Details

analyze212.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 60.975638%

Guaranteed chance to sample good point: 96.28125%

sample27.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	14
1	155	14
2	430	14
3	1195	14
4	2526	14
5	5001	14

prune3.0ms

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

localize16.0ms

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) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.7b	(* (* b b) (+ 3.0 a))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
8.0ms	(* (* a a) (- 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (+ 3.0 a))

series60.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
5.0ms	(* (* a a) (- 1.0 a))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(* (* b b) (+ 3.0 a))

simplify69.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	549	670
1	2714	602
2	5001	598

prune148.0ms

Filtered

63 candidates to 93 candidates (-47.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 0.0b

Counts

94 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.2b	(* (pow a 2) (pow b 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
28×	`prod-exp`
25×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`-un-lft-identity` `associate-l*` `add-cbrt-cube` `add-log-exp`
10×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `associate-r`
6×	`pow1`
4×	`sum-log` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

7.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
4.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

series37.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
9.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
10.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	375	699
1	1613	621
2	5001	616

prune173.0ms

Filtered

60 candidates to 113 candidates (-88.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Merged error: 0.0b

Counts

116 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.7b	(* (* b b) (+ 3.0 a))
21.7b	(sqrt (* (* a a) (- 1.0 a)))
21.7b	(sqrt (* (* a a) (- 1.0 a)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
10×	`add-exp-log`
9×	`*-un-lft-identity` `pow-prod-down` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`sqrt-pow1` `associate-*r/`
4×	`sqrt-div` `associate-r` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `prod-exp` `cbrt-unprod`
2×	`flip3--` `pow1/2` `sqrt-prod` `flip--`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

4.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (+ 3.0 a))
6.0ms	(sqrt (* (* a a) (- 1.0 a)))
6.0ms	(sqrt (* (* a a) (- 1.0 a)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (+ 3.0 a))
6.0ms	(sqrt (* (* a a) (- 1.0 a)))
5.0ms	(sqrt (* (* a a) (- 1.0 a)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	428	473
1	1772	441
2	5001	435

prune157.0ms

Filtered

59 candidates to 81 candidates (-37.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Merged error: 0.0b

Counts

84 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* b b) (+ 3.0 a))
0.7b	(* (* b b) (+ 3.0 a))
4.2b	(+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
31.9b	(/ (+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`add-exp-log` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`pow1`
12×	`times-frac`
8×	`associate-r` `add-log-exp`
7×	`distribute-lft-out`
6×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-+r+` `distribute-neg-in` `flip3-+` `associate-r/` `flip-+` `associate-/l`
3×	`div-sub` `associate-/r*`
2×	`neg-sub0` `associate-+r-` `associate-l` `unsub-neg` `sum-log` `associate-/r/` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3--` `frac-2neg` `div-exp` `neg-log` `clear-num` `flip--` `div-inv`

Counts

4 → 106

Calls

4 calls:

10.0ms	(* (* b b) (+ 3.0 a))
8.0ms	(* (* b b) (+ 3.0 a))
8.0ms	(+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
15.0ms	(/ (+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (* b b) (+ 3.0 a))
5.0ms	(* (* b b) (+ 3.0 a))
89.0ms	(+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
97.0ms	(/ (+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	548	2980
1	2859	2653
2	5002	2591

prune338.0ms

Filtered

79 candidates to 118 candidates (-49.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	117	4	121

Merged error: 0b

Counts

121 → 4

Details

analyze212.0ms

sample27.0ms

simplify73.0ms

prune3.0ms

localize16.0ms

rewrite29.0ms

series60.0ms

simplify69.0ms

prune148.0ms

localize13.0ms

rewrite28.0ms

series37.0ms

simplify57.0ms

prune173.0ms

localize18.0ms

rewrite26.0ms

series40.0ms

simplify46.0ms

prune157.0ms

localize25.0ms

rewrite43.0ms

series197.0ms

simplify97.0ms

prune338.0ms

regimes196.0ms

bsearch1.0ms

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