Details

sample65.0ms

Algorithm

intervals

Results

32.0ms

502×

body

valid

simplify80.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.1b	(* (* y 4.0) (- (* z z) t))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

13.0ms	(- (* z z) t)
13.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
74.0ms	(* (* y 4.0) (- (* z z) t))

series243.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(- (* z z) t)
123.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
85.0ms	(* (* y 4.0) (- (* z z) t))

simplify46.0ms

Counts: 63 → 63

prune173.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize30.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* y 4.0) (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))))
6.7b	(cbrt (- (* z z) t))
6.7b	(cbrt (- (* z z) t))
6.7b	(cbrt (- (* z z) t))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
16×	`pow1` `add-exp-log`
12×	`cbrt-prod` `add-cbrt-cube`
10×	`add-sqr-sqrt` `associate-*r/`
9×	`flip3--` `flip--`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`frac-times` `add-log-exp`
3×	`pow1/3` `difference-of-squares`
2×	`associate-*l/`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

150.0ms	(* (* y 4.0) (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))))
10.0ms	(cbrt (- (* z z) t))
10.0ms	(cbrt (- (* z z) t))
10.0ms	(cbrt (- (* z z) t))

series456.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (* y 4.0) (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))))
118.0ms	(cbrt (- (* z z) t))
96.0ms	(cbrt (- (* z z) t))
110.0ms	(cbrt (- (* z z) t))

simplify111.0ms

Counts: 84 → 84

prune364.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (- (* t t)) (pow z 4)) 4.0)
3.3b	(+ (- (* t t)) (pow z 4))
9.9b	(* (* (+ (- (* t t)) (pow z 4)) 4.0) y)
20.1b	(/ (* (* (+ (- (* t t)) (pow z 4)) 4.0) y) (+ (* z z) t))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
13×	`*-un-lft-identity`
11×	`pow1` `add-sqr-sqrt`
10×	`associate-*l/`
9×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r`
5×	`flip3-+` `associate-l` `flip-+`
4×	`pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/r*`
2×	`sum-log` `associate-/r/` `*-commutative` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `frac-2neg` `neg-log` `clear-num` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

61.0ms	(* (+ (- (* t t)) (pow z 4)) 4.0)
19.0ms	(+ (- (* t t)) (pow z 4))
78.0ms	(* (* (+ (- (* t t)) (pow z 4)) 4.0) y)
99.0ms	(/ (* (* (+ (- (* t t)) (pow z 4)) 4.0) y) (+ (* z z) t))

series429.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (+ (- (* t t)) (pow z 4)) 4.0)
89.0ms	(+ (- (* t t)) (pow z 4))
98.0ms	(* (* (+ (- (* t t)) (pow z 4)) 4.0) y)
143.0ms	(/ (* (* (+ (- (* t t)) (pow z 4)) 4.0) y) (+ (* z z) t))

simplify72.0ms

Counts: 94 → 94

prune365.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ z (sqrt t))
0.0b	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
0.1b	(* (* y 4.0) (+ z (sqrt t)))
0.1b	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `associate-r/` `associate-r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`
4×	`frac-times` `flip3--` `flip--` `associate--r+`
2×	`associate-l` `associate-l/` `-commutative` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `diff-log` `sum-log` `sqrt-prod` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

11.0ms	(+ z (sqrt t))
15.0ms	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
37.0ms	(* (* y 4.0) (+ z (sqrt t)))
101.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ z (sqrt t))
118.0ms	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
80.0ms	(* (* y 4.0) (+ z (sqrt t)))
147.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

simplify102.0ms

Counts: 99 → 99

prune296.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.2b

regimes473.0ms

Accuracy

61.3% (1.3b remaining)

Error of 3.7b against oracle of 2.4b and baseline of 5.9b

bsearch171.0ms

Steps

Iters	Range		Point
9	1.738421405470883e+109	2.8596548018024563e+114	2.818024192072389e+114
9	-1.9123081486922834e+151	-2.154883565044792e+143	-1.8786075113975688e+151

simplify59.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s

15869×

body

valid