Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	249×	body	80	valid
3.0ms	10×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify69.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.6b	(+ x (/ (* (- y z) (- t x)) (- a z)))
19.2b	(/ (* (- y z) (- t x)) (- a z))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

44.0ms	(* (- y z) (- t x))
47.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
47.0ms	(/ (* (- y z) (- t x)) (- a z))

series451.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (- y z) (- t x))
227.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
170.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify67.0ms

Counts: 90 → 90

prune636.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
200.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
13.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- a z))
191.0ms	(cbrt (- a z))
401.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
211.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify86.0ms

Counts: 146 → 146

prune666.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
4.1b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

5.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
12.0ms	(cbrt (- a z))
9.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt (- a z))
180.0ms	(cbrt (- a z))
188.0ms	(cbrt (- a z))
183.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify153.0ms

Counts: 68 → 68

prune421.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 4.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
5.3b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
14.0ms	(cbrt (- a z))
11.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (- a z))
183.0ms	(cbrt (- a z))
152.0ms	(cbrt (- a z))
213.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify43.0ms

Counts: 68 → 68

prune429.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.3b

regimes586.0ms

Accuracy

24% (6.9b remaining)

Error of 10.2b against oracle of 3.3b and baseline of 12.4b

bsearch156.0ms

Steps

Iters	Range		Point
9	3.2887365613225345e-126	1.279342195381289e-119	1.636812059871429e-123
9	-8.056021348608936e-95	-2.5192591207542805e-102	-1.0574901986274641e-101

simplify110.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

552.0ms	7736×	body	80	valid
115.0ms	471×	body	640	valid
110.0ms	411×	body	320	valid
59.0ms	245×	body	1280	valid
56.0ms	318×	body	160	valid
7.0ms	15×	body	2560	valid