Details

sample264.0ms

Algorithm

intervals

Results

102.0ms	96×	body	2560	valid
61.0ms	100×	body	1280	valid
58.0ms	57×	body	10240	exit
11.0ms	31×	body	640	valid
8.0ms	313×	pre	80	overflowed
3.0ms	12×	body	320	valid
1.0ms	11×	body	80	valid
1.0ms	6×	body	160	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 61.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.5b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* a eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite50.0ms

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:

31.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series167.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
37.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (52.0ms)

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

prune485.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 47.9b

localize32.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
5.9b	(- (exp (* (+ a b) eps)) 1.0)
16.1b	(* (pow a 2) (pow eps 2))
18.8b	(* (pow a 3) (pow eps 3))

rewrite50.0ms

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` `associate-*r/` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `pow-prod-down` `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)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))
12.0ms	(* (pow a 3) (pow eps 3))

series920.0ms

Counts

4 → 12

Calls

4 calls:

770.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow a 2) (pow eps 2))
67.0ms	(* (pow a 3) (pow eps 3))

simplify134.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	790	1822
1	4490	1421
2	5001	1416

prune734.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

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:

17.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify68.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (12.0ms)

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

prune81.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
0.6b	(cbrt (/ 1 b))
0.6b	(cbrt (/ 1 b))
0.6b	(cbrt (/ 1 b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 161

Calls

4 calls:

18.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
2.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))

series737.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
178.0ms	(cbrt (/ 1 b))
177.0ms	(cbrt (/ 1 b))
181.0ms	(cbrt (/ 1 b))

simplify42.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	223	1172
1	902	1064
2	5001	904

prune351.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (3.4b remaining)

Error of 3.6b against oracle of 0.1b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample7.7s

Algorithm

intervals

Results

2.7s	2547×	body	2560	valid
2.0s	3430×	body	1280	valid
1.9s	1915×	body	10240	exit
370.0ms	1023×	body	640	valid
249.0ms	9919×	pre	80	overflowed
100.0ms	378×	body	320	valid
49.0ms	479×	body	80	valid
27.0ms	147×	body	160	valid