Details

sample35.0ms

Algorithm

intervals

Results

21.0ms	265×	body	80	valid
1.0ms	7×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify79.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (tanh (/ t y)) (tanh (/ x y)))
0.0b	(tanh (/ x y))
0.9b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
1.4b	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

rewrite36.0ms

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:

7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
1.0ms	(tanh (/ x y))
23.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
0.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

series771.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
80.0ms	(tanh (/ x y))
214.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
255.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	560	1798
1	2257	1400
2	5001	1397

prune365.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y)))))
1.1b	(* z (- (tanh (/ x y))))
1.4b	(fma y (+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y))))) x)
1.5b	(* 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:

7.0ms	(+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y)))))
8.0ms	(* z (- (tanh (/ x y))))
0.0ms	(fma y (+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y))))) x)
5.0ms	(* z (tanh (/ t y)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y)))))
89.0ms	(* z (- (tanh (/ x y))))
241.0ms	(fma y (+ (* z (tanh (/ t y))) (* z (- (tanh (/ x y))))) x)
90.0ms	(* z (tanh (/ t y)))

simplify70.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (61.0ms)

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

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (tanh (/ t y)) (tanh (/ x y)))
0.0b	(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
0.0b	(tanh (/ x y))
6.3b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

45×	`prod-diff`
41×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+r+` `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-def` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `diff-log` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 142

Calls

4 calls:

7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
6.0ms	(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
1.0ms	(tanh (/ x y))
29.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
334.0ms	(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
76.0ms	(tanh (/ x y))
160.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify93.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	771	2264
1	3331	1740
2	5002	1733

prune418.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (tanh (/ t y)) 3)
0.3b	(* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
1.4b	(fma y (/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y)))))) x)
10.4b	(/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

6780×	`frac-add`
6093×	`frac-times`
5429×	`tanh-def`
3407×	`associate-/r/`
2053×	`associate-*r/`
2031×	`associate-*l/`
288×	`prod-diff`
181×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
159×	`unpow-prod-down` `cube-prod`
155×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
57×	`sqr-pow`
49×	`cube-mult` `unpow3`
39×	`cube-div`
25×	`associate-r`
18×	`frac-sub`
16×	`flip3-+` `flip-+` `difference-of-squares`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/`
7×	`pow1`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod`
1×	`difference-cubes` `pow-to-exp` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `div-inv` `associate-/l` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 3824

Calls

4 calls:

2.0ms	(pow (tanh (/ t y)) 3)
96.0ms	(* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
0.0ms	(fma y (/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y)))))) x)
372.0ms	(/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

series7.4s

Counts

4 → 12

Calls

4 calls:

123.0ms	(pow (tanh (/ t y)) 3)
945.0ms	(* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
2.7s	(fma y (/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y)))))) x)
3.6s	(/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

simplify2.3s

Algorithm

egg-herbie

Counts

3836 → 3836

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	13729	299934

prune38.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

regimes204.0ms

Accuracy

70.1% (1.4b remaining)

Error of 1.8b against oracle of 0.4b and baseline of 5.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	43
1	43	43
2	44	43
3	44	43

end0.0ms

sample965.0ms

Algorithm

intervals

Results

667.0ms	8339×	body	80	valid
25.0ms	80×	body	640	valid
23.0ms	53×	body	1280	valid
13.0ms	62×	body	320	valid
5.0ms	37×	body	160	valid