5.1b remaining)

Error of 54.8b against oracle of 49.7b and baseline of 60.3b

bsearch343.0ms

Steps

Iters	Range		Point
9	3.9457466347433044e+57	2.543299118628485e+63	3.146231950313865e+60
9	-3.112004471340841e+50	-3.441044939126456e+43	-1.9491922328941345e+49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	55
1	73	55
2	73	55

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2606×	body	2560	valid
1.7s	1981×	body	10240	exit
1.6s	3414×	body	1280	valid
276.0ms	1060×	body	640	valid
148.0ms	9984×	pre	80	true
64.0ms	355×	body	320	valid
28.0ms	448×	body	80	valid
13.0ms	120×	body	160	valid