Details

sample24.0ms

Algorithm

intervals

Results

11.0ms	263×	body	80	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	1280	valid
0.0ms	2×	body	640	valid
0.0ms	3×	body	160	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	54	8
1	146	7
2	337	7
3	1017	7
4	3659	7
5	5001	7

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.9b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ t y))
0.2b	(- (tanh (/ t y)) (tanh (/ x y)))
0.3b	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
0.7b	(* z (- (tanh (/ t y)) (tanh (/ x y))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
18×	`frac-sub`
13×	`tanh-def`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-l`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

2.0ms	(tanh (/ t y))
11.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
1.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
11.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(tanh (/ t y))
221.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
255.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
218.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

simplify64.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	546	1798
1	2180	1400
2	5003	1397

prune360.0ms

Filtered

126 candidates to 87 candidates (69.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	6	128

Merged error: 0.2b

Counts

128 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y)))))
0.3b	(fma y (+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y))))) x)
2.1b	(* z (- (tanh (/ x y))))
2.1b	(* z (tanh (/ t y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*r/`
14×	`add-sqr-sqrt`
13×	`associate-r`
12×	`distribute-neg-frac`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`frac-add`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `tanh-def`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `distribute-rgt-neg-out`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-mul-1` `fma-def` `flip3-+` `unsub-neg` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

8.0ms	(+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y)))))
1.0ms	(fma y (+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y))))) x)
7.0ms	(* z (- (tanh (/ x y))))
5.0ms	(* z (tanh (/ t y)))

series623.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y)))))
247.0ms	(fma y (+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y))))) x)
88.0ms	(* z (- (tanh (/ x y))))
87.0ms	(* z (tanh (/ t y)))

simplify68.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	570	898
1	2499	831
2	5002	827

prune350.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	102	6	108

Merged error: 0.2b

Counts

108 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))) x)
0.0b	(tanh (/ t y))
0.2b	(- (tanh (/ t y)) (tanh (/ x y)))
4.1b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

45×	`prod-diff`
40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
18×	`frac-sub`
13×	`tanh-def`
11×	`associate-*r/`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`sub-neg` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 140

Calls

4 calls:

15.0ms	(+ (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))) x)
2.0ms	(tanh (/ t y))
7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
16.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(+ (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))) x)
82.0ms	(tanh (/ t y))
220.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
160.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify84.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	727	2213
1	3077	1695
2	5002	1674

prune440.0ms

Filtered

152 candidates to 106 candidates (69.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	152	6	158

Merged error: 0.2b

Counts

158 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (* t z) y) (* z (- (tanh (/ x y)))))
2.1b	(* z (- (tanh (/ x y))))
2.9b	(/ (* t z) y)
5.3b	(fma y (+ (/ (* t z) y) (* z (- (tanh (/ x y))))) x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-r`
7×	`fma-def`
6×	`pow1` `times-frac` `associate-*r/` `distribute-neg-frac` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l` `frac-add` `associate-/r*` `distribute-rgt-neg-out`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `tanh-def`
1×	`+-commutative` `neg-mul-1` `frac-2neg` `flip3-+` `unsub-neg` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `associate-/l` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

8.0ms	(+ (/ (* t z) y) (* z (- (tanh (/ x y)))))
7.0ms	(* z (- (tanh (/ x y))))
4.0ms	(/ (* t z) y)
1.0ms	(fma y (+ (/ (* t z) y) (* z (- (tanh (/ x y))))) x)

series531.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(+ (/ (* t z) y) (* z (- (tanh (/ x y)))))
281.0ms	(* z (- (tanh (/ x y))))
19.0ms	(/ (* t z) y)
88.0ms	(fma y (+ (/ (* t z) y) (* z (- (tanh (/ x y))))) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	438	598
1	1923	540
2	5001	535

prune281.0ms

Filtered

101 candidates to 80 candidates (79.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	101	6	107

Merged error: 0.2b

Counts

107 → 6

regimes150.0ms

Accuracy

40.4% (2.6b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 4.5b

bsearch89.0ms

Steps

Iters	Range		Point
8	6.941549984938914e+136	1.8229199781597628e+139	1.378183989815973e+137
9	-1.3746948083644196e+255	-2.926307827355199e+247	-2.9957314611234766e+247

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample595.0ms

Algorithm

intervals

Results

334.0ms	8278×	body	80	valid
14.0ms	92×	body	640	valid
8.0ms	39×	body	1280	valid
8.0ms	74×	body	320	valid
3.0ms	35×	body	160	valid