Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	231×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	2560	valid

simplify9.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (39.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
4.0b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

26.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series245.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- t z) (- a t))
199.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: 3 (345.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune209.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
4.5b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

12.0ms	(/ 1 (- a t))
46.0ms	(* (- t z) (/ 1 (- a t)))
0.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series297.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a t))
48.0ms	(* (- t z) (/ 1 (- a t)))
208.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify2.0s

Counts

114 → 114

Iterations

Useful iterations: 3 (862.0ms)

Iter	Nodes	Cost
0	149	1273
1	328	1040
2	908	936
3	3048	934
done	5001	934

prune263.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.5b	(* (cbrt (- t z)) (cbrt (- t z)))
9.8b	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 102

Calls

4 calls:

6.0ms	(cbrt (- t z))
4.0ms	(cbrt (- t z))
37.0ms	(* (cbrt (- t z)) (cbrt (- t z)))
0.0ms	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

series681.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (- t z))
162.0ms	(cbrt (- t z))
146.0ms	(* (cbrt (- t z)) (cbrt (- t z)))
206.0ms	(fma (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) y (+ x y))

simplify1.2s

Counts

114 → 114

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	156	1563
1	307	1455
2	751	1271
3	1939	1148
done	5001	1121

prune379.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- t z)) (cbrt (- t z))))
0.6b	(cbrt (cbrt (- t z)))
0.9b	(pow (cbrt (cbrt (- t z))) 4)
10.8b	(fma (* (* (cbrt (* (cbrt (- t z)) (cbrt (- t z)))) (pow (cbrt (cbrt (- t z))) 4)) (/ (cbrt (- t z)) (- a t))) y (+ x y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
24×	`cbrt-div`
14×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`unpow-prod-down`
10×	`add-cube-cbrt`
7×	`flip3--` `flip--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-pow` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `pow-exp` `fma-udef` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

16.0ms	(cbrt (* (cbrt (- t z)) (cbrt (- t z))))
5.0ms	(cbrt (cbrt (- t z)))
11.0ms	(pow (cbrt (cbrt (- t z))) 4)
0.0ms	(fma (* (* (cbrt (* (cbrt (- t z)) (cbrt (- t z)))) (pow (cbrt (cbrt (- t z))) 4)) (/ (cbrt (- t z)) (- a t))) y (+ x y))

series775.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (* (cbrt (- t z)) (cbrt (- t z))))
168.0ms	(cbrt (cbrt (- t z)))
233.0ms	(pow (cbrt (cbrt (- t z))) 4)
208.0ms	(fma (* (* (cbrt (* (cbrt (- t z)) (cbrt (- t z)))) (pow (cbrt (cbrt (- t z))) 4)) (/ (cbrt (- t z)) (- a t))) y (+ x y))

simplify1.4s

Counts

89 → 89

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	216	1503
1	429	1430
2	920	1312
3	2454	1293
done	5001	1021

prune368.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

regimes362.0ms

Accuracy

24.5% (6.0b remaining)

Error of 9.4b against oracle of 3.4b and baseline of 11.4b

bsearch176.0ms

Steps

Iters	Range		Point
8	7.211409718158765e-41	4.368925936751328e-38	1.1069999393996592e-40
8	1.0580405024462336e-109	1.6175603667685704e-105	3.145583687882107e-109
6	5.784745363791774e-215	8.791099331666811e-214	5.938458244588502e-214
9	-1.145167140852163e-61	-1.589429483747503e-66	-1.907334337913708e-66

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	69
1	35	69
done	35	69

end0.0ms

sample757.0ms

Algorithm

intervals

Results

238.0ms	7418×	body	80	valid
54.0ms	439×	body	640	valid
39.0ms	279×	body	1280	valid
30.0ms	356×	body	320	valid
21.0ms	243×	body	160	valid
3.0ms	20×	body	2560	valid