Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

283×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	5
1	36	4
2	59	4
3	103	4
4	173	4
5	236	4
6	265	4
7	311	4
8	375	4
9	511	4
10	674	4
11	1179	4
12	1300	4
13	1308	4
14	1308	4

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
2.1b	(* y (/ (- z t) (- a t)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `flip3--` `fma-def` `associate-l` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 122

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- a t))))
12.0ms	(/ (- z t) (- a t))
25.0ms	(* y (/ (- z t) (- a t)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(+ x (* y (/ (- z t) (- a t))))
47.0ms	(/ (- z t) (- a t))
68.0ms	(* y (/ (- z t) (- a t)))

simplify52.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	433	776
1	1705	730
2	5002	730

prune321.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (- (/ z (- a t)) (/ t (- a t)))))
0.0b	(/ z (- a t))
0.0b	(/ t (- a t))
2.1b	(* y (- (/ z (- a t)) (/ t (- a t))))

rewrite654.0ms

Algorithm

rewrite-expression-head

Rules

2591×	`*-un-lft-identity`
2583×	`add-sqr-sqrt`
2568×	`times-frac`
1764×	`prod-diff`
1541×	`add-cube-cbrt`
886×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
524×	`distribute-lft-out--`
518×	`difference-of-squares`
344×	`associate-/r/`
173×	`flip3--` `flip--`
172×	`div-inv`
18×	`associate-r`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u`
3×	`distribute-rgt-out--` `fma-def` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `sub-div` `unswap-sqr`

Counts

4 → 1905

Calls

4 calls:

137.0ms	(+ x (* y (- (/ z (- a t)) (/ t (- a t)))))
5.0ms	(/ z (- a t))
5.0ms	(/ t (- a t))
236.0ms	(* y (- (/ z (- a t)) (/ t (- a t))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ x (* y (- (/ z (- a t)) (/ t (- a t)))))
28.0ms	(/ z (- a t))
46.0ms	(/ t (- a t))
87.0ms	(* y (- (/ z (- a t)) (/ t (- a t))))

simplify442.0ms

Algorithm

egg-herbie

Counts

1917 → 1917

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	3351	49171
1	5001	44380

prune5.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ z (- a t))
0.0b	(log1p (expm1 (/ t (- a t))))
0.0b	(/ t (- a t))
2.1b	(* y (- (/ z (- a t)) (log1p (expm1 (/ t (- a t))))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
176×	`*-un-lft-identity`
126×	`prod-diff`
122×	`add-cube-cbrt`
121×	`times-frac`
65×	`distribute-rgt-in` `distribute-lft-in`
28×	`difference-of-squares`
27×	`distribute-lft-out--`
16×	`associate-/r/`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`flip3--` `flip--`
8×	`div-inv`
6×	`pow1` `associate-r` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `associate-*r/` `div-exp` `clear-num`
1×	`log1p-udef` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 244

Calls

4 calls:

5.0ms	(/ z (- a t))
0.0ms	(log1p (expm1 (/ t (- a t))))
5.0ms	(/ t (- a t))
86.0ms	(* y (- (/ z (- a t)) (log1p (expm1 (/ t (- a t))))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ z (- a t))
106.0ms	(log1p (expm1 (/ t (- a t))))
50.0ms	(/ t (- a t))
122.0ms	(* y (- (/ z (- a t)) (log1p (expm1 (/ t (- a t))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	621	5643
1	2181	3130
2	5001	2734

prune489.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
2.1b	(* y (fma 1 (/ z (- a t)) (- (* (/ t (cbrt (- a t))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t))))))))
53.8b	(fma (- (/ t (cbrt (- a t)))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ t (cbrt (- a t))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
3.0ms	(* y (fma 1 (/ z (- a t)) (- (* (/ t (cbrt (- a t))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t))))))))
0.0ms	(fma (- (/ t (cbrt (- a t)))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ t (cbrt (- a t))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t))))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (- a t))
160.0ms	(cbrt (- a t))
91.0ms	(* y (fma 1 (/ z (- a t)) (- (* (/ t (cbrt (- a t))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t))))))))
398.0ms	(fma (- (/ t (cbrt (- a t)))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ t (cbrt (- a t))) (/ 1 (* (cbrt (- a t)) (cbrt (- a t))))))

simplify123.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	291	944
1	909	826
2	4473	774
3	5001	744

prune409.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes143.0ms

Accuracy

0% (1.4b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample538.0ms

Algorithm

intervals

Results

277.0ms	8738×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid