Details

sample38.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
10.0ms	224×	body	80	nan

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	14
1	165	14
2	826	14
3	3867	14
4	5002	14

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
0.3b	(* PI t)
0.5b	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`flip3--` `sqrt-div` `associate-r` `associate-/r/` `flip--`
7×	`associate-l` `pow-prod-down`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
55.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
3.0ms	(* PI t)
14.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series781.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 5.0 (* v v))
555.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
22.0ms	(* PI t)
180.0ms	(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify102.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	755	1158
1	4281	1002
2	5001	1002

prune294.0ms

Filtered

106 candidates to 72 candidates (67.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (* 1.0 1.0) (* (* v v) (* v v)))))
0.3b	(* PI t)
0.5b	(* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`flip3--` `sqrt-div` `associate-r` `associate-/r/` `flip--`
7×	`associate-l` `pow-prod-down`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
149.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (* 1.0 1.0) (* (* v v) (* v v)))))
3.0ms	(* PI t)
41.0ms	(* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 5.0 (* v v))
378.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (* 1.0 1.0) (* (* v v) (* v v)))))
19.0ms	(* PI t)
223.0ms	(* (* PI t) (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	718	1393
1	4142	1185
2	5002	1185

prune480.0ms

Filtered

106 candidates to 72 candidates (67.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
0.3b	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
16×	`pow1`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
9×	`flip3--` `associate-l` `flip--`
8×	`associate-/r/`
7×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`associate-*l/` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
100.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
28.0ms	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
11.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series966.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* 5.0 (* v v))
592.0ms	(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
190.0ms	(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
152.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	779	1300
1	4195	1138
2	5001	1138

prune334.0ms

Filtered

108 candidates to 77 candidates (71.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `sqrt-prod`
9×	`associate-l`
5×	`associate-r`
4×	`sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--`
1×	`unswap-sqr`

Counts

4 → 70

Calls

4 calls:

30.0ms	(* (sqrt PI) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
11.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series349.0ms

Counts

4 → 8

Calls

4 calls:

192.0ms	(* (sqrt PI) (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
157.0ms	(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	270	530
1	1138	497
2	5002	495

prune248.0ms

Filtered

78 candidates to 59 candidates (75.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes324.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	35
1	44	35

end0.0ms

sample988.0ms

Algorithm

intervals

Results

382.0ms	8001×	body	80	valid
345.0ms	8016×	body	80	nan