Details

sample220.0ms

Algorithm

intervals

Results

78.0ms	84×	body	2560	valid
59.0ms	120×	body	1280	valid
52.0ms	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

simplify94.0ms

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: 61.1b

localize16.0ms

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)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
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 → 73

Calls

4 calls:

14.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series308.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
37.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	488	957
1	2299	794
2	5001	789

prune328.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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:

11.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify64.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (26.0ms)

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

prune46.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

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)))

rewrite73.0ms

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×	`add-cbrt-cube` `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 → 159

Calls

4 calls:

29.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
80.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
80.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
81.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	389	1813
1	1557	1563
2	5001	1403

prune310.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
14×	`distribute-lft-out`
12×	`times-frac`
10×	`log-prod` `exp-sum`
8×	`add-sqr-sqrt` `add-cube-cbrt` `div-inv`
4×	`exp-prod` `add-log-exp`
3×	`pow1` `log-div` `exp-diff`
2×	`add-exp-log` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `sum-log` `log-pow` `rem-exp-log`

Counts

2 → 44

Calls

2 calls:

11.0ms	(+ (/ 1 b) (/ 1 a))
12.0ms	(exp (log (+ (/ 1 b) (/ 1 a))))

series20.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify140.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	167	250
1	503	227
2	1300	214
3	3530	206
4	5001	206

prune74.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes81.0ms

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

sample6.7s

Algorithm

intervals

Results

2.5s	2554×	body	2560	valid
1.7s	1965×	body	10240	exit
1.7s	3472×	body	1280	valid
282.0ms	1040×	body	640	valid
165.0ms	9966×	pre	80	true
64.0ms	357×	body	320	valid
24.0ms	460×	body	80	valid
14.0ms	118×	body	160	valid