Details

sample186.0ms

Algorithm

intervals

Results

158.0ms

654×

body

valid

simplify971.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2160
3	649
2	198
1	56
0	19

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
0.1b	(* (* b b) (- 1 (* 3 a)))
0.1b	(* (* a a) (+ 1 a))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
8×	`fma-def`
7×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

94.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
26.0ms	(* (* b b) (- 1 (* 3 a)))
22.0ms	(* (* a a) (+ 1 a))
12.0ms	(pow (+ (* a a) (* b b)) 2)

series303.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
50.0ms	(* (* b b) (- 1 (* 3 a)))
79.0ms	(* (* a a) (+ 1 a))
50.0ms	(pow (+ (* a a) (* b b)) 2)

simplify17.2s

Counts

118 → 118

Iterations

Iter	Nodes
3	8139
2	1886
1	540
0	191

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4 (* (* b b) (- 1 (* 3 a))))
0.1b	(* (* b b) (- 1 (* 3 a)))
0.1b	(* (* a 4) (fma a a a))
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) (* (* a 4) (fma a a a)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

26×	`distribute-rgt-in` `distribute-lft-in`
23×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`prod-diff`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`sub-neg` `associate-*r/`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef`
2×	`flip3--` `flip--`
1×	`unswap-sqr`

Counts

4 → 114

Calls

4 calls:

50.0ms	(* 4 (* (* b b) (- 1 (* 3 a))))
31.0ms	(* (* b b) (- 1 (* 3 a)))
15.0ms	(* (* a 4) (fma a a a))
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) (* (* a 4) (fma a a a)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 4 (* (* b b) (- 1 (* 3 a))))
50.0ms	(* (* b b) (- 1 (* 3 a)))
105.0ms	(* (* a 4) (fma a a a))
138.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) (* (* a 4) (fma a a a)))

simplify12.9s

Counts

126 → 126

Iterations

Iter	Nodes
3	8881
2	1971
1	541
0	196

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (+ (* a a) (* b b)) 2)) (cbrt (pow (+ (* a a) (* b b)) 2)))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
52×	`add-sqr-sqrt`
31×	`unpow-prod-down`
25×	`unswap-sqr`
22×	`*-un-lft-identity` `add-cube-cbrt`
17×	`unpow2` `sqr-pow`
11×	`pow1` `swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

54.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2)) (cbrt (pow (+ (* a a) (* b b)) 2)))
6.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

series391.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2)) (cbrt (pow (+ (* a a) (* b b)) 2)))
94.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
94.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
99.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

simplify927.0ms

Counts

148 → 148

Iterations

Iter	Nodes
4	3307
3	1126
2	518
1	238
0	126

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

9.7b	(cbrt (+ (* a a) (* b b)))
9.7b	(cbrt (+ (* a a) (* b b)))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
6.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

series383.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ (* a a) (* b b)))
91.0ms	(cbrt (+ (* a a) (* b b)))
98.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))
103.0ms	(cbrt (pow (+ (* a a) (* b b)) 2))

simplify2.9s

Counts

82 → 82

Iterations

Iter	Nodes
4	6414
3	1791
2	567
1	203
0	91

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	17

end0.0ms

sample3.5s

Algorithm

intervals

Results

3.1s

20707×

body

valid