Details

sample104.0ms

Algorithm

intervals

Results

68.0ms

648×

body

valid

simplify1.6s

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
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` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

90.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
70.0ms	(* (* a a) (+ 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
73.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
79.0ms	(* (* a a) (+ 1.0 a))
178.0ms	(pow (+ (* a a) (* b b)) 2.0)
88.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.2s

Counts: 91 → 91

prune391.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `associate-*r/` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

46.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
73.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
107.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series729.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
94.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
281.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
268.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify904.0ms

Counts: 92 → 92

prune517.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-sqr-sqrt`
9×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
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:

47.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
64.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
90.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
99.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
315.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
330.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
353.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify775.0ms

Counts: 82 → 82

prune637.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.0b	(* (pow a 2) (pow b 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
28×	`prod-exp`
23×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`unpow2` `sqr-pow`
9×	`associate-r` `add-cbrt-cube`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `add-log-exp`

Counts

2 → 76

Calls

2 calls:

37.0ms	(* 2 (* (pow a 2) (pow b 2)))
34.0ms	(* (pow a 2) (pow b 2))

series122.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(* 2 (* (pow a 2) (pow b 2)))
57.0ms	(* (pow a 2) (pow b 2))

simplify654.0ms

Counts: 82 → 82

prune255.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes158.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.8s

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.9s

20422×

body

valid