Details

sample39.0ms

Algorithm

intervals

Results

25.0ms

267×

body

valid

simplify130.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- t a))
0.9b	(+ (* x y) (* z (- t a)))
22.7b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

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

series468.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ y (* z (- b y)))
42.0ms	(* z (- t a))
46.0ms	(+ (* x y) (* z (- t a)))
348.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify78.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	608	1288
1	2360	956
2	5001	942

prune513.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.4b	(/ 1 (fma (- b y) z y))
0.9b	(+ (* x y) (* z (- t a)))
22.5b	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `associate-r/` `associate-/r` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

12.0ms	(* z (- t a))
2.0ms	(/ 1 (fma (- b y) z y))
6.0ms	(+ (* x y) (* z (- t a)))
18.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* z (- t a))
99.0ms	(/ 1 (fma (- b y) z y))
50.0ms	(+ (* x y) (* z (- t a)))
341.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

simplify78.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	533	1248
1	2155	961
2	5001	930

prune457.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.5b	(fma x y (* z (- t a)))
22.7b	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

14.0ms	(* z (- t a))
5.0ms	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

series1.4s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* z (- t a))
1.2s	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
50.0ms	(fma x y (* z (- t a)))
149.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify65.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	520	1776
1	2146	1503
2	5001	1426

prune433.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.8b

localize17.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (* z (- t a)))
14.7b	(cbrt (* z (- t a)))
14.7b	(cbrt (* z (- t a)))
22.7b	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

rewrite23.0ms

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:

3.0ms	(cbrt (* z (- t a)))
4.0ms	(cbrt (* z (- t a)))
3.0ms	(cbrt (* z (- t a)))
11.0ms	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

series975.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (* z (- t a)))
176.0ms	(cbrt (* z (- t a)))
183.0ms	(cbrt (* z (- t a)))
432.0ms	(/ (+ (* 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 (107.0ms)

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

prune354.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.8b

regimes397.0ms

Accuracy

59.5% (5.2b remaining)

Error of 15.9b against oracle of 10.7b and baseline of 23.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	26
1	30	26

end0.0ms

sample1.0s

Algorithm

intervals

Results

707.0ms

8443×

body

valid