Details

sample23.0ms

Algorithm

intervals

Results

10.0ms	266×	body	80	valid
1.0ms	4×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	1280	valid
0.0ms	2×	body	160	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ t y))
0.1b	(- (tanh (/ t y)) (tanh (/ x y)))
0.5b	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))

rewrite39.0ms

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:

1.0ms	(tanh (/ t y))
10.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
0.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
23.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(tanh (/ t y))
220.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
245.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
222.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (49.0ms)

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

prune363.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b	(* z (+ (- (* (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y)))) (tanh (/ x y))) (* (tanh (/ x y)) (+ (- 1) 1))))
6.5b	(cbrt (tanh (/ t y)))
6.5b	(cbrt (tanh (/ t y)))
6.5b	(cbrt (tanh (/ t y)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

4761×	`cbrt-div`
3819×	`frac-times`
2980×	`associate-*r/`
2853×	`tanh-def`
2101×	`frac-add`
2079×	`frac-sub`
1464×	`associate-*l/`
765×	`flip3-+` `flip-+`
11×	`add-sqr-sqrt` `flip3--` `flip--`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 2173

Calls

4 calls:

657.0ms	(* z (+ (- (* (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y)))) (tanh (/ x y))) (* (tanh (/ x y)) (+ (- 1) 1))))
1.0ms	(cbrt (tanh (/ t y)))
1.0ms	(cbrt (tanh (/ t y)))
1.0ms	(cbrt (tanh (/ t y)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* z (+ (- (* (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y)))) (tanh (/ x y))) (* (tanh (/ x y)) (+ (- 1) 1))))
167.0ms	(cbrt (tanh (/ t y)))
165.0ms	(cbrt (tanh (/ t y)))
170.0ms	(cbrt (tanh (/ t y)))

simplify1.4s

Algorithm

egg-herbie

Counts

2185 → 2185

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	8512	176236

prune25.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)) (cbrt (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)))
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
54×	`add-cube-cbrt` `prod-diff`
33×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
27×	`frac-sub`
21×	`associate-r`
18×	`tanh-def`
17×	`pow1`
16×	`cbrt-prod`
15×	`associate-l`
12×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`unswap-sqr`
6×	`sub-neg` `pow1/3` `swap-sqr`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 207

Calls

4 calls:

5.0ms	(* (cbrt (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)) (cbrt (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)))
23.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
23.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
28.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

series1.2s

Counts

4 → 12

Calls

4 calls:

541.0ms	(* (cbrt (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)) (cbrt (fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)))
220.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
213.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
217.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	562	3636
1	2366	2804
2	5001	2705

prune684.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ t y))
0.0b	(tanh (/ x y))
0.1b	(- (tanh (/ t y)) (tanh (/ x y)))
5.7b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

1.0ms	(tanh (/ t y))
1.0ms	(tanh (/ x y))
7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
25.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(tanh (/ t y))
83.0ms	(tanh (/ x y))
220.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
159.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	650	1841
1	2880	1440
2	5002	1437

prune356.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes138.0ms

Accuracy

0% (1.6b remaining)

Error of 2.2b against oracle of 0.5b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

sample590.0ms

Algorithm

intervals

Results

331.0ms	8344×	body	80	valid
18.0ms	119×	body	640	valid
10.0ms	46×	body	1280	valid
8.0ms	69×	body	320	valid
2.0ms	28×	body	160	valid