Details

sample157.0ms

Algorithm

intervals

Results

58.0ms

565×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1194
3	333
2	110
1	47
0	23

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* i t) (* z c))
3.8b	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
4.4b	(fma (- (* a c) (* y i)) j (fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x)))
6.6b	(* (- (* z y) (* t a)) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`flip3--` `associate-*l/` `fma-udef` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

9.0ms	(- (* i t) (* z c))
0.0ms	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
0.0ms	(fma (- (* a c) (* y i)) j (fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x)))
23.0ms	(* (- (* z y) (* t a)) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* i t) (* z c))
289.0ms	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
734.0ms	(fma (- (* a c) (* y i)) j (fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x)))
100.0ms	(* (- (* z y) (* t a)) x)

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1074
1	297
0	122

prune892.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* i t) (* z c))
3.8b	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
4.5b	(* (- (* a c) (* y i)) j)
6.6b	(* (- (* z y) (* t a)) x)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 70

Calls

4 calls:

13.0ms	(- (* i t) (* z c))
1.0ms	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
47.0ms	(* (- (* a c) (* y i)) j)
38.0ms	(* (- (* z y) (* t a)) x)

series539.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* i t) (* z c))
296.0ms	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
91.0ms	(* (- (* a c) (* y i)) j)
106.0ms	(* (- (* z y) (* t a)) x)

simplify1.3s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1444
1	382
0	149

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.1b

localize93.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (* (- (* a c) (* y i)) (* (cbrt j) (cbrt j))) (cbrt j))
3.3b	(* (- (* a c) (* y i)) (* (cbrt j) (cbrt j)))
3.8b	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
6.6b	(* (- (* z y) (* t a)) x)

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-*l/`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3--` `*-commutative` `flip--`
2×	`unswap-sqr`
1×	`fma-udef`

Counts

4 → 83

Calls

4 calls:

95.0ms	(* (* (- (* a c) (* y i)) (* (cbrt j) (cbrt j))) (cbrt j))
42.0ms	(* (- (* a c) (* y i)) (* (cbrt j) (cbrt j)))
0.0ms	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
22.0ms	(* (- (* z y) (* t a)) x)

series866.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* (- (* a c) (* y i)) (* (cbrt j) (cbrt j))) (cbrt j))
302.0ms	(* (- (* a c) (* y i)) (* (cbrt j) (cbrt j)))
339.0ms	(fma b (- (* i t) (* z c)) (* (- (* z y) (* t a)) x))
111.0ms	(* (- (* z y) (* t a)) x)

simplify1.6s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	2007
1	460
0	171

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize77.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x))
3.8b	(fma b (- (* i t) (* z c)) (* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x)))
4.5b	(* (- (* a c) (* y i)) j)
5.2b	(* (- (* z y) (* t a)) (* (cbrt x) (cbrt x)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-*l/`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3--` `*-commutative` `flip--`
2×	`unswap-sqr`
1×	`fma-udef`

Counts

4 → 83

Calls

4 calls:

106.0ms	(* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x))
0.0ms	(fma b (- (* i t) (* z c)) (* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x)))
24.0ms	(* (- (* a c) (* y i)) j)
44.0ms	(* (- (* z y) (* t a)) (* (cbrt x) (cbrt x)))

series915.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x))
409.0ms	(fma b (- (* i t) (* z c)) (* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x)))
85.0ms	(* (- (* a c) (* y i)) j)
289.0ms	(* (- (* z y) (* t a)) (* (cbrt x) (cbrt x)))

simplify1.6s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	2015
1	452
0	171

prune923.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.6b

regimes3.1s

Accuracy

27.9% (7.4b remaining)

Error of 9.8b against oracle of 2.4b and baseline of 12.6b

bsearch278.0ms

Steps

Iters	Range		Point
6	2.0896367406142687e-84	2.3227454427546907e-83	1.6135922766508473e-83
8	-4.584783334784623e+78	-9.061135516040537e+73	-7.426419963249853e+76

simplify15.0ms

Iterations

Iter	Nodes
done	64
1	64
0	45

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.3s

19345×

body

valid