Details

sample223.0ms

Algorithm

intervals

Results

79.0ms	84×	body	2560	valid
60.0ms	120×	body	1280	valid
53.0ms	60×	body	10240	exit
8.0ms	29×	body	640	valid
5.0ms	316×	pre	80	true
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	valid
0.0ms	4×	body	160	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.1b

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)))
2.2b	(- (exp (* a eps)) 1.0)
2.8b	(- (exp (* b eps)) 1.0)
4.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite34.0ms

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:

16.0ms	(/ (* 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)

series315.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
34.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (60.0ms)

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

prune423.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:

12.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify67.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (11.0ms)

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

prune86.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 167

Calls

4 calls:

33.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
82.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
259.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
86.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	402	1859
1	1619	1609
2	5002	1449

prune332.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))
2.7b	(exp (log (+ (/ 1 b) (/ 1 a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
21×	`times-frac`
15×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`distribute-lft-out`
13×	`fma-def`
10×	`log-prod` `exp-sum`
9×	`div-inv`
4×	`exp-prod` `add-log-exp`
3×	`pow1` `log-div` `exp-diff`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `log-pow` `rem-exp-log`

Counts

2 → 61

Calls

2 calls:

13.0ms	(+ (/ 1 b) (/ 1 a))
13.0ms	(exp (log (+ (/ 1 b) (/ 1 a))))

series21.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(+ (/ 1 b) (/ 1 a))
10.0ms	(exp (log (+ (/ 1 b) (/ 1 a))))

simplify150.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	175	266
1	528	241
2	1424	228
3	4002	222
4	5001	222

prune121.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes79.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b 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	2554×	body	2560	valid
1.7s	1965×	body	10240	exit
1.7s	3472×	body	1280	valid
293.0ms	1040×	body	640	valid
172.0ms	9966×	pre	80	true
67.0ms	357×	body	320	valid
28.0ms	460×	body	80	valid
14.0ms	118×	body	160	valid