Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

280×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.3b	(* y (/ (- z t) (- a t)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 106

Calls

2 calls:

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

series119.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- z t) (- a t))
69.0ms	(* y (/ (- z t) (- a t)))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	356	664
1	1414	623
2	5001	623

prune266.0ms

Filtered

112 candidates to 75 candidates (67.0%)

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	(- (/ z (- a t)) (/ t (- a t)))
0.0b	(/ z (- a t))
0.0b	(/ t (- a t))
2.3b	(* y (- (/ z (- a t)) (/ t (- a t))))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

2003×	`*-un-lft-identity`
1985×	`add-sqr-sqrt`
1971×	`times-frac`
1323×	`prod-diff`
1173×	`add-cube-cbrt`
443×	`distribute-rgt-in` `distribute-lft-in`
413×	`distribute-lft-out--`
401×	`difference-of-squares`
266×	`associate-/r/`
135×	`flip3--` `flip--`
133×	`div-inv`
21×	`fma-neg`
18×	`associate-r`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `distribute-rgt-out--` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 1496

Calls

4 calls:

72.0ms	(- (/ z (- a t)) (/ t (- a t)))
5.0ms	(/ z (- a t))
5.0ms	(/ t (- a t))
241.0ms	(* y (- (/ z (- a t)) (/ t (- a t))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (/ z (- a t)) (/ t (- a t)))
30.0ms	(/ z (- a t))
50.0ms	(/ t (- a t))
90.0ms	(* y (- (/ z (- a t)) (/ t (- a t))))

simplify393.0ms

Algorithm

egg-herbie

Counts

1508 → 1508

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2021	47467
1	5001	38512

prune2.8s

Filtered

1508 candidates to 555 candidates (36.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ z (- a t)) (/ 1 (/ (- a t) t)))
0.0b	(/ z (- a t))
0.6b	(/ 1 (/ (- a t) t))
2.3b	(* y (- (/ z (- a t)) (/ 1 (/ (- a t) t))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

9405×	`times-frac`
7072×	`add-sqr-sqrt`
7036×	`*-un-lft-identity`
4716×	`add-cube-cbrt`
3906×	`prod-diff`
1304×	`distribute-rgt-in` `distribute-lft-in`
1164×	`difference-of-squares`
1154×	`distribute-lft-out--`
447×	`div-inv`
440×	`associate-/r/`
190×	`flip3--` `flip--`
24×	`associate-/r*`
21×	`fma-neg`
19×	`add-exp-log`
17×	`associate-r`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-r/` `associate-l*`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub`
1×	`pow-flip` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 4138

Calls

4 calls:

128.0ms	(- (/ z (- a t)) (/ 1 (/ (- a t) t)))
5.0ms	(/ z (- a t))
9.0ms	(/ 1 (/ (- a t) t))
524.0ms	(* y (- (/ z (- a t)) (/ 1 (/ (- a t) t))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (/ z (- a t)) (/ 1 (/ (- a t) t)))
35.0ms	(/ z (- a t))
43.0ms	(/ 1 (/ (- a t) t))
87.0ms	(* y (- (/ z (- a t)) (/ 1 (/ (- a t) t))))

simplify1.7s

Algorithm

egg-herbie

Counts

4150 → 4150

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5002	181330

prune15.7s

Filtered

4150 candidates to 2530 candidates (61.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (/ (- a t) t))
7.9b	(cbrt (/ (- a t) t))
7.9b	(cbrt (/ (- a t) t))
23.0b	(fma (- (/ (cbrt 1) (cbrt (/ (- a t) t)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (- a t) t)) (cbrt (/ (- a t) t)))) (* (/ (cbrt 1) (cbrt (/ (- a t) t))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (- a t) t)) (cbrt (/ (- a t) t))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt (/ (- a t) t))
303.0ms	(cbrt (/ (- a t) t))
298.0ms	(cbrt (/ (- a t) t))
632.0ms	(fma (- (/ (cbrt 1) (cbrt (/ (- a t) t)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (- a t) t)) (cbrt (/ (- a t) t)))) (* (/ (cbrt 1) (cbrt (/ (- a t) t))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (- a t) t)) (cbrt (/ (- a t) t))))))

simplify77.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	257	1218
1	626	1124
2	2539	1070
3	5001	1004

prune768.0ms

Filtered

112 candidates to 94 candidates (83.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes199.0ms

Accuracy

-5.4% (1.4b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 1.4b

bsearch99.0ms

Steps

Iters	Range		Point
8	7.254603126169503e-72	3.935207622333976e-69	7.467028472666028e-71
8	-2.9094027944766536e-270	-3.6457286778949607e-274	-1.0071455594193599e-271

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	13
1	33	13

end0.0ms

sample568.0ms

Algorithm

intervals

Results

289.0ms	8734×	body	80	valid
0.0ms	1×	body	640	valid