Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

274×

body

valid

simplify128.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune6.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z (- t a)))
0.0b	(* z (- t a))
0.0b	(* z (- b y))
22.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

6.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(* z (- t a))
12.0ms	(* z (- b y))
12.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* x y) (* z (- t a)))
41.0ms	(* z (- t a))
40.0ms	(* z (- b y))
597.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify87.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune495.0ms

Filtered

173 candidates to 100 candidates (57.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
0.4b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
22.7b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
90×	`times-frac`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `distribute-lft-in`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
11×	`associate-/r/`
10×	`associate-r`
9×	`pow1`
8×	`div-exp`
6×	`flip3-+` `associate-l` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 211

Calls

4 calls:

13.0ms	(* z (- t a))
12.0ms	(* z (- b y))
11.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
12.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

46.0ms	(* z (- t a))
41.0ms	(* z (- b y))
936.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
306.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify125.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	799	2569
1	3770	2096
2	5001	2079

prune643.0ms

Filtered

223 candidates to 131 candidates (58.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.0b	(* z (- t a))
0.4b	(/ 1 (fma z (- b y) y))
22.6b	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-l`
13×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `cbrt-unprod` `fma-udef` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `div-inv`
1×	`flip3--` `pow-flip` `frac-2neg` `associate-*l/` `clear-num` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 128

Calls

4 calls:

0.0ms	(fma z (- b y) y)
12.0ms	(* z (- t a))
2.0ms	(/ 1 (fma z (- b y) y))
14.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma z (- b y) y)
40.0ms	(* z (- t a))
68.0ms	(/ 1 (fma z (- b y) y))
535.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

simplify64.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	419	981
1	1667	758
2	5002	732

prune415.0ms

Filtered

140 candidates to 81 candidates (57.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 4 expressions with local error:

14.4b	(cbrt (* z (- t a)))
14.4b	(cbrt (* z (- t a)))
14.4b	(cbrt (* z (- t a)))
22.9b	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-div` `associate-*r/` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3--` `pow1/3` `associate-/r` `flip--` `associate-/l`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 72

Calls

4 calls:

4.0ms	(cbrt (* z (- t a)))
4.0ms	(cbrt (* z (- t a)))
3.0ms	(cbrt (* z (- t a)))
12.0ms	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

series1.0s

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (* z (- t a)))
194.0ms	(cbrt (* z (- t a)))
195.0ms	(cbrt (* z (- t a)))
454.0ms	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

simplify118.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	332	1140
1	1065	1043
2	4040	1006
3	5001	992

prune372.0ms

Filtered

84 candidates to 76 candidates (90.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 13.3b

regimes437.0ms

Accuracy

28.8% (9.0b remaining)

Error of 19.9b against oracle of 10.9b and baseline of 23.5b

bsearch63.0ms

Steps

Iters	Range		Point
3	3.325624108380948e+76	4.649576028066181e+76	3.904853073243237e+76
6	-1.6491291254077062e+218	-1.0848229914024191e+217	-1.1016366134119363e+217

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	12
1	35	12

end0.0ms

sample654.0ms

Algorithm

intervals

Results

353.0ms

8416×

body

valid