Details

sample120.0ms

Algorithm

intervals

Results

44.0ms	91×	body	1280	valid
25.0ms	71×	body	640	valid
22.0ms	257×	body	80	valid
11.0ms	47×	body	320	valid
3.0ms	18×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	7
1	58	7
2	95	7
3	209	7
4	459	7
5	629	7
6	1415	7
7	2148	7
8	5002	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
0.0b	(+ (exp (- im)) (exp im))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-l` `sum-log` `*-commutative`

Counts

2 → 35

Calls

2 calls:

27.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
9.0ms	(+ (exp (- im)) (exp im))

series84.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
26.0ms	(+ (exp (- im)) (exp im))

simplify39.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	249	347
1	1229	286
2	5001	284

prune101.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp im) (exp im))
0.0b	(pow (exp im) 3)
0.0b	(pow (exp (- im)) 3)
7.3b	(- (* (exp im) (exp im)) (* (exp (- im)) (exp im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`exp-prod`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
15×	`pow-pow`
13×	`pow1`
8×	`add-cbrt-cube`
6×	`unpow-prod-down` `pow-unpow` `cube-prod` `add-log-exp`
4×	`add-exp-log` `pow-prod-down` `pow-sqr` `pow-prod-up`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `swap-sqr` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `neg-sub0` `exp-neg` `neg-mul-1` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-plus` `exp-diff` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

8.0ms	(* (exp im) (exp im))
2.0ms	(pow (exp im) 3)
5.0ms	(pow (exp (- im)) 3)
7.0ms	(- (* (exp im) (exp im)) (* (exp (- im)) (exp im)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (exp im) (exp im))
23.0ms	(pow (exp im) 3)
30.0ms	(pow (exp (- im)) 3)
46.0ms	(- (* (exp im) (exp im)) (* (exp (- im)) (exp im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	364	469
1	2073	398
2	5003	361

prune364.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
0.0b	(+ (exp (- im)) (exp im))
0.1b	(exp (log (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))))
3.9b	(log (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
15×	`add-exp-log`
10×	`*-un-lft-identity`
9×	`pow-prod-down` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `associate-*r/` `prod-exp` `log-pow` `add-log-exp`
4×	`log-div` `flip3-+` `associate-r` `flip-+`
3×	`rem-log-exp` `cbrt-unprod`
2×	`log-prod` `exp-diff` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-l` `exp-sum` `sum-log` `*-commutative` `rem-exp-log`

Counts

4 → 68

Calls

4 calls:

27.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
9.0ms	(+ (exp (- im)) (exp im))
48.0ms	(exp (log (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))))
14.0ms	(log (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
22.0ms	(+ (exp (- im)) (exp im))
60.0ms	(exp (log (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))))
88.0ms	(log (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

simplify44.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	300	704
1	1413	604
2	5001	599

prune197.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (* 0.5 (pow (exp im) -2)) (* 0.5 (- (exp (+ im im))))) (cos re)) (- (exp (- im)) (exp im)))
0.0b	(pow (exp im) -2)
7.4b	(+ (* 0.5 (pow (exp im) -2)) (* 0.5 (- (exp (+ im im)))))
7.4b	(- (exp (- im)) (exp im))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `times-frac` `associate-/r*`
4×	`pow-pow`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `distribute-rgt-neg-out` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unsub-neg` `pow-exp` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `associate-/l*` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

20.0ms	(/ (* (+ (* 0.5 (pow (exp im) -2)) (* 0.5 (- (exp (+ im im))))) (cos re)) (- (exp (- im)) (exp im)))
2.0ms	(pow (exp im) -2)
3.0ms	(+ (* 0.5 (pow (exp im) -2)) (* 0.5 (- (exp (+ im im)))))
11.0ms	(- (exp (- im)) (exp im))

series314.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (* (+ (* 0.5 (pow (exp im) -2)) (* 0.5 (- (exp (+ im im))))) (cos re)) (- (exp (- im)) (exp im)))
17.0ms	(pow (exp im) -2)
104.0ms	(+ (* 0.5 (pow (exp im) -2)) (* 0.5 (- (exp (+ im im)))))
39.0ms	(- (exp (- im)) (exp im))

simplify58.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	458	973
1	2062	801
2	5002	787

prune297.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes136.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	2900×	body	1280	valid
775.0ms	2480×	body	640	valid
761.0ms	8439×	body	80	valid
277.0ms	1219×	body	320	valid
95.0ms	597×	body	160	valid