Details

sample214.0ms

Algorithm

intervals

Results

64.0ms	72×	body	2560	valid
58.0ms	55×	body	10240	exit
57.0ms	118×	body	1280	valid
9.0ms	32×	body	640	valid
5.0ms	311×	pre	80	true
3.0ms	15×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	3×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.8b	(- (exp (* b eps)) 1.0)
3.4b	(- (exp (* a eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite48.0ms

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:

29.0ms	(* (- (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)

series169.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
38.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (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

prune474.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 47.4b

localize31.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))
4.5b	(- (exp (* (+ a b) eps)) 1.0)
12.4b	(* (pow eps 2) (pow b 2))
15.2b	(* (pow eps 3) (pow b 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

0.0ms	(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)
9.0ms	(* (pow eps 2) (pow b 2))
11.0ms	(* (pow eps 3) (pow b 3))

series254.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))
67.0ms	(* (pow eps 3) (pow b 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	492	1008
1	2299	829
2	5002	783

prune675.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 47.2b

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* a eps)) 1.0)
3.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
4.5b	(- (exp (* (+ a b) eps)) 1.0)
12.4b	(* (pow eps 2) (pow b 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`add-exp-log`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff` `add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
10×	`unpow2` `sqr-pow`
8×	`associate-r` `associate-l` `add-log-exp`
6×	`pow-to-exp` `fma-neg` `pow-exp`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

5.0ms	(- (exp (* a eps)) 1.0)
22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (exp (* a eps)) 1.0)
889.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))

simplify105.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	706	1575
1	3575	1200
2	5002	1191

prune518.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

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:

16.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify71.0ms

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	5002	98

prune70.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes96.0ms

Accuracy

0% (3.2b remaining)

Error of 3.5b against oracle of 0.3b 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	2546×	body	2560	valid
1.7s	1962×	body	10240	exit
1.7s	3434×	body	1280	valid
291.0ms	1050×	body	640	valid
168.0ms	9966×	pre	80	true
68.0ms	370×	body	320	valid
25.0ms	470×	body	80	valid
18.0ms	134×	body	160	valid