Details

sample282.0ms

Algorithm

intervals

Results

123.0ms	89×	body	2560	valid
95.0ms	118×	body	1280	valid
15.0ms	82×	body	80	overflowed
13.0ms	23×	body	640	valid
8.0ms	338×	pre	80	true
5.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	9×	body	80	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: 61.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.5b	(- (exp (* a eps)) 1.0)
4.1b	(- (exp (* b eps)) 1.0)
6.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

27.0ms	(* (- (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)

series164.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216

prune452.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 50.8b

localize27.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
6.3b	(- (exp (* (+ a b) eps)) 1.0)
12.9b	(* (pow eps 2) (pow b 2))
14.5b	(* (pow eps 3) (pow b 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
23×	`*-un-lft-identity`
22×	`prod-exp`
21×	`add-cube-cbrt`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

18.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
11.0ms	(* (pow eps 2) (pow b 2))
12.0ms	(* (pow eps 3) (pow b 3))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
64.0ms	(* (pow eps 3) (pow b 3))

simplify148.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	785	1762
1	4542	1404
2	5001	1399

prune707.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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:

20.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify66.0ms

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

prune79.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 1 expressions with local error:

13.6b

(/ (+ b a) (* b a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

9.0ms

(/ (+ b a) (* b a))

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(/ (+ b a) (* b a))

simplify46.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	149	142
1	531	120
2	2110	120
3	5001	120

prune46.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes69.0ms

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

sample8.0s

Algorithm

intervals

Results

3.5s	2600×	body	2560	valid
2.8s	3437×	body	1280	valid
569.0ms	1031×	body	640	valid
298.0ms	2007×	body	80	overflowed
242.0ms	10011×	pre	80	true
134.0ms	336×	body	320	valid
70.0ms	463×	body	80	valid
39.0ms	137×	body	160	valid