Details

sample251.0ms

Algorithm

intervals

Results

98.0ms	116×	body	1280	valid
93.0ms	73×	body	2560	valid
19.0ms	37×	body	640	valid
10.0ms	70×	body	80	overflowed
8.0ms	326×	pre	80	true
4.0ms	10×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	4×	body	160	valid

simplify105.0ms

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: 59.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.9b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite49.0ms

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

series168.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
33.0ms	(- (exp (* a eps)) 1.0)
36.0ms	(- (exp (* b 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

prune460.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.5b

localize33.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
12.6b	(* (pow a 2) (pow eps 2))
15.2b	(* (pow a 3) (pow eps 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 170

Calls

4 calls:

5.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))
12.0ms	(* (pow a 3) (pow eps 3))

series181.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (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))

simplify94.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	564	1114
1	2481	873
2	5002	825

prune738.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.3b	(fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
12.6b	(* (pow a 2) (pow eps 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))

series207.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
33.0ms	(- (exp (* b eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow a 2) (pow eps 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	456	966
1	1756	697
2	5002	686

prune575.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 48.7b

localize31.0ms

Local error

Found 4 expressions with local error:

2.3b	(fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2)) (pow (cbrt eps) 2)) (* a eps)))
3.0b	(- (exp (* b eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)
11.5b	(* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`add-exp-log`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`unswap-sqr`
15×	`prod-exp`
12×	`unpow-prod-down`
10×	`pow-exp` `unpow2` `sqr-pow`
8×	`associate-l` `add-log-exp`
7×	`pow-to-exp`
6×	`fma-neg` `associate-r` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 120

Calls

4 calls:

0.0ms	(fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2)) (pow (cbrt eps) 2)) (* a eps)))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2))

series307.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2)) (pow (cbrt eps) 2)) (* a eps)))
37.0ms	(- (exp (* b eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
114.0ms	(* (pow a 2) (pow (* (cbrt eps) (cbrt eps)) 2))

simplify62.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	500	1185
1	1895	932
2	5002	901

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.7b

regimes268.0ms

Accuracy

48.1% (4.3b remaining)

Error of 53.3b against oracle of 49.0b and baseline of 57.2b

bsearch392.0ms

Steps

Iters	Range		Point
9	1.64577538054275e-40	6.465754957999803e-34	7.604732750432952e-35
9	-3.2189945075889483e+120	-1.936652528360916e+115	-2.140357494799946e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	54
1	65	54

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.5s	2586×	body	2560	valid
2.7s	3461×	body	1280	valid
548.0ms	1023×	body	640	valid
283.0ms	2044×	body	80	overflowed
230.0ms	10045×	pre	80	true
136.0ms	355×	body	320	valid
65.0ms	450×	body	80	valid
33.0ms	126×	body	160	valid