Details

sample42.0ms

Algorithm

intervals

Results

23.0ms	385×	body	80	valid
0.0ms	1×	body	320	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (40.0ms)

Iter	Nodes	Cost
0	38	10
1	118	9
2	428	9
3	1763	9
4	5002	8

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- t 1.0) a)
0.0b	(fma b (- (+ y t) 2.0) x)
0.0b	(- (fma b (- (+ y t) 2.0) x) (* (- t 1.0) a))
0.0b	(- (+ y t) 2.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`prod-diff`
11×	`add-log-exp`
7×	`fma-neg`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-l` `distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r` `flip--` `distribute-lft-out--`
2×	`sub-neg` `associate-*l/` `associate--l+` `fma-udef` `difference-of-squares`
1×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

6.0ms	(* (- t 1.0) a)
1.0ms	(fma b (- (+ y t) 2.0) x)
3.0ms	(- (fma b (- (+ y t) 2.0) x) (* (- t 1.0) a))
7.0ms	(- (+ y t) 2.0)

series169.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- t 1.0) a)
48.0ms	(fma b (- (+ y t) 2.0) x)
77.0ms	(- (fma b (- (+ y t) 2.0) x) (* (- t 1.0) a))
17.0ms	(- (+ y t) 2.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	356	607
1	1267	472
2	5002	469

prune383.0ms

Filtered

102 candidates to 71 candidates (69.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Merged error: 0.0b

Counts

103 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- 1.0 y) z (- (fma b y (fma b t x)) (* (- t 1.0) a)))
0.0b	(* (- t 1.0) a)
0.0b	(fma b y (fma b t x))
0.0b	(- (fma b y (fma b t x)) (* (- t 1.0) a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `fma-udef`
2×	`flip3--` `associate-*l/` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

1.0ms	(fma (- 1.0 y) z (- (fma b y (fma b t x)) (* (- t 1.0) a)))
6.0ms	(* (- t 1.0) a)
1.0ms	(fma b y (fma b t x))
3.0ms	(- (fma b y (fma b t x)) (* (- t 1.0) a))

series289.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(fma (- 1.0 y) z (- (fma b y (fma b t x)) (* (- t 1.0) a)))
32.0ms	(* (- t 1.0) a)
41.0ms	(fma b y (fma b t x))
74.0ms	(- (fma b y (fma b t x)) (* (- t 1.0) a))

simplify33.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	246	432
1	901	381
2	5001	370

prune216.0ms

Filtered

77 candidates to 62 candidates (80.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0.0b

Counts

79 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma b (/ (- (* (+ y t) (+ y t)) (* 2.0 2.0)) (+ (+ y t) 2.0)) x) (* (- t 1.0) a))
0.0b	(- (* (+ y t) (+ y t)) (* 2.0 2.0))
0.0b	(* (+ y t) (+ y t))
10.2b	(/ (- (* (+ y t) (+ y t)) (* 2.0 2.0)) (+ (+ y t) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `distribute-lft-out`
20×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`flip3-+` `flip-+` `difference-of-squares`
6×	`swap-sqr`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-times` `fma-neg` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u` `associate-/l*`
3×	`flip3--` `associate--l+` `flip--`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

3.0ms	(- (fma b (/ (- (* (+ y t) (+ y t)) (* 2.0 2.0)) (+ (+ y t) 2.0)) x) (* (- t 1.0) a))
12.0ms	(- (* (+ y t) (+ y t)) (* 2.0 2.0))
9.0ms	(* (+ y t) (+ y t))
16.0ms	(/ (- (* (+ y t) (+ y t)) (* 2.0 2.0)) (+ (+ y t) 2.0))

series295.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(- (fma b (/ (- (* (+ y t) (+ y t)) (* 2.0 2.0)) (+ (+ y t) 2.0)) x) (* (- t 1.0) a))
34.0ms	(- (* (+ y t) (+ y t)) (* 2.0 2.0))
14.0ms	(* (+ y t) (+ y t))
52.0ms	(/ (- (* (+ y t) (+ y t)) (* 2.0 2.0)) (+ (+ y t) 2.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	586	1327
1	2712	1208
2	5002	1198

prune395.0ms

Filtered

142 candidates to 96 candidates (67.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	142	2	144

Merged error: 0.0b

Counts

144 → 2

regimes148.0ms

Accuracy

63.8% (2.5b remaining)

Error of 2.5b against oracle of 0.0b and baseline of 6.8b

bsearch124.0ms

Steps

Iters	Range		Point
7	4.2630856627807317e+21	9.378010696681881e+22	4.212055861749654e+22
6	-4.775231863886843e+117	-9.453160545365133e+116	-1.0750263452155605e+117

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

668.0ms	12492×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid