Details

sample49.0ms

Algorithm

intervals

Results

12.0ms	192×	body	80	valid
7.0ms	24×	body	1280	valid
5.0ms	22×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	8×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.0b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.0b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite783.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity` `times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `associate-/r/` `flip-+`
12×	`distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`associate-r/` `associate-l` `associate-l/`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

32.0ms	(* (+ alpha beta) (- beta alpha))
170.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
526.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
49.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ alpha beta) (- beta alpha))
204.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
251.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
72.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify114.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	767	2103
1	4353	1976
2	5003	1976

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.0b	(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
2.6b	(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

5126×	`times-frac`
3533×	`*-un-lft-identity`
2233×	`add-sqr-sqrt`
1787×	`add-cube-cbrt`
650×	`distribute-lft-out`
223×	`distribute-lft-out--` `difference-of-squares`
183×	`div-inv`
167×	`associate-/r/`
113×	`associate-/r*`
76×	`flip3-+` `flip-+`
41×	`add-exp-log`
32×	`add-cbrt-cube`
28×	`div-exp`
25×	`associate-/l*`
19×	`cbrt-undiv`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1`
3×	`frac-2neg` `1-exp` `clear-num`
1×	`+-commutative` `flip3--` `div-sub` `sum-log` `flip--`

Counts

4 → 1734

Calls

4 calls:

41.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
277.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.1s	(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
206.0ms	(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
135.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
253.0ms	(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
209.0ms	(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

simplify435.0ms

Algorithm

egg-herbie

Counts

1746 → 1746

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5001	48152

prune10.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
2.0b	(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
2.6b	(log (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0))
2.6b	(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

4952×	`times-frac`
3381×	`*-un-lft-identity`
2121×	`add-sqr-sqrt`
1713×	`add-cube-cbrt`
630×	`distribute-lft-out`
204×	`distribute-lft-out--` `difference-of-squares`
176×	`div-inv`
154×	`associate-/r/`
89×	`associate-/r*`
71×	`flip3-+` `flip-+`
35×	`add-exp-log`
25×	`add-cbrt-cube`
24×	`div-exp`
16×	`associate-/l*`
15×	`cbrt-undiv`
8×	`log-prod`
6×	`pow1` `add-log-exp`
4×	`log-div` `exp-prod` `exp-sum`
3×	`1-exp`
2×	`exp-diff` `log-pow`
1×	`+-commutative` `frac-2neg` `rem-log-exp` `clear-num` `sum-log` `rem-exp-log` `associate-/l/`

Counts

4 → 1601

Calls

4 calls:

760.0ms	(exp (log (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
1.1s	(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
763.0ms	(log (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0))
209.0ms	(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series958.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(exp (log (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
249.0ms	(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
251.0ms	(log (+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0))
208.0ms	(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

simplify408.0ms

Algorithm

egg-herbie

Counts

1613 → 1613

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5001	46168

prune10.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0)))
0.5b	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
2.0b	(+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0)
2.6b	(log (+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

158×	`times-frac`
146×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
26×	`associate-/r*`
20×	`distribute-lft-out`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
9×	`associate-/r/` `add-cbrt-cube`
7×	`pow1` `div-exp`
6×	`log-prod` `add-log-exp`
5×	`div-inv`
4×	`log-div` `exp-prod` `flip3--` `flip--`
3×	`cbrt-undiv` `flip3-+` `exp-sum` `flip-+` `associate-/l*`
2×	`rec-exp` `exp-diff` `1-exp` `log-pow`
1×	`+-commutative` `pow-flip` `frac-2neg` `rem-log-exp` `clear-num` `sum-log` `rem-exp-log` `inv-pow`

Counts

4 → 170

Calls

4 calls:

99.0ms	(exp (log (+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0)))
124.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
98.0ms	(+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0)
98.0ms	(log (+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0))

series831.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(exp (log (+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0)))
77.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
252.0ms	(+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0)
250.0ms	(log (+ (* (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) 1) (+ (+ alpha beta) (* 2.0 i)))) 1.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	672	2909
1	3076	2634
2	5001	2447

prune952.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.9b

regimes987.0ms

Accuracy

59% (3.2b remaining)

Error of 7.4b against oracle of 4.2b and baseline of 12.1b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	41
1	54	41

end0.0ms

sample1.1s

Algorithm

intervals

Results

412.0ms	6389×	body	80	valid
174.0ms	528×	body	1280	valid
133.0ms	525×	body	640	valid
128.0ms	8000×	pre	80	true
66.0ms	353×	body	320	valid
26.0ms	205×	body	160	valid