Details

sample55.0ms

Algorithm

intervals

Results

19.0ms	242×	body	80	valid
5.0ms	18×	body	640	valid
5.0ms	12×	body	1280	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1620
5	661
4	266
3	103
2	43
1	20
0	11

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
3.0b	(+ x (/ (* (- y z) (- t x)) (- a z)))
14.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `associate-/r` `times-frac` `associate-r` `associate-l*` `add-log-exp`
4×	`associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
3×	`insert-posit16`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

26.0ms	(* (- y z) (- t x))
17.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
27.0ms	(/ (* (- y z) (- t x)) (- a z))

series449.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (- y z) (- t x))
218.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
164.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1858
1	481
0	165

prune502.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.5b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.1b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite123.0ms

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`
4×	`insert-posit16`
3×	`associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 138

Calls

4 calls:

5.0ms	(cbrt (- a z))
5.0ms	(cbrt (- a z))
95.0ms	(* (/ (- 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)))))

series950.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- a z))
161.0ms	(cbrt (- a z))
407.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
230.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify2.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5002
2	2907
1	748
0	258

prune719.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
8.9b	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite23.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 60

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
10.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series838.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (- a z))
202.0ms	(cbrt (- a z))
200.0ms	(cbrt (- a z))
235.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	3037
2	741
1	264
0	110

prune529.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (cbrt (- a z)))
9.1b	(+ x (* (/ (- y z) (* (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
19×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`flip3--` `flip--`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`frac-times` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`pow1/3`
2×	`associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 65

Calls

4 calls:

4.0ms	(cbrt (- a z))
11.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
5.0ms	(cbrt (cbrt (- a z)))
9.0ms	(+ x (* (/ (- y z) (* (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (- a z))
140.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
191.0ms	(cbrt (cbrt (- a z)))
196.0ms	(+ x (* (/ (- y z) (* (/ (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify3.4s

Counts

77 → 77

Iterations

Iter	Nodes
done	5002
3	4875
2	1189
1	436
0	204

prune596.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

regimes746.0ms

Accuracy

29.7% (6.4b remaining)

Error of 9.7b against oracle of 3.2b and baseline of 12.4b

bsearch164.0ms

Steps

Iters	Range		Point
8	8.883612526165312e-94	2.7867056099957307e-91	1.3917837591469568e-93
10	-6.087560554388729e-120	-5.880771378225135e-135	-3.4167661692054223e-133

simplify8.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

574.0ms	7793×	body	80	valid
408.0ms	435×	body	320	valid
89.0ms	474×	body	640	valid
71.0ms	288×	body	1280	valid
25.0ms	258×	body	160	valid
6.0ms	20×	body	2560	valid