Details

sample57.0ms

Algorithm

intervals

Results

40.0ms

620×

body

valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	15
1	161	15
2	459	15
3	1323	15
4	2992	15
5	5001	15

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0)
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-*r/`
3×	`distribute-rgt-in` `sub-neg` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
2×	`flip3--` `diff-log` `associate-l` `*-commutative` `flip--` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate--l+` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

10.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0)
8.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
11.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0)
55.0ms	(* (* a a) (+ 1.0 a))
109.0ms	(pow (+ (* a a) (* b b)) 2.0)
51.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	492	799
1	2397	713
2	5002	713

prune233.0ms

Filtered

94 candidates to 61 candidates (64.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 0.0b

Counts

95 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series520.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
152.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
155.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
156.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	266	651
1	1020	585
2	5001	579

prune285.0ms

Filtered

82 candidates to 64 candidates (78.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	82	6	88

Merged error: 0.0b

Counts

88 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.1b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series633.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
161.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
164.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
155.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	102	632
1	220	588
2	765	580
3	3241	572
4	5003	572

prune318.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 0.0b

Counts

78 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
9.9b	(/ (- (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) (* 1.0 1.0)) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
21×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt`
19×	`pow1`
17×	`add-cube-cbrt`
16×	`times-frac`
9×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
5×	`distribute-lft-out` `difference-of-squares`
4×	`flip3--` `associate-/r` `flip--` `associate-/l` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 116

Calls

4 calls:

11.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
25.0ms	(/ (- (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) (* 1.0 1.0)) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))

series622.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
57.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
57.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
458.0ms	(/ (- (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) (* 1.0 1.0)) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	441	3278
1	2195	2974
2	5003	2912

prune345.0ms

Filtered

128 candidates to 80 candidates (62.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	2	3
Picked	1	0	1
Done	1	1	2
Total	129	5	134

Merged error: 0.0b

Counts

134 → 5

Details

sample57.0ms

simplify100.0ms

prune3.0ms

localize17.0ms

rewrite36.0ms

series326.0ms

simplify66.0ms

prune233.0ms

localize21.0ms

rewrite23.0ms

series520.0ms

simplify39.0ms

prune285.0ms

localize30.0ms

rewrite21.0ms

series633.0ms

simplify106.0ms

prune318.0ms

localize24.0ms

rewrite56.0ms

series622.0ms

simplify89.0ms

prune345.0ms

regimes180.0ms

bsearch3.0ms

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